Measurement and Computation of Streamflow: Volume 1 Measurement of Stage and DischargePaper 2175 1982

Measurement and Computation
of Streamflow: Volume 1.
Measurement of Stage
and Discharge
By S. E. RANTZ and others
GEOLOGICAL SURVEY WATER-SUPPLY PAPER 2175
UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON: 1982

UNITED STATES DEPARTMENT OF THE INTERIOR
JAMES G. WATT, Secretary
GEOLOGICAL SURVEY
Dallas L. Peck, Director
First printing 1982
Second printing 1933
Library of Congress Cataloging in Publication Data
Measurement and computation of streamflow.
(Geological Survey Water-Supply Paper 2175)
Includes bibliographies.
Contents: v. 1. Measurement of stage and discharge.-
v. 2. Computation of discharge. 1. Stream
measurements.
I. Rantz, S. E. (Saul Edward), 1911- . II. Series.
TC175.M42 551.43’3’0237 81-607399
AACR2
For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington, D.C. 20402

PREFACE
The science and, in part, art of stream gaging has evolved through
the years, largely from the collective experiences and innovations of
its practitioners. The earliest truly comprehensive manual on
stream-gaging procedures and equipment, based on techniques de-veloped
up to that time, was published in 1943 by the Geological
Survey as Water-Supply Paper 888, “Stream-Gaging Procedures,” by
D. M. Corbett and others. That report was an instant classic; it was
received enthusiastically by the hydraulic-engineering profession
throughout the world and became a major training document for at
least two generations of stream gagers, hydrologists, and hydraulic
engineers, both in the United States and abroad.
The need for updating Water-Supply Paper 888 has been obvious
for some time as a result of later developments in stream-gaging
techniques and equipment. Furthermore, it has been felt for some
time that the scope of that report should be expanded to cover not only
the newer field techniques but also the office procedures required to
produce a published annual record of stream discharge. In recognition
of those needs, the Geological Survey has sporadically produced sup-plementary
reports that update the description of specific techniques
and equipment or that describe specific field or office procedures not
covered by Water-Supply Paper 888. These reports-some adminis-trative,
some open-file, and others in the published series titled
“Techniques of Water-Resources Investigations”-are fragmentary
in the sense that they deal only with selected aspects of the broad
subject of stream gaging. Similar, but less detailed, reports on
selected topics have also been produced by international agencies in
the form of Technical Notes by the World Meteorological Organiza-tion
and in the form of Recommendations and Standards by the In-ternational
Standards Organization.
The present report evolved from that background. Its two volumes
provide a comprehensive compilation of time-tested techniques pre-sented
as an up-to-date (1980) standardized manual of stream-gaging
procedures.
Acknowledgments.-The material presented in the manual is
based on the work of many hydraulic engineers and technicians, each
of whom has contributed to the current state-of-the-art in the meas-urement
and computation of streamflow. Many of those who contrib-uted
directly to the manual are listed in the references appended to
each chapter. However, the authors wish to acknowledge a special
group of colleagues who have made major contributions to this man-ual
in the form of written (cited) methods and techniques, significant
suggestions for correction and revision of the manuscript and illus-
III

IV PREFACE
trations, and all-out efforts to bring about development and publica-tion
of the material. These colleagues include:
Harry H. Barnes, Jr. Thomas J. Buchanan
Rolland W. Carter Frederick A. Kilpatrick
George F. Smoot Ernest D. Cobb
Howard F. Matthai Manual A. Benson
Alvin F. Pendleton, Jr. Tate Dalrymple
Harry Hulsing Carl E. Kindsvater
G. Lawrence Bodhaine Hubert J. Tracy
Jacob Davidian James F. Wilson
The authors also wish to acknowledge with thanks the suggestions
of their many other colleagues, who are too numerous to mention.

CONTENTS
[Art& headmgs are hsted in the table of contents only m the volume of the manual m which they occur, but all
chapter titles for the two volumes are hsted ,n both volumes A complete Index covermg both volumes of the
manual appears m each volume 1
VOLUME 1. MEASUREMENT OF STAGE AND DISCHARGE
Page
Preface-------------------------------------------------------------------- III
Conversion factors _-----------____-___-------------------~----------------XIV
Chapter l.-Introduction
Purposeofthemanual ____----------__________________________------------
Scopeofthemanual--------------------------------------------------------
Streamflow records ________-_-_----_-______________________----------------
General stream-gaging procedures _- ____________________________ ------------
Selectedreference----------------------------------------------------------
Chapter 2.-Selection of Gaging-Station Sites
Introduction ------__________-_--____________________----------------------
Considerations in specific site selection __________________ ---------__-_-- ___-_
Selected references ________________--______________________----------------
Chapter 3.-Gaging-Station Controls
Typesofcontrol----__------------------------------------------------------
Attributes of a satisfactory control ---- _________________ -_-_----_-___-_- ___-_
Artificial controls __________-_--------____________________------------------
Choice of an artificial control -_--- _______ ---_-_--_-_-__-_- _-__-________
Choice between weir and flume ____________ ------_-__-_-__-___- ____
Choice between critical-flow flume and supercritical-flow flume....------
Summary__-_-__---------------------------------------------------
Design of an artificial control --- _________ -_-----------_- ______-________
Selected references _--_---__-_____-_-______________________----------------
Chapter 4.-Measurement of Stage
General ___.__-__---------_-____________________--------------------------
Datum of gage -__-____________-_-_____________________--------------------
Nonrecording stream-gaging stations _- ______________ -----------__--_- _-____-
Staffgage __________________-_----------------------------------------
Wire-weightgage-_-_--------------------------------------------------
Float-tape gage--------------------------------------------------------
Electric-tapegage------------------------------------------------------
Chain gage------ ____ ------- ____ -_-___--_----------------- ____ -- _____ -_
Recording stream-gaging stations --_--__------_-_--------------------------
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V

VI CONTENTS
Recording stream-gaging stations-continued Page
Methods of sensing stage for automatic recording __-_-_-_________---_____ 32
Float sensor ----___---------___----------------~-----~~--~-------- 32
Bubble-gage sensor _------___-------___---------------------------- 32
Water-stagerecorders___----_____-------_____________-_______---------- 34
Digitalrecorder_____----_______________________-------------------- 36
Graphic recorder ----_-_-----_-____--____________________---------- 39
Stillingwells_----______----_________________________--------~-~------- 41
Instrumentshelters----------------------------__------------------------ 51
Reference and auxiliary gages at recording gaging stations _-_________-__ 53
Telemeteringsystems___-----_____------_____________-_______---~------ 54
Position-motor system -______-------__---------------------------- 55
Impulse system------------------------_-____-------~---~---------~~--- 55
Telemarksystem ___---_______-----______________________-~-------- 55
Resistancesystem___------____------------------~-~----------~----- 57
Satellite data-collection system __------ _____ ---- _-______ -- __-___ --- 57
Operation of a recording stream-gaging station -- -_____ --- ________ -- _--____ _- 59
Factors affecting the accuracy of the stage record __-__ -_--_ _-______ - ___-____ - 63
Nonrecordinggages-____------____------~-~--------------------~------- 64
Staffgage -----____------____--------~-------------------~--~----- 64
Wire-weight gage ___-- ________ --- ______ --------__---------_-------- 64
Float-tapegage_------_-_------___-____________________---~-------- 65
Electric-tapegage___-----_____-------____________-_______---------- 66
Chaingage-----____-------------------------------~--------------- 67
Accuracyoffloat-operated recorders _-___----_-_--_-_-__________________ 68
Accuracy ofbubble-gage recorders _------___---------~~------------~~--- 71
Special purpose gages --_____-----_____------~-~---------------------------- 74
ModelTrecorder -______---_______----~--~~~--------~------------------ 74
SRrecorder____-----_____________-_________---------------------------- 76
Crest-stage gage -_-_---_-_--___-________________________-----~-------- 77
Selectedreferences -----____------_-__--------------------~-----------~---- 78
Chapter L-Measurement of Discharge
by Conventional Current-Meter Method
Introduction -----____-------__--____________________---------------------- 79
General description of a conventional current-meter measurement of discharge 80
Instruments and equipment -___-------___------ ____-_ ---- ______ --- _--____ -- 82
Current meters ---------__-_------_---------------------------~----~--- 84
Vertical-axiscurrentmeters-------------------------____------___ 85
Horizontal-axis current meters- ____ ----- ____ ------ -_-__ ----- _-____ -- 88
Comparison of performance of vertical-axis and horizontal-axis current’
meters __-----____-----________________________---------~-------- 89
Opticalcurrentmeter-------------------------------____-----------~-- 91
Care ofthe current meter -----_--------_-_------------------------- 93
Rating of current meters _---- __-_ ------ -_-___ -_- _-_____ --- -____ _-- 94
Sounding equipment --__----------_-------~-------------~------------- 97
Wadingrods _--------__------_------------------------------------ 97
Sounding weights and accessories _-----_____-------________________ 101
Soundingreels __--- _-__ -_---- -___ ----- __-___ ---- -_--_ __--- __-__ --- 102
Handlines --____---__-_-_----_------------------------------------ 104
Sonic sounder-_______--_-_----------------------------------------- 108

CONTENTS VII
Instruments and equipment-Continued
Width-measuringequipment--------------------------------------------
Equipmentassemblies--------------------------------------------------
Cablewayequipment ----------------_-______________________------
Bridgeequipment---------------_-----------------------~----------
Boatequipment----------------------------------------------------
Iceequipment __-_-_----------------------------------------------
Velocity-azimuth-depth assembly------------------------------------
Miscellaneousequipment --------_--_--------____________________------
Measurementofvelocity----_--------------------------~--------------------
Vertical-velocity curve method ____-__-- - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Two-pointmethod_-_______-________-_----------------------------------
Six-tenths.depthmethod------------------------------------------------
Three-point method ----------------------------------------------------
Two-tenths-depthmethod --------------------____________________------
Subsurface-velocity method __-_--_-------------____________________----
Surface-velocity method ------------------------------------------------
Integration method -------_-_-_-_--_-_-____________________~~~~~~~~~~~~
Five-pointmethod------------------------------------------------------
Six-point method -----------------------------~-~----------------------
Procedure for conventional current-meter measurement of discharge _--_--_-__
Current-meter measurements by wading---------------------------------.
Current-meter measurements from cableways ~~~~~~~~~~~~~~~~~~~~________
Current-meter measurements from bridges ------------------------------
Current-meter measurements from ice cover _--__----___________________
Current-meter measurements from boats ____-_--_-----------------------
Networksofcurrentmeters --------------__----____________________----
Special problems in conventional current-meter measurements----------------
Measurement of deep, swift streams --------------------________________
Case A. Depthcanbesounded--------------------------------------
Case B. Depth cannot be sounded, but standard cross section is available
Case C. Depth cannot be sounded and no standard cross section is avail-able
_-___-____-_____________________________--------------------
Case I). Meter cannot be submerged -------_----------_-____________
Computation of mean gage height of a discharge measurement-____--_-___
Measurement procedures during rapidly changing stage _-_--_-_-_----_--_
Case A. Largestreams ----------------_-_-____________________----
Case B. Small streams -_-_----_-_--__--__- _-___ - ~~~~~~~~~_~~~~~~~~
Correction of discharge for storage during measurement ~~~~~~~~~__~~~____
Summary of factors affecting the accuracy of a discharge measurement --------
Accuracy of a clischarge measurement made under average conditions --------
Selected references ____________--------------------------------------------
Chapter 6.-Measurement of Discharge by the
Moving-Boat Method
Page
110
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117
120
124
129
130
131
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134
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168
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183
Introduction -------------_____-_------------------------------------------ 183
Theoryofthe moving-boat method ------_-_-____--________________________-- 184
Equipment--______-------_________----------------------~-------------------- 187
Vane and angle indicator ____________ -----------_-___-_-_-------------- 187

VIII CONTENTS
Equipment-Continued Page
Current meter -__-_-__________________________________---------------- 188
Rate indicator and counter _____________ -----------_- ______ _ _____ - ______ 190
Batterycharger_-----------------------------~-------------~---~-~--~-- 193
Sonicsounder-----------------------------~-~-----------------------~~- 193
Boat______-_--_____-___-____________________--------~~--~-~~~~-------- 195
Measurement procedures _-____-_--_-_-_--------------~~--~-~~--~~-~------- 197
Selection and preparation of the measurement site ______________________ 197
Preparationoftheequipment --_-__--____------------------------------ 198
Assembly of the equipment ______-_- ---_-_--__- _________ - _________- 199
Selection of the instrument settings __-_---------------------------- 200
Function of the crew members __-__-___ -----_------_--___ _______ - ____ ___ 201
Boatoperator------------------_-_-~~--~-------------------- 201
Angle observer -_-__-_-____-__-__-_____________________------------ 202
Notekeeper------------------------~~~----------------------------- 203
Computation of the discharge measurement---------------------------------- 204
Computation of unadjusted discharge___----------------- ____________-___ 204
Adjustment of total width and area-----_-_------------------------------ 207
Adjustment of mean velocity and total discharge __-_____________________ 208
Determination of vertical-velocity adjustment factor _ ________________ 210
Application of velocity adjustment to computed discharge ____________ 211
Selectedreferences --------------------____________________---------------- 211
Chapter 7.-Measurement of Discharge by Tracer Dilution
General _____-_-____-_-----------------~~~~~~~~~~~~---------------------~- 211
Theory of tracer-dilution methods -------_____________---------------------- 212
Theory of the constant-rate-injection method __________-_---------------- 213
Theory of the sudden-injection method -~-----------------------~-------- 214
Factors affecting the accuracy of tracer-dilution methods------------~~---- 215
Turbidity---------_____________-_-------~---~~~~~~~~~~-~~~~~~~~~~---------- 215
Lossoftracer-----_____________-_----------------------------------------- 216
Criteria for satisfactory mixing -----__________--------------------- 216
Calibration of measurement reach -------_____-_---------------------------- 220
Effect of inflow or outflow between injection and sampling sites ______--______ 222
Measurement of discharge by fluorescent-dye dilution ________~~-------------- 223
Fluorescent dyes --____________---_--____________________~------------- 223
Fluorometer ------__________________________________----~------------- 223
Description of fluorometer ________ ~_-~ __________________ ~~~~-~------ 224
Effectoftemperature on fluorometry -__________________~------------ 226
Calibration characteristics of the flurometer ~---------------~~~_____ 226
Preparation of standard dye solutions for flurometer calibration ______ 228
Operationofthe fluorometer--------____________________---------------------- 231
Dye-injectionapparatus ____________-_-_________________________--~----- 232
Mariotte vessel ---____________------~~~-~~~~~~~~~----------------~- 232
Floatingsiphon---_____________-___-------------------------------- 233
Pressuretank-----___________-------------------------------------- 234
Determination of quantities of fluorescent dye for measuring discharge __-_ 235
Quantity of dye needed for measurement by the constant-rate-injection
method----------__________-_---_--------~~~~~~-~-~~~~~~~~~~~---------- 235
Quantity of dye needed for measurement by the sudden-injection method 236

CONTENTS IX
Measurement of discharge by fluorescent+lye dilution-Continued Page
Procedures for measuring discharge by the dye-dilution method --____---- 237
Field procedures ____--------______--------~~--------------~------- 237
Analysis and computations --_____-_-------___--------------------- 240
Sample computation-constant-rate-injection method ___-_____--_-__- 241
Simplified procedures for making numerous dye-dilution measurements of
discharge_----------------------------------------------------------- 246
Measurement of discharge by sodium dichromate dilution ___--------___-_---- 249
General __--_________---________________________---------------------- 249
Principle of calorimetric analysis ______ - _________ --- _______ ------ ____ ---- 249
Method of analysis by calorimeter ----- _______ ----- _______ ------ ____ ---- 250
Measurement of discharge by salt dilution ______------______---------------- 250
General ----____--------________________________---------------------- 250
Preparation and injection of the concentrated salt solution---------------- 251
Measurement of relative conductance at the sampling site -____-_---____-_ 252
Computation ofdischarge ____________-___________________________------ 255
Measurement of discharge by dilution of radioactive tracers ___-_______ - __-___ 256
General ________________________________________---------------------- 256
Methodology ____--------___----------~---------~---------------------- 258
Selected references __------_____---------~--------------------------------- 259
Chapter 8.--Measurement of Discharge by Miscellaneous Methods
General ---_____----------______________________-------------------------- 260
Floats -----_______-------_____________________---------------------------- 261
Volumetric measurement --__----------__-_------~----------~-------------- 262
Portable weir plate _____--_________---------------------------------------- 263
Portable Parshall flume ---- ______ ------- ____ --------__------- ___-- ---_- __-_ 265
Measurement, of unstable flow-roll waves or slug flow ____------_-_-----__-- 268
Characteristics of unstable flow __________________________ ------__----___ 268
Determination of discharge ----------___-------____________________---- 269
Examples of discharge determination ____ ----- ______ ------ -_-_-______-___ 270
Proposed instrumentation __________-_____________________________------ 272
Selected references __-__---__________-_____________________---------------- 272
Chapter 9.-Indirect Determination of Peak Discharge
Introduction ____________-___________________________---------------------- 273
Collection of field data----- ___________ -_- __________ --- _________ ---- ____ ----- 274
Slope-areamethod ---____-----------______________________--~------------- 274
Contracted-opening method ____ --------- _______ ------ _____ -------___------- 277
Flow over dams and weirs- ___________ -_- ___________ - ___________ --- _____ -_-- 279
Flow through culverts----- _____ --------- ________ ----- ____ -------___------__ 279
General classification of flow--__-_------------------------------- ______- 281
Estimating discharge from superelevation in bends ----____-_------__-------- 281
Selected references -------___-----------~~~------------~----------~-------- 284
Index
VOLUME 2. COMPUTATION OF DISCHARGE
Chapter Page
10 Discharge ratings using simple stage-discharge relations --___--- 285

X CONTENTS
11 Discharge ratings using slope as a parameter ------------------ 390
12 Discharge ratings using a velocity index as a parameter -------- 429
13 Discharge ratings for tidal streams ---------------------------- 471
14 Discharge ratings for miscellaneous hydraulic facilities -------- 486
15 Computation of discharge records -- ______-________________ -_--- 544
16 Presentation and publication of stream-gaging data ------------ 601
ILLUSTRATIONS
FIGURE 1. Gage, concrete control, outside gage on bridge, and an engineer
making a wading measurement, Kaskaskia River at Bondville,
111 ---------------------~------------------------~---------
2. Gage and natural control, Little Spokane River at Elk, Wash_---
3. Rectangular weir on Trifolium Drain 23 of Imperial Irrigation Dis-trict,
near Westmorland, Calif -----_________________________
4. Four-foot Parshall flume discharging 62 ft”/s (1.76 n-&s) under
free-flow conditions ----------_____----------------------~~~
5. Flow through a 3-ft trapezoidal supercritical-flow flume showing
9
13
14
15
16
17
18
transition from subcritical to supercritical flow _________-_---
6. Concrete artificial control on Mill Creek near Coshocton, Ohio _-
7. Artificial control on Delaware River near Red Bluff, N. Mex., with
shallow V notch in the broad-crested weir _______-------------
8. Cover of book and weekly report card for recording manual gage
observations --___________-_-________________________----
9. Vertical staff gage------------____---------------------~~~~~~~
10. Type-A wire-weight gage-----________~_-----------------------
11. Float-tape gage _____--------___________________________-----~
12. Electric-tape gage ________ --- ________________ __-_-------------
13. Chaingage -_______---------_______________________-------~~~
14. Major units of the bubble gage ___________ ------------------~__
15. Installation of bubble orifice in unstable streambed ______------
16. Digitalrecorder___----------_-_________________________-~~~~~
17. Sample digitalrecordertape ~__________________---------------
18. Digital-recorder timer _______________-________________________
19. Continuous strip-chart recorder ___-___________ -----------------
20. Horizontal-drum recorder _--___-__________-------------------
21. Section of a typical strip chart ________--~----------------~-~~~
22. Reinforced-concrete well and shelter -------------------~~_____
23. Concrete well and wooden shelter with asphalt-shingle siding __
24. Corrugated-galvanized-steel-pipe well and shelter ___-----------
25. Concrete-pipe well and shelter ____-_______ -----------------___
26. Concrete-block shelter _------ ____________ ------------------___
27. Steel-pipe well and look-in shelter attached to bridge abutment--
28. Corrugated-steel-pipe well and wooden shelter attached to bridge
25
27
28
29
30
31
33
35
36
38
39
40
41
42
43
44
45
46
47
48
pier ----_________--_-_______________________-------------- 49
29. Flushing system for intakes ~-----------___~_---------------~~ 50
30. Statictubeforintakes____--------------_-___________________ 50
31. Typical bubble-gage installation __------ ___________ -_--------- 52
32. Telemarkgage --_________------------------~-----------~-~~~ 56
33. Resistance system transmitter unit _____ _ ____________ -_------- 57
34. Resistance system indicator unit ______ -- ____-________ -_------- 58

CONTENTS XI
FIGURE 35. Sample log sheet for bubble gage ____________-_---------------- 62
36. Diagram for determining allowable length of bubble tubing for
maximum friction error of 0.01 ft- ___________ -_-_------------ 72
37. Diagram for determining required bubble rate_______----------- 73
38. ModelT recorder -------------___________________________---- 75
39. ModelSRrecorder-__-_-_-_____-------------------------------- 76
40. Crest-stagegage---------------_------------------------------ 78
41. Definition sketch of midsection method of computing cross-section
area for discharge measurements __------------------________ 81
42. Computation notes of a current-meter measurement by the midsec-tionmethod__-___---------------~~~------------------------
83
43. Comparison of pulsations for two different mean velocities mea-sured
in a laboratory flume, 12 ft wide ------------------_-__ 85
44. Price type AA meter, top; Price pygmy meter, bottom ___- ___-_- 86
45. Vane ice meter, top; vane meter with cable-suspension yoke, bot-torn------------______-------------------~~~~~~~-~-----------
87
46. Ottcurrentmeter ____---------___________________________--~- 88
47. Velocity components measured by Ott and Price current meters 88
48. Hoff current meter ----------- _________ ------------_-_- ____ -_ 89
49. Comparison of mean velocities measured simultaneously by var-ious
current meters during 2-min periods, Stella Niagara section,
Panel point5 __----------------______________________--~--- SO
50. Optical current meter ____ ----- _______________ -_-------------- 91
51. Current-meter rating table----- _____________ --------------_-_- 95
52. Top-setting wading rod with meter attached-------------------- 98
53. Round wading rod with meter attached --------------_-________ 99
54. Lower section of ice rod for use with vane ice meter ____________ 100
55. Lower section of ice rod for use with Price meter--------_-______ 101
56. Columbus 15, 30-, 50-, 75-, and loo-lb sounding weights---_---- 102
57. Sounding-weight hangers and hanger pins ------------‘--___-_- 103
58. Canfield reel _----------------___---------------- ____________ 104
59. E56 reel----____-_---_-------------------------------------- 105
60. Computing depth indicator ----- _______________ ------------_-__ 105
61. Handline ____-----------------~~~~~-------------------------- 106
62. Handline in use from a bridge -___-_---------------------~---- 107
63. Handlinereels ____-_---------_________________________------ 108
64. Sounding weight with compass and sonic transducer ready for as-sembly
________---------------~~~--------------~----------- 109
65. Sonic measuring assembly ---___-__------_-_- _________________ 109
66. Tag-line reels ________________ - _____________ -_-_-_------------ 111
67. Sitdo n cable car __----------- ___________ -----------------___ 112
68. Standup cable car -------------____--_------------------------ 112
69. Cable-car puller for follower-brake cable cars, left; for standard
cars,right ----______----------____________________--~~-~-- 113
70. Power-operated cable cars ----- ____ -----------___- ____________ 114
71. Sitdown cable car with Canfield reel clamped to side of car ______ 115
72. Portable reel seat on sitdown-type cable car -__ __________-______ 116
73. Carrier (bank-operated) cableway __________ -_------------_- ____ 117
74. Type-A crane with three-wheel base __----------_- ____________ 118
75. Type-A crane with four-wheel base with boom in retracted position 119
76. Bridge board in use _________ - ________________ ---------------- 120
77. Truck-mounted crane used on the Mississippi River ____________ 121
78. Horizontal-axis boat tag-line reel without a brake ___.__________ 122

XII CONTENTS
FIGURE 79. Horizontal-axis boat tag-line reel with a brake --_____--_____-- 123
80. Vertical-axis boat tag-line reel - ____ ----___-_- _____ --- ____ --___ 124
81. Boom and crosspiece for use on boats __- ______ _ _______________ 125
82. Measuring equipment set up in a boat -_-----____----____-____ 126
83. Gasoline-powered ice drill _~---____---- -____ - __-____ - ________- 127
84. Collapsible reel support and ice-weight assembly _----_____-___ 128
85. Velocity-azimuth-depth assembly __-----__----____---__________ 129
86. Automatic counter (left) and headphone (right) ____---____---__ 130
87. Ice creepers for boots and waders ___-_-- -___ -- ______ -- -________ 131
88. Typical vertical-velocity curve -__------__----____------------- 133
89. Relation of surface-velocity coefficient to distance from vertical
wall of a smooth rectangular channel - ____ -- ______ -- _________ 137
90. Measurement of horizontal angle with measurement-note sheet __ 143
91. Measurement of horizontal angle with folding foot-rule-------_-- 144
92. Wading measurement using top-setting rod ----___-----___---__ 145
93. Ice rod being used to support current meter for a discharge mea-surement,
top; ice drill being used to cut holes, bottom __-___-_ 152
94. Method of computing meter settings for measurements under ice
cover___----____---___----~-~-----~~----------------------- 153
95. Typical vertical-velocity curve under ice cover --_____--______-__ 154
96. Part of notes for discharge measurement under ice cover --____-- 156
97. Determining position in the cross section, stadia method _--__-__ 157
98. Determining position in the cross section, angular method ____-_ 157
99. Position of sounding weight and line in deep, swift water-------- 160
100. Sketch of geometry of relation of actual to measured vertical angle
when flow direction is not normal to measurement section __-_ 166
101. Computation of discharge-weighted mean gage height __---___-- 172
102. Discharge-measurement notes with discharge adjusted for channel
storage ---------------_-------~-------------------------~-- 178
103. Sketch of stream with markers -- ______ - _______-_______---_____ 185
104. Diagram of velocity vectors ----____--- ______ - ___-___________- 186
105. Sketch of boat showing equipment -----__----- _____ --_ ________ 188
106. Component propeller-type meter _~-----____--- _______________-
107. Control panel of rate indicator and counter ----_------____---__
108. Sample tables of meter rating, Lb, and sine o( _- ________________
109. Sonic sounder and control panel ___---- _____ -- _____ ___ ________
110. Boat with mounted vane assembly ------~------__~---_________
111. Detailed view of vane-mounting assembly ___~~- _______________-
112. Definition sketch of midsection method of computation
189
190
191
194
196
196
superimposed on a facsimile of a sonic-sounder chart---------- 205
113. Sample computation notes of a moving-boat measurement _____- 206
114. Comparison of actual and computed values of incremental widths 209
115. Constant-rate-injection system ___----___------__--____________ 213
116. Concentration-time curve at downstream sampling site for
constant-rate injection __--------------_---_________ _-_______ 214
117. Concentration-time curve at downstream sampling site for sudden
injection _------__-----_-_---____________________-------~-- 215
118. Comparison of concentration-time curves obtained by SI and CR1
methods, observed at three points in sampling cross section, for
sampling reaches of three different lengths --_ _-___ -- _______- 218
119. Concentration-distribution curve illustrating the graphical method
of determining the percentage of mixing ___________________- 220

CONTENTS XIII
FIGURE 120. Schematic diagram of the fluorometer--------- _________________ 224
121. Mariotte vessel (constant-head device) --------------_-_---____ 232
122. Floating siphon (constant-head device) --------------_-________ 234
123. Pressurized constant-rate injection tanks for injection of dye into
streams---------------------------------------------------- 235
124. Sample analysis sheet used for computing discharge by the
constant-rate-injection method of dye dilution ----_--__-_-____ 244
125. Dye-injection rate of various stock dye concentrations related to
estimated stream discharge ----------------_-______________ 248
126. Schematic diagram of conductance meter used in salt-dilution
method of measuring discharge_-____------------------------ 253
127. Sample computation of discharge using salt dilution in the
sudden-injection method ------- ___________ -_-_--------_---__ 256
128. Curve of relative conductance versus time for the ionic wave in the
sample problem ----------------________________________---- 257
129. Portable weir-plate sizes - ______ -----------------_-_- _____ - ____ 264
130. Working drawing of a modified 3-in Parshall flume ____________ 267
131. Modified 3-in Parshall flume installed for measuring discharge -_ 268
132. Schematic sketch of longitudinal water-surface profile during pul-sating
flow ________________________________________-------- 269
133. Discharge hydrograph at Santa Anita Wash above Sierra Madre
Wash, Calif., April 16, 1965, and plot of discharges computed
fromobservationsofflow------_-____----------------------~- 271
134. Definition sketch of a slope-area reach ------------____________ 276
135. Definition sketch of an open-channel contraction-- ______________ 278
136. Graphical presentation of the Bernoulli equation in culvert flow 280
137. Classification of culvert flow ___----_- _________________________ 282
138. Idealized sketch of a bend (plan view) ----_-_- __________________ 283
TABLES
Page
TABLE 1. Range of velocities that can be measured with optical current
meter----------______-------------------~-~----------------- 92
2. Coefficients for standard vertical-velocity curve --------------__ 133
3. Current-meter and velocity-measurement method for various
depths (wading measurement) --____________---------------- 145
4. Velocity-measurement method for various meter suspensions and
depths --------________________________________----------~- 148
5. Air-correction table, giving difference, in feet, between vertical
length and slant length of sounding line above water surface for
selected vertical angles -- ______ ------------ ________________ 161
6. Air-correction table, giving difference, m meters, between vertical
length and slant length of soundmg line above water surface for
selected vertical angles ____ ---- __________________ ---------- 162
7. Wet-lme table, giving difference, in feet, between wet-line length
and vertical depth for selected vertical angles -- ______________ 164
8. Wet-line table, giving difference, in meters, between wet-line
length and vertical depth for selected vertical angles---------- 165
9. Degrees to be added to observed vertical angles to obtain actual
vertical angles when flow direction is not normal to measure-mentsection
--____------------______________________------ 167

XIV CONTENTS
TABLE 10. Summary table for setting the meter at 0.8-depth position in deep,
swift streams -------------_____---------------------~-~~~~~ 168
11. Registration errors, in percentage of stream velocity, caused by
vertical motion of current meter __________~~_--------------- 181
12. Spacing of vertical-line markings, in inches, on the sonic-sounder
chart for various combinations of chart speed and range distance 195
13. Temperature-correction coefficients for Rhodamine WT dye ___-_- 227
14. Rating table for 3-in modified Parshall flume __________-__-_-__ 266
15. Characteristics of types of culvert flow __________-__-_-________ 281
CONVERSION FACTORS
[Factors for convertmg Inch-pound to metnc “ruts are shown to four slgnlficant figures However, ,n the text the
metrx equwalents, where shown, are carned only to the number of svgnficant figures consistent wth the values
for the Enghsh umts.]
Inch-pound Multrply by-acres
4.047 x 103
acre-ft (acre-feet) 1.233x lo3
acre-ftiyr (acre feet per year) 1.233x lo”
ft (feet) 3.048x 10-l
ft/hr (feet per hour) 3.048x 10-l
ft/s (feet per second) 3.048x 10-l
ft”/s (cubic feet per second) 2.832 x lo-”
in (inches) 2.540x 10
lb (pounds) 4.536x 10-l
mi (miles) 1.609
mi’ (square miles) 2.590
02 (ounces) 2.835x 1O-y
M&lC
m2 (square meters)
n? (cubic meters)
mVyr (cubic meters per year)
m (meters)
m/hr (meters per hour)
m/s (meters per second)
mYs (cubic meters per second)
mm (millimeters)
kg (kilograms)
km (kilometers)
km’ (square kilometers)
kg (kilograms)

MEASUREMENT AND COMPUTATION
OF STREAMFLOW
VOLUME 1. MEASUREMENT OF STAGE AND
DISCHARGE
By S. E. RANTZ and others
CHAPTER I.-INTRODUCTION
PURPOSE OF THE MANUAL
The purpose of this manual is to provide a comprehensive descrip-tion
of state-of-the-art standardized stream-gaging procedures,
within the scope described below. The manual is intended for use as a
training guide and reference text, primarily for hydraulic engineers
and technicians in the U.S. Geological Survey, but the manual is also
appropriate for use by other stream-gaging practitioners, both in the
United States and elsewhere.
SCOPE OF THE MANUAL
The technical work involved in obtaining systematic records of
streamflow is discussed, in two volumes, in accordance with the fol-lowing
six major topics:
Volume 1. Measurement of stage and discharge
a. Selection of gaging-station sites
b. Measurement of stage
c. Measurement of discharge
Volume 2. Computation of discharge
d. Computation of the stage-discharge relation
e. Computation of daily-discharge records
f. Presentation and publication of stream-gaging data
In order to make the text as broadly usable as possible, discussions
of instrumentation and measurement are aimed at the technician,
and discussions of computational procedure are aimed at the junior
engineer who has a background in basic hydraulics.
Many of the procedures for determining discharge that are dis-cussed
in volume 2 require specialized instrumentation to obtain field
data that supplement the observation of stage. The descriptions of
such specialized equipment and associated observational techniques

2 MEASUREMENT OF STAGE AND DISCHARGE
are given in appropriate chapters in volume 2 so that the reader may
have unified discussions of the methodologies applicable to each type
of problem in determining discharge.
In general the authors have attempted to prepare a manual that
will stand independently-references are given to supplementary
published material, but the reader should find relatively few occa-sions
when there is pressing need to consult those references. There
are three notable exceptions to that statement.
1. The subject of indirect determination of peak discharge (v. 1, chap.
9) is treated here only in brief because of space limitations; the
subject is treated fully in five reports in the Geological Survey
report series, “Techniques of Water-Resources Investigations.” The
five reports are named in the reference section of chapter 9.
2. Among the methods discussed in this manual for computing the
discharge of tidal streams are four mathematical techniques for
evaluating the differential equations of unsteady flow (v. 2, chap.
13). The four techniques are given only cursory treatment because
a detailed description of the complex mathematical techniques is
considered to be beyond the scope of the manual.
3. The processing of streamflow records by digital computer (v. 2,
chap. 15) is a subject that is given only generalized treatment here.
It was not practicable to include a detailed description of each step
in the sequence of operation of an automated computing system
because of space limitations, and also because the particulars of
each step are somewhat in a state of flux in response to continual
improvement in storage and access procedures.
STREAMFLOW RECORDS
Streamflow serves man in many ways. It supplies water for domes-tic,
commercial, and industrial use; irrigation water for crops; dilu-tion
and transport for removal of wastes; energy for hydroelectric
power generation; transport channels for commerce; and a medium
for recreation. Records of streamflow are the basic data used in devel-oping
reliable surface-water supplies because the records provide in-formation
on the availability of streamflow and its variability in time
and space. The records are therefore used in the planning and design
of surface-water related projects, and they are also used in the man-agement
or operation of such projects after the projects have been
built or activated.
Streamflow, when it occurs in excess, can create a hazard-floods
cause extensive damage and hardship. Records of flood events ob-tained
at gaging stations serve as the basis for the design of bridges,
culverts, dams, and flood-control reservoirs, and for flood-plain de-lineation
and flood-warning systems.

1. INTRODUCTION 3
The streamflow records referred to above are primarily continuous
records of discharge at stream-gaging stations, a gaging station being
a stream-site installation so instrumented and operated that a con-tinuous
record of stage and discharge can be obtained. Networks of
stream-gaging stations are designed to meet the various demands for
streamflow information, including inventory of the total water re-source.
The networks of continuous-record stations, however, are
often augmented by auxiliary networks of partial-record stations to
fill a particular need for streamflow information at relatively low
cost. For example, an auxiliary network of sites, instrumented and
operated to provide only instantaneous peak-discharge data, is often
established to obtain basic information for use in regional flood-frequency
studies. An auxiliary network of uninstrumented sites for
measuring low flow only is often established to provide basic data for
use in regional studies of drought and of fish and wildlife mainte-nance
or enhancement.
GENERAL STREAM-GAGING PROCEDURES
After the general location of a gaging station has been determined
from a consideration of the need for streamflow data, its precise loca-tion
is so selected as to take advantage of the best locally available
conditions for stage and discharge measurement and for developing a
stable stage-discharge relation.
A continuous record of stage is obtained by installing instruments
that sense and record the water-surface elevation in the stream. Dis-charge
measurements are initially made at various stages to define
the relation between stage and discharge. Discharge measurements
are then made at periodic intervals, usually monthly, to verify the
stage-discharge relation or to define any change in the relation
caused by changes in channel geometry and (or) channel roughness.
At many sites the discharge is not a unique function of stage; vari-ables
other than stage must also be continuously measured to obtain
a discharge record. For example, stream slope is measured by the
installation of a downstream auxiliary stage gage at stations where
variable backwater occurs. At other sites a continuous measure of
stream velocity at a point in the cross section is obtained and used as
an additional variable in the discharge rating. The rate of change of
stage can be an important variable where flow is unsteady and chan-nel
slopes are flat.
Artificial controls such as low weirs or flumes are constructed at
some stations to stabilize the stage-discharge relations in the low-flow
range. These control structures are calibrated by stage and dis-charge
measurements in the field.
The data obtained at the gaging station are reviewed and analyzed

by engineering personnel at the end of the water year. Discharge
ratings are established, and the gage-height record is reduced to
mean values for selected time periods. The mean discharge for each
day and extremes of discharge for the year are computed. The data
are then prepared for publication.
SELECTED REFERENCE
Carter, R. W., and Davidian, Jacob, 1968, General procedure for gaging streams: U.S.
Geol. Survey Techniques Water-Resources Inv., book 3, chap. A6, p. 1-2.
CHAPTER 2.--SELECTION OF GAGING-STATION
SITES
INTRODUCTION
The general location of a gaging station is dependent on the specific
purpose of the streamflow record. If the streamflow record is needed
for the design or operation of a water project, such as a dam and
reservoir, the general location of the gaging station obviously will be
in the vicinity of the water project. The selection of a gaging-station
site becomes complicated, however, when the station is to be one of a
network of stations whose records are required for study of the gen-eral
hydrology of a region. Such studies are used to inventory the
regional water resource and formulate long-range water-development
plans. In that situation, attention to hydrologic princi-ples
is required in selecting the general locations of the individual
stations in the network to ensure that optimum information is ob-tained
for the money spent in data collection.
A discussion of the design of gaging-station networks is beyond the
scope of this manual and for the purpose of this chapter we will
assume that the general location of a proposed gaging station has
been determined. The discussion that follows will be concerned with
the hydraulic considerations that enter into the selection of the pre-cise
location of the gage to obtain the best locally available conditions
for the measurement of stage and discharge and for the development
of a stable discharge rating.
CONSIDERATIONS IN SPECIFIC SITE SELECTION
After the general location of a gaging station has been determined, a
specific site for its installation must be selected. For example, if the
outflow from a reservoir is to be gaged to provide the streamflow data
needed for managing reservoir releases, the general location of the
gaging station will be along the stretch of stream channel between
the dam and the first stream confluence of significant size

2. SELECTION OF GAGING-STATION SITES 5
downstream from the dam. From the standpoint of convenience alone,
the station should be established close to the dam, but it should be far
enough downstream from the outlet gates and spillway outlet to allow
the flow to become uniformly established across the entire width of
the stream. On the other hand the gage should not be located so far
downstream that the stage of the gaged stream may be affected by the
stage of the confluent stream. Between those upstream and
downstream limits for locating the gage, the hydraulic features
should be investigated to obtain a site that presents the best possible
conditions for stage and discharge measurement and for developing a
stable stage-discharge relation. If the proposed gaging station is to be
established for purely hydrologic purposes, unconnected with the de-sign
or operation of a project, the general location for the gage will be
the stretch of channel between two large tributary or confluent
streams. The same consideration will apply in the sense that the gage
should be far enough downstream from the upper tributary so that
flow is fairly uniformly established across the entire width of stream,
and far enough upstream from the lower stream confluence to avoid
variable backwater effect. Those limits often provide a reach of chan-nel
of several miles whose hydraulic features must be considered in
selecting a specific site for the gage installation.
The ideal gage site satisfies the following criteria:
1. The general course of the stream is straight for about 300 ft (ap-prox.
100 m) upstream and downstream from the gage site.
2. The total flow is confined to one channel at all stages, and no flow
bypasses the site as subsurface flow.
3. The streambed is not subject to scour and fill and is free of aquatic
growth.
4. Banks are permanent, high enough to contain floods, and are free
of brush.
5. Unchanging natural controls are present in the form of a bedrock
outcrop or other stable riffle for low flow and a channel constric-tion
for high flow-or a falls or cascade that is unsubmerged at
all stages (chap. 3).
6. A pool is present upstream from the control at extremely low
stages to ensure a recording of stage at extremely low flow, and
to avoid high velocities at the streamward end of gaging-station
intakes during periods of high flow.
7. The gage site is far enough upstream from the confluence with
another stream or from tidal effect to avoid any variable influ-ence
the other stream or the tide may have on the stage at the
gage site.
8. A satisfactory reach for measuring discharge at all stages is avail-able
within reasonable proximity of the gage site. (It is not nec-

essary that low and high flows be measured at the same stream
cross section.)
9. The site is readily accessible for ease in installation and operation
of the gaging station.
Rarely will an ideal site be found for a gaging station and judgment
must be exercised in choosing between adequate sites, each of which
has some shortcomings. Often, too, adverse conditions exist at all
possible sites for installing a needed gaging station, and a poor site
must be accepted. For example, all streams in a given region may
have unstable beds and banks, which result in continually changing
stage-discharge relations.
The reconnaissance for a gaging site properly starts in the office
where the general area for the gage site is examined on topographic,
geologic, and other maps. Reaches having the following pertinent
characteristics should be noted: straight alinement, exposed consoli-dated
rock as opposed to alluvium, banks subject to overflow, steep
banks for confined flow, divided channels, possible variable
backwater effect from a tributary or confluent stream or from a reser-voir,
and potential sites for discharge measurement by current meter.
The more favorable sites will be given critical field examination; they
should be marked on the map, access roads should be noted, and an
overall route for field reconnaissance should be selected.
In the field reconnaissance the features discussed earlier are inves-tigated.
With regard to low flow, a stable well-defined low-water con-trol
section is sought. In the absence of such a control, the feasibility
of building an artificial low-water control is investigated. If a site on a
stream with a movable bed must be accepted-for example, a sand-channel
stream-it is best to locate the gage in as uniform a reach as
possible, away from obstructions in the channel, such as bridges,
which tend to intensify scour and fill. (See page 377.) Possible
backwater resulting from aquatic growth in the channel should also
be investigated. If the gage is to be located at a canyon mouth where
the stream leaves the mountains or foothills to flow onto an alluvial
plain or fan, reconnaissance current-meter measurements of dis-charge
should be made during a low-flow period to determine where
the seepage of water into the alluvium becomes significant. The sta-tion
should be located upstream from the area of water seepage in
order to gage as much of the surface flow as possible; the subsurface
flow or underflow that results from channel seepage is not “lost” wa-ter,
but is part of the total water resource.
With regard to high stages, high-water marks from major floods of
the past are sought and local residents are questioned concerning
historic flood heights. Such information is used by the engineer in
making a judgment decision on the elevation at which the stage-

recorder must be placed to be above any floods that are likely to occur
in the future. The recorder shelter should be so located as to be shel-tered
from waterborne debris during major floods. Evidence is also
sought concerning major channel changes, including scour and depo-sition
at streambanks, that occurred during notable floods of the past.
That evidence, if found, gives some indication of changes that might
be expected from major floods of the future.
The availability of adequate cross sections for current-meter meas-urement
of discharge should also be investigated. Ideally, the meas-urement
cross section should be of fairly uniform depth, and flow lines
should be parallel and fairly uniform in velocity throughout the cross
section. The measurement section should be in reasonable proximity
to the gage to avoid the need for adjusting measured discharge for
change in storage, if the stage should change rapidly during a dis-charge
measurement. However a distance of as much as 0.5 mi (ap-prox.
1 km) between gage and measuring section is acceptable if such
a distance is necessary to provide both a good stage-measurement site
and a good discharge-measurement site. Low-flow discharge meas-urements
of’ all but the very large streams are made by wading. For
flows that cannot be safely waded, the current meter is operated from
a bridge, cableway, or boat. It is most economical to use an existing
bridge for that purpose, but in the absence of a bridge, or if the
measuring section at a bridge site is poor, a suitable site should be
selected for constructing a cableway. If construction of a cableway is
not feasible because of excessive width of the river, high-water meas-urements
will be made by boat when safe to do so. The cross section
used for measuring high flows is rarely suitable for measuring low
flows, and wading measurements are therefore made wherever
measuring conditions are most favorable.
Consideration should be given to the possibility of variable
backwater effect from a stream confluence or reservoir downstream
from the general location of the required gaging station. Without
knowledge of stage and discharge at a potential gage site and of
concurrent stage at the stream confluence or reservoir, the engineer
can only conjecture concerning the location on the stream where
backwater effect disappears for various combinations of discharge
and stage. A safe rule is the following: Given a choice of several
acceptable gaging sites on a stream, the gaging site selected should be
the one farthest upstream from the possible source of variable
backwater. If it is necessary to accept a site where variable backwater
occurs, a uniform reach for measurement of slope should be sought,
along with a site for the installation of an auxiliary gage. If a gaging
station must be placed in a tide-affected reach, the unsteady flow that
must be gaged will also require an auxiliary gage, but in addition line

power must be available to insure the synchronized recording of stage
at the two gages. The availability of line power or telephone lines is
also a consideration, where needed for special instrumentation or for
the telemetering units that are often used in flood-forecasting and
flood-warning systems.
In cold regions the formation of ice always presents a problem in
obtaining reliable winter records of streamflow. However in regions
that are only moderately cold, and therefore subject to only moderate
ice buildup, forethought in the selection of gage sites may result in
streamflow records that are free of ice effect. Gage sites that are
desirable from that standpoint are as follows:
1. Below an industrial plant, such as a paper mill, steel mill, thermal
powerplant, or coal mine. “Waste” heat may warm the water
sufficiently or impurities in the water may lower the freezing
point to the extent that open-water conditions always prevail.
2. Immediately downstream from a dam with outlet gages. Because
the density of water is maximum at a temperature of 4”C, the
water at the bottom of a reservoir is commonly at or near that
temperature in winter. Most outlet gates are placed near the
bottom of the dam, and the water released is therefore approxi-mately
4°C above freezing. It would take some time for that
water to lose enough heat to freeze.
3. On a long fairly deep pool just upstream from a riffle. A deep pool
will be a tranquil one. Sheet ice will form readily over a still
pool, but the weather must be extremely cold to give complete
cover on the riffle. At the first cold snap, ice will form over the
pool and act as an insulating blanket between water and air.
Under ice cover the temperature of the streambed is generally
slightly above the freezing point and may, by conduction and
convection, raise the water temperature slightly above freezing,
even though water enters the pool at 0°C. That rise in tempera-ture
will often be sufficient to prevent ice formation on the riffle.
After the many considerations discussed on the preceding pages
have been weighed, the precise sites for the recording stage gage and
for the cableway for discharge measurements (if needed) are selected.
Their locations in the field are clearly marked and referenced. The
maximum stage at which the low-water control will be effective
should be estimated; the intakes to the stage recorder should be lo-cated
upstream from the low-water control, a distance equal to at
least three times the depth of water on the control at that estimated
maximum stage. If the intakes are located any closer than that to the
control, they may lie in a region where the streamlines have vertical
curvature; intake location in that region is hydraulically undesirable.
The gaging station on the Kaskaskia River at Bondville, Ill., shown

in figure 1, satisfies most of the requirements discussed in this chap-ter.
Low-flow measurements are made by wading upstream from the
control. The bridge site provides accessibility, convenience to power
lines, and a good location for an outside reference gage, which is
shown on the downstream parapet wall of the bridge.
Up to this point there has been no discussion of specific site location
for crest-stage gages. Those gages provide peak-discharge data only.
Where possible they should be installed upstream from road culverts,
which act as high-water controls. The specific site for a gage is at a
distance of one culvert width upstream from the culvert inlet. In the
absence of such control structures, the crest-stage gage should be
installed in a straight reach of channel that can be utilized in comput-ing
peak discharge by the slope-area method (chap. 9).
SELECTED REFERENCES
World Meteorological Organization, 1974, Guide to hydrometeorological practices [3d
ed.]: WMO-no. 168, p. 3.1-3.4, 3.13-3.16.
FIGURE l.-Gage, concrete control, outside gage on bridge, and an engineer making a
wading measurement, Kaskaskia River at Bondville, Ill.

CHAPTER 3.-GAGING-STATION CONTROLS
TYPES OF CONTROL
The conversion of a record of stage to a record of discharge is made
by the use of a stage-discharge relation. The physical element or
combination of elements that controls the relation is known as a
control. The major classification of controls differentiates between
section controls and channel controls. Another classification differ-entiates
between natural and artificial controls. (Artificial controls
are structures built for the specific purpose of controlling the stage-discharge
relation; a highway bridge or paved floodway channel that
serves incidentally as a control is not classed as an artificial control.)
A third classification differentiates between complete, partial, and
compound controls.
Section control exists when the geometry of a single cross section a
short distance downstream from the gage is such as to constrict the
channel, or when a downward break in bed slope occurs at the cross
section. The constriction may result from a local rise in the
streambed, as at a natural riffle or rock ledge outcrop, or at a
constructed weir or dam; or it may result from a local constriction in
width, which may occur naturally or be caused by some manmade
channel encroachment, such as a bridge whose waterway opening is
considerably narrower than the width of the natural channel. Exam-ples
of a downward break in bed slope are the head of a cascade or the
brink of a falls.
Channel control exists when the geometry and roughness of a long
reach of channel downstream from the gaging station are the ele-ments
that control the relation between stage and discharge. The
length of channel that is effective as a control increases with dis-charge.
Generally speaking, the flatter the stream gradient, the
longer the reach of channel control.
A complete control is one that governs the stage-discharge relation
throughout the entire range of stage experienced at the gaging sta-tion.
More commonly, however, no single control is effective for the
entire range of stage, and so the result is a compound control for the
gaging station. A common example of a compound control is the situ-ation
where a section control is the control for low stages and channel
control is effective at high stages. The compound control sometimes
includes two section controls, as well as channel control. In that situ-ation
the upstream section control is effective for the very low stages,
a section control farther downstream is effective for intermediate
stages, and channel control is effective at the high stages.
With regard to complete controls, a section control may be a
complete control if the section control is a weir, dam, cascade, or falls

3. GAGING-STATION CONTROLS 11
of such height that it does not become submerged at high discharges.
A channel control may be a complete control if a section control is
absent, as in a sand channel that is free of riffles or bars, or in an
artificial channel such as a concrete-lined floodway.
A partial control is a control that acts in concert with another
control in governing the stage-discharge relation. That situation
exists over a limited range in stage whenever a compound control is
present. As an example consider the common situation where a sec-tion
control is the sole control for low stages and channel control is
solely operative at high stages. At intermediate stages there is a
transition from one control to the other, during which time sub-mergence
is “drowning out” the section control. During that transi-tion
period the two controls act in concert, each as a partial control. In
effect we have a dam (low-flow control) being submerged by tailwater;
before complete submergence (channel control), the upstream stage
for the particular discharge is dependent both on the elevation of the
dam and on the tailwater elevation. Where the compound control
includes two section controls, the degree of submergence of the
upstream section control will be governed by the downstream section
control, during a limited range in stage. When that occurs, each of the
section controls is acting as a partial control. A constriction in chan-nel
width, unless unusually severe, usually acts as a partial control,
the upstream stage being affected also by the stage downstream from
the constriction.
ATTRIBUTES OF A SATISFACTORY CONTROL
The two attributes of a satisfactory control are permanence (stabil-ity)
and sensitivity. If the control is stable, the stage-discharge
relation will be stable. If the control is subject to change, the
stage-discharge relation is likewise subject to change, and frequent
discharge measurements are required for the continual recalibration
of the stage-discharge relation. That not only increases the operating
cost of a gaging station, but results in impairment of the accuracy of
the streamflow record.
The primary cause of changes in natural controls is the high veloc-ity
associated with high discharge. Of the natural section controls, a
rock ledge outcrop will be unaffected by high velocities, but boulder,
gravel, and sand-bar riffles are likely to shift, boulder riffles being the
most resistant to movement and sand bars the least resistant. Of the
natural channel controls those with unstable bed and banks, as found
in sand-channel streams, are the most likely to change as a result of
velocity- induced scour and deposition.
Another cause of changes in natural controls is vegetal growth. The
growth of aquatic vegetation on section controls increases the stage

for a given discharge, particularly in the low-flow range. Vegetal
growth on the bed and banks of channel controls also affects the
stage-discharge relation by reducing velocity and the effective
waterway area. In the temperate climates, accumulations of water-logged
fallen leaves on section controls each autumn clog the in-terstices
of alluvial riffles and raise the effective elevation of all natu-ral
section controls. The first ensuing stream rise of any significance
usually clears the control of fallen leaves.
Controls, particularly those for low flow, should be sensitive; that
is, a small change in discharge should be reflected by a signficant
change in stage. To meet that requirement it is necessary that the
width of flow at the control be greatly constricted at low stages. In a
natural low-water control such constriction occurs if the control is in
effect notched, or if the controlling cross section roughly has a flat
V-shape or a flat parabolic shape. Those shapes will ensure that the
width of flow over the control decreases as discharge decreases. Gen-erally
speaking, a low-water control is considered to be sensitive if a
change of no more than 2 percent of the total discharge is represented
by a change of one unit of recorded stage. For example, in the U.S.A.,
stage is recorded in units of hundredths of a foot; therefore, for the
low-water control to be regarded as sensitive, a change in stage of
0.01 ft (0.003 m) should represent a change of no more than about 2
percent of the total discharge.
In the interest of economy a gaging station should be located
upstream from a suitable natural control (fig. 2). However, where
natural conditions do not provide the stability or the sensitivity
required, artificial controls should be considered. The artificial con-trols
are all section controls; it is not feasible to pave or otherwise
improve a long reach of channel solely for the purpose of stabilizing
the stage-discharge relation.
ARTIFICIAL CONTROLS
An artificial control is a structure built in a stream channel to
stabilize and constrict the channel at a section, and thereby simplify
the procedure of obtaining accurate records of discharge. The artifi-cial
controls built in natural streams are usually broad-crested weirs
that conform to the general shape and height of the streambed. (The
term “broad-crested weir,” as used in this manual, refers to any type
of weir other than a thin-plate weir.) In canals and drains, where the
range of discharge is limited, thin-plate weirs and flumes are the
controls commonly built. Thin-plate weirs are built in those channels
whose flow is sediment free and whose banks are high enough to
accommodate the increase in stage (backwater) caused by the instal-lation
of a weir (fig. 3). Flumes are largely self cleaning and can

therefore be used in channels whose flow is sediment laden, but their
principal advantage in canals and drains is that they cause relatively
little backwater (head loss) and can therefore be used in channels
whose banks are relatively low. Flumes are generally more costly to
build than weirs.
Flumes may be categorized with respect to the flow regime that
principally controls the measured stage; that is, a flume is classed as
either a critical-flow flume or a supercritical-flow flume. The Parshall
flume (fig. 4) is the type of critical-flow flume most widely used.
Supercritical-flow flumes are used in streams that transport heavy
loads of sediment that include rocks that are too large to pass through
a critical-flow flume without being deposited in the structure. Of
those flumes the trapezoidal supercritical-flow flume (fig. 5) is the
most widely used by the U.S. Geological Survey.
Artificial controls eliminate or alleviate many of the undesirable
characteristics of natural section controls. Not only are they physi-cally
stable, but they are not subject to the cyclic or progressive
growth of aquatic vegetation other than algae. Algal slimes that
sometimes form on artificial controls can be removed with a wire
brush, and the controls are self cleaning with regard to fallen leaves.
In moderately cold climates artificial controls are less likely to be
affected by the formation of winter ice than are natural controls. The
artificial control can, of course, be designed to attain the degree of
sensitivity required for the gaging station. In addition, an artificial
FIGURE 2.-Gage and natural control, Little Spokane River at Elk, Wash.

control may often provide an improved discharge-measurement sec-tion
upstream from the control by straightening the original angular-ity
of flow lines in that cross section.
In canals or drains, where the range of discharge is limited, artifi-cial
controls are usually built to function as complete controls
throughout the entire range in stage. In natural channels it is gen-erally
impractical to build the control high enough to avoid sub-mergence
at high discharges, and the broad-crested weirs that are
usually built are effective only for low, or for low and medium, dis-charges.
Figures 6 and 7 illustrate broad-crested weirs of two differ-ent
shapes; the crests of both have a flat upward slope from the center
of the stream to the banks, but in addition, the weir in figure 7 has a
shallow V-notch in the center for greater sensitivity.
FIGURE 3.-Rectangular weir on Trifolium Drain 23 of Imperial Irrigation District,
near Westmorland, Cald (View looking downstream.)

The attributes desired in an artificial control include the following:
1. The control should have structural stability and should be perma-nent.
The possibility of excessive seepage under and around the
control should be considered, and the necessary precautions
should be taken for the prevention of seepage by means of sheet
piling or concrete cut-off walls and adequate abutments.
2. The crest of the control should be as high as practicable to possibly
eliminate the effects of variable downstream conditions or to
limit those effects to high stages only.
3. The profile of the crest of the control should be designed so that a
small change in discharge at low stages will cause a measurable
change in stage. If the control is intended to be effective at all
stages, the profile of the crest should be designed to give a
stage-discharge relation (rating curve) of such shape that it can
be extrapolated to peak stages without serious error.
4. The shape of the control structure should be such that the passage
of water creates no undesirable disturbances in the channel
upstream or downstream from the control.
FIGURE 4.-Four-foot Parshall flume discharging 62 ft”/s (1.76 m:‘/s) under free-flow
conditions. Scour protection is required with this height of fall. (Courtesy U.S.
Bureau of Reclamation.)

5. If the stream carries a heavy sediment load, the artificial control
should be designed to be self-cleaning. Flumes have that attri-bute;
broad-crested weirs can often be made self-cleaning by a
design modification in which the vertical upstream face of the
weir is replaced by an upstream apron that slopes gently from
the streambed to the weir crest.
Artificial controls are often built in conformance with the dimen-sions
of laboratory-rated or field-rated weirs or flumes. The question
arises whether to use the precalibrated rating or to calibrate in place
each new installation. There are two schools of thought on the sub-ject.
In many countries, the precalibrated rating is accepted, and dis-charge
measurements by current meter or by other means are made
only periodically to determine if any statistically significant changes
in the rating have occurred. If a change is detected, the new rating is
defined by as many discharge measurements as are deemed neces-
FIGURE K-Flow through a 3-ft trapezoidal supercritlcal-flow flume showing transitlon
from subcritical to supercritlcal flow.

sary. In other countries, including the U.S.A., the position is taken
that it is seldom desirable to accept the rating curve prepared for the
model structure without checking the entire rating of the prototype
structure in the field by current-meter measurements, or by other
methods of measuring discharge. The experience in the U.S.A. and
elsewhere has been that differences between model and prototype
invariably exist, if only in approach-channel conditions, and these
differences are sufficient to require complete in place calibration of
the prototype structure. In place calibration is sometimes dispensed
with where the artificial control is a standard thin-plate weir having
negligible velocity of approach.
CHOICE OF AN ARTIFICIAL CONTROL
Cost is usually the major factor in deciding whether or not an
artificial control is to be built to replace an inferior natural control.
The cost of the structure is affected most by the width of the stream
and by the type or condition of bed and bank material. Stream width
governs the size of the structure, and bed and bank material govern
the type of construction that must be used to minimize leakage under
and around the structure.
If an artificial control is to be used, the type and shape of the
structure to be built is dependent upon channel characteristics, flow
conditions, range of discharge to be gaged, sensitivity desired, and
the maximum allowable head loss (backwater).
FIGURE 6.-Concrete artificial control on Mill Creek near Coshocton, Ohio.

CHOICE BETWEEN WEIR AND FLUME
As a general rule a weir is more advantageous for use as a control
structure than a flume for the following reasons.
1. Weirs are usually cheaper to build than flumes.
2. A weir can be designed to have greater sensitivity at low flows
with less sacrifice of range of discharge that can be accommo-dated,
than is possible with a flume. Sensitivity is increased for
a weir by notching the crest or by shaping the longitudinal pro-file
of the crest in the form of a flat V or catenary. Sensitivity at
low flow for a flume is usually attained by narrowing the effec-tive
width (converging sidewalls), or by using a trapezoidal cross
section (narrower width at low stages), or by doing both; those
measures significantly reduce the capacity of the flume.
3. The high water end of the stage-discharge relation for a weir can
be extended beyond the stages at which the weir is effective as a
control, with more confidence than can be done for a flume. In
other words the stage-discharge relation for a flume becomes
completely uncertain when any part of the structure upstream
from the stage-measurement site is overtopped; the stage-discharge
relation for a weir becomes completely uncertain only
when the bank or abutment is overtopped and flow occurs
around the end(s) of the weir.
If a flume is installed with the expectation that it will be overtop-
FIGURE 7.-Artificial control on Delaware River near Red Bluff, New Mex., with shal-low
V notch in the broad-crested weir.

ped by floodflows, it is advisable to install a nonrecording stage gage
in a straight reach of channel, upstream or downstream from the
flume but beyond the influence of the flume structure. Simultaneous
observations of stage at the flume and in the unobstructed channel
can be used to obtain a relation between the two stage gages. A
stage-discharge relation for the site of the nonrecording gage can thus
be derived from the flume rating, up to the discharge at which over-flow
starts at the flume. If for some reason, such as one of those
discussed on page 273, high-flow discharge measurements are not
available, the stage-discharge relation for the nonrecording gage can
be extrapolated to flood stages; that extrapolation can then be used
with the stage relation to define the overflow portion of the discharge
rating for the flume.
However, in the following situations the use of a flume is more
advantageous than the use of a weir.
1. If a heavy sediment load is carried by the stream, a weir will trap
the sediment; accumulation of the sediment in the approach
reach will alter the stage-discharge relation by changing the
velocity of approach. Flumes however are usually self cleaning
by virtue of their converging sidewalls and (or) steep floor. They
therefore are more likely to maintain an unchanging stage-discharge
relation. However, if the size of the sediment is not
large, it is often possible to make a broad-crested weir self clean-ing
by including in its design an upstream apron that slopes
downward from crest. An apron slope of 1 vertical to 5 horizontal
will usually result in the transport of small sediment over the
weir.
2. Weirs are usually not suitable for use in steep channels where the
Froude number (V/d&) is greater than about 0.75. Best results
are obtained with weirs where the velocity head is a very minor
part of the total head, and that is not the case in steep channels
where the velocity head becomes excessively large. Further-more,
as explained above, weirs act as sediment traps on steep
streams.
3. Flumes create less backwater for a given discharge than do weirs.
Consequently it is more advantageous to use a flume if the
channel has low banks. However for most natural streams it is
impractical to design any type of structure to act solely as a
metering device for the entire range of stage that may be experi-enced.
In other words, for most natural streams sporadic over-bank
Rooding is to be expected, with or without a control struc-ture
in the stream. Consequently the advantage of reduced
backwater for a flume is usually realized only where the flow can
be controlled to give some preassigned value of maximum dis-

charge. That situation occurs only in diversion canals or in nat-ural
streams having a bypass floodway.
CHOICE BETWEEN CRITICAL-FLOW FLUME AND
SUPERCRITICAL-FLOW FLUME
After it has been decided for a particular site that the use of a flume
is more desirable than the use of a weir, a decision must be made as to
whether to use a critical-flow flume or a supercritical-flow flume.
Both types of flume will transport debris of considerable size with-out
deposition in the structure, but if the transported rocks are exces-sively
large, they may be deposited at or immediately upstream from
the critical-depth section of a critical-flow flume. That will cause a
change in the discharge rating of the flume. Therefore where that
situation is likely to occur, a supercritical-flow flume should be
selected for use.
If a critical-flow flume will pass the transported sediment load, that
type of flume should be selected for use because the discharge rating
for a critical-flow flume is more sensitive than that for a
supercritical-flow flume.
The artificial controls recommended for natural streams are as fol-lows:
Sedment-transport characterzstm Recommended structure
Light load, small-size sediment __-----------~~~__ Weir.
Medium load, medium-size sediment __---------- Parshall flume.
Heavy load, large-size sediment ______~~---------- TrapezoIdal supercritlcal-flow
flume.
The adjectives used above-light, medium, heavy, small, and
large-are relative. Observation of both the study site and of the
operation of control structures installed in an environment similar to
that of the study site will provide the principle basis for the selection
of the optimum type of control for use. In short, do not use a flume
where a weir will do; if the use of a flume is indicated, do not use a
supercritical-flow flume where a critical-flow flume (Parshall flume)
will do.
The above recommendations also apply to canals or natural chan-nels
whose flow is controlled to limit the maximum discharge to some
preassigned value. However, there is one exception; if the banks have
little freeboard at the maximum discharge before the installation of
an artificial control, a flume installation is generally preferable to a
weir, in order to minimize the backwater caused by the structure.

DESIGN OF AN ARTIFICIAL CONTROL
Having decided on the type of artifical control to be used-weir,
Parshall flume, or trapezoidal supercritical-flow flume-the next step
is to design the structure. A standard design will usually be used,
although channel conditions may make it necessary to make minor
modification of the standard dimensions of the structure selected. The
four factors-channel characteristics, range of discharge to be gaged,
sensitivity desired, and maximum allowable head loss
(backwater)-must be considered simultaneously in the precise de-termination
of the shape, dimensions, and crest elevation of the con-trol
structure. However, two preliminary steps are necessary.
First, the head-discharge relations for various artificial controls of
standard shape and of the type selected are assembled. Several such
relations are to be found in hydraulics handbooks (King and Brater,
1963; World Meterological Organization, 1971). In addition, head-discharge
relations for artificial controls that were field calibrated
will usually be available in the files of water-resources agencies in
the area-some are given in chapter 10. The head-discharge relations
that are assembled need only be approximately correct, because
channel conditions at the site of the proposed control will seldom
match those for the model control.
The second preliminary step is to determine an approximate
stage-discharge relation for the anticipated range in stage in the
unobstructed channel at the site of the proposed control. That may be
done by the use of an open-channel discharge equation, such as the
Manning equation, in which uniform flow is assumed for the site and
a value of the roughness coefficient is estimated. The reliability of the
computed stage-discharge relation will be improved if one or more
discharge measurements are made to verify the value of the rough-ness
coefficient used in the computations. The purpose of the compu-tations
is to determine the tailwater elevation that is applicable to
any given discharge after an artificial control is installed.
The next. step is to consider the lower discharges that will be gaged.
The tailwater elevations corresponding to those discharges are used
to determine the minimum crest elevation permissible for the pro-posed
artificial control at the lower discharges, under conditions of
free flow or allowable percentage of submergence. If a flume is to be
installed, t,he throat section should be narrow enough to ensure sen-sitivity
at low discharges. If a weir is to be installed and the stream is
of such width that a horizontal crest will be insensitive at low dis-charges,
the use of a flat V crest is recommended-for example, one
whose sides have a slope of 1 vertical to 10 horizontal. The sensitivity
desired is usually such that the discharge changes no more than 2
percent for each change in stage of 0.01 ft (0.003 m). For a weir or

critical-flow flume (Parshall flume) it is also desirable that the
minimum discharge to be gaged have a head of at least 0.2 ft (0.06 m)
to eliminate the effects of surface tension and viscosity.
Stage-discharge relations for the several controls under considera-tion
are next prepared for the anticipated range in discharge. A struc-ture
is then selected that best meets the demands of the site in acting
as a control for as much of the range as possible, without exceeding
the maximum allowable backwater (head loss) at the higher stages
and with minor submergence effect and acceptable sensitivity at
lower stages. In other words, a high crest elevation minimizes sub-mergence
but maximizes backwater effect which may cause or aggra-vate
flooding; a low crest elevation maximizes submergence but
minimizes backwater effect; and where flumes are concerned, the
attainment of the desired range of discharge may require some sac-rifice
of sensitivity at extremely low discharges. The engineer must
use judgment in selecting a control design that is optimum for the
local conditions. For example, to design a flume whose throat is suffi-ciently
wide to accommodate the desired range of discharge, it may be
necessary to relax the 2-percent sensitivity criterion at extremely low
flows; in that situation the engineer may accept a sensitivity such
that a change in stage of 0.01 ft (0.003 m) results in as much as a
&percent change in discharge.
From a practical viewpoint the use of artificial controls is limited to
streams with stable channels. Artificial controls seldom operate satis-factorily
in sand channels having highly mobile beds. The transport
of sediment, as bedload continually changes the characteristics of the
approach channel, and the control itself may be buried or partially
buried by the movement of sand dunes.
SELECTED REFERENCES
Corbett, D. M., and others, 1943, Stream-gaging procedure: U.S. Geol. Survey Water-
Supply Paper 888, p. 109-115.
King, H. W., and Brater, E. F., 1963, Handbook of hydraulics [5th ed.]: New York,
McGraw-Hill, 1373 p.
World Meteorological Organization, 1971, Use of weirs and flumes in stream gaging:
WMO-No. 280 Technical Note No. 117, Geneva, 57 p.
CHAPTER 4.-MEASUREMENT OF STAGE
GENERAL
The stage of a stream or lake is the height of the water surface
above an established datum plane. The water-surface elevation re-

4. STAGE MEASUREMENT 23
ferred to some arbitrary or predetermined gage datum is called the
“gage height.” Gage height is often used interchangeably with the
more general term “stage,” although gage height is more appropriate
when used to indicate a reading on a gage. Stage or gage height is
usually expressed in feet and hundredths of a foot, or in meters and
hundredths or thousandths of a meter.
Records of gage height are used with a stage-discharge relation in
computing records of stream discharge. The reliability of the dis-charge
record is therefore dependent on the reliability of the gage-height
record as well as on the accuracy of the stage-discharge rela-tion.
Records of stream stage are also useful in themselves for such
purposes as the design of structures affected by stream elevation and
the planning of flood-plain use. The gage-height record of a lake or
reservoir provides, in addition to elevations, indexes of surface area
and volume of the water body.
A record of stage may be obtained by systematic observations of a
nonrecording gage or by means of a water-stage recorder. Special-purpose
gages that do not give a complete record of stage are dis-cussed
on pages 74-78. The advantages of the nonrecording gage are
the low initial cost and the ease of installation. The disadvantages are
the need for an observer and the lack of accuracy of the estimated
continuous-stage graph drawn through the plotted points of observed
stage. For long-term operation the advantages of the recording gage
far outweigh those of the nonrecording gage, and therefore the use of
the nonrecording gage as a base gage is not recommended. However,
at a recording-gage station, one or more nonrecording gages should be
maintained as auxiliary gages for the operation of the station (p.
53-54). Telemetering systems are often used to transmit gage-height
information to points distant from the gaging station (p. 54-59).
DATUM OF GAGE
The datum of the gage may be a recognized datum, such as mean
sea level, or an arbitrary datum plane chosen for convenience. An
arbitrary datum plane is selected for the convenience of using rela-tively
low numbers for gage heights. To eliminate the possibility of
minus values of gage height, the datum selected for operating pur-poses
is below the elevation of zero flow on a natural control. Where
an artificial control is used, the gage datum is usually set at the
elevation of zero flow.
As a general rule a permanent datum should be maintained so that
only one datum for the gage-height record is used for the life of the
station. An exception occurs at gage sites where excessive streambed
scour, after installation of the station, results in low-flow stages hav-ing
a negative gage height. In that situation a change in gage datum

to eliminate the negative numbers is recommended, to avoid possible
confusion involving the algebraic sign of the gage heights. Another
exception occurs when channel changes at a station make it impracti-cal
to maintain the station at the existing site. It may then be neces-sary
to move the station a distance, such that there is significant fall
in the water-surface elevation between the old and new sites, even
though discharges at the two sites are equivalent. In that situation
there is generally little to be gained by establishing the datum at the
new site at the same sea-level elevation as the datum at the original
site. That is especially true if the station is moved downstream a
distance such that negative gage heights would result from use of the
original datum. When datum changes are made for whatever reason,
a record of the change should be a part of the published station de-scription.
In any event, when a station is established, it should be assumed
that a permanent datum will be maintained at the site. To maintain a
permanent datum, each gaging station requires at least two or three
reference marks; that is, permanent points of known gage-height ele-vation
that are independent of the gage structure. The datum at each
gaging station is periodically checked by running levels from the
reference marks to the gages at the station.
If an arbitrary datum plane is used, it is desirable that it be re-ferred
by levels to a bench mark of known elevation above mean sea
level, so that the arbitrary datum may be recovered if the gage and
reference marks are destroyed.
NONRECORDING STREAM-GAGING STATIONS
On page 23 it was mentioned that a record of stage could be ob-tained
by systematic observation of a nonrecording gage. The advan-tages
(low initial cost) and disadvantages (need for an observer, lack
of accuracy) of a nonrecording gaging station were briefly discussed.
On pages 53-54 the use of nonrecording gages as auxiliary and as
reference (base) gages at recording-gaging stations will be discussed.
Chapter 15 (p. 559-560) will describe the manner in which an ob-server’s
gage readings are used to compute a record of stage at a
nonrecording gaging station. This section of the manual describes the
various types of nonrecording gages.
Of the five types to be described, the two most generally used at
nonrecording stations are either the staff or wire-weight gage. At
such stations the nonrecording gage is usually read twice daily by an
observer, and additional readings are made during periods of rapidly
changing stage. The observer systematically records and reports his
readings to headquarters. The record book and report cards shown in

figure 8 are used by the U.S. Geological Survey, the book being the
permanent record of nonrecording-gage readings. The weekly report
card serves as an interim report of the observations made. The weekly
report cards are read promptly on their arrival at the headquarters
office so that any problems or difficulties that arise can be handled
without delay.
On each routine visit to a nonrecording stream-gaging station, the
hydrographer also visits the observer to enter in the stage-record
book the gage reading(s) that the hydrographer has made. At that
time he also inspects the record book to check for discrepancies in the
observer’s readings. Such visits by the hydrographer are important; if
they are not made the observer tends to feel that no one pays any
attention to his work, and he may become less conscientious about his
gage readings.
Descriptions of five types of nonrecording stage gages follow. The
special-purpose crest-stage gage and its use as an adjunct to the non-recording
gaging station are described on pages 77-78.
OBSERVATIONSO F GAGEH EIGHT
FIGURE S.--Cover of book and weekly report card for recording manual gage observa-tions.

STAFF GAGE
Staff gages are either vertical or inclined. The standard Geological
Survey vertical staff gage consists of porcelain-enameled iron sec-tions,
each 4 in (0.1 m) wide, 3.4 ft (1.04 m) long, and graduated every
0.02 ft (0.0067 m). (See fig. 9.) The vertical staff gage is used in
stilling wells as an inside reference gage, or in the stream as an
outside gage.
An inclined staff gage is usually a graduated heavy timber securely
attached to permanent foundation piers. Inclined gages built flush
with the streambank are less likely to be damaged by floods, floating
ice, or drift than are projecting vertical staff gages. Copper barrelhoop
staples and bronze numerals are generally used for the graduations.
Inclined gages are used only as outside gages.
WIRE-WEIGHT GAGE
The wire-weight gage used in the U.S.A. is known as the type A
wire-weight gage. It consists of a drum wound with a single layer of
cable, a bronze weight attached to the end of the cable, a graduated
disc, and a Veeder counter, all within a cast-aluminum box. (See fig.
10.) Thedisc is graduated in tenths and hundredths of a foot and is
permanently connected to the counter and to the shaft of the drum.
The cable is made of 0.045in-diameter stainless-steel wire and is
guided to its position on the drum by a threading sheave. The reel is
equipped with a paw1 and ratchet for holding the weight at any de-sired
elevation. The diameter of the drum of the reel is such that each
complete turn represents a 1-ft (0.305 m) movement of the weight. A
horizontal checking bar is mounted at the lower edge of the instru-ment
so that when it is moved to the forward position the bottom of
the weight will rest on it. The gage is set so that when the bottom of
the weight is at the water surface, the gage height is indicated by the
combined readings of the counter and the graduated disc. The type A
wire-weight gage is commonly mounted on a bridge handrail, parapet
wall, or pier for use as an outside gage.
FLOAT-TAPE GAGE
A float-type gage consists of float, graduated steel tape, counter-weight,
and pulley. (See fig. 11.) The float pulley is usually 6 in (0.152 m)
in diameter, grooved on the circumference to accommodate the tape,
and mounted in a standard. An arm extends from the standard to a
point slightly beyond the tape to carry an adjustable index. The tape
is connected to the float by a clamp that also may be used for making
adjustments to the tape reading if the adjustments necessary are too

FIGURE 9.-Vertical staff gage.

large to be accommodated by the adjustable index. A lo-in (0.25 m)-
diameter copper float and a 2-lb (0.9 kg) lead counterweight are nor-mally
used. The float-type gage is used chiefly in stilling wells as an
inside reference or auxiliary gage.
ELECTRIC-TAPE GAGE
The electric-tape gage consists of a steel tape graduated in feet and
hundredths of a foot, to which is fastened a cylindrical weight, a reel
in a frame for the tape, a 4%volt battery, and a voltmeter. (See fig.
12.) One terminal of the battery is attached to a ground connection,
and the other to one terminal of the voltmeter. The other terminal of
the voltmeter is connected through the frame, reel, and tape, to the
weight. The weight is lowered until it contacts the water surface; this
contact completes the electric circuit and produces a signal on the
voltmeter. With the weight held in the position of first contact, the
tape reading is observed at the index provided on the reel mounting.
The electric-tape gage is used as an inside reference gage and occa-sionally
as an outside gage. If oil is floating on the water surface, the
gage will give the gage height of the interface, because oil is a dielec-tric.
In some electric-tape gages a light or audible signal is substi-tuted
for the voltmeter.
FIGURE lO.-Type A wire-weight gage.

FIGURE Il.-Float-tape gage.

30 MEASUREMENT OF STAGE AND DISCHARt
;E
FIGURE 12.-Electric-tape gage.

CHAIN GAGE
A chain gage (fig. 13) is used where outside staff gages are difficult
to maintain and where a bridge, dock, or other structure over the
water is not available for the installation of a wire-weight gage. The
chain gage can be mounted on a cantilevered arm which extends out
over the stream, or which is made in such a way that it can be tilted to
extend over the stream.
The chain gage consists of the cantilevered arm, one or more
enamelled gage sections mounted horizontally on the cantilever, and
a heavy sash chain that runs over a pulley on the streamward end of
the cantilever. (See figure 13.) The chain is mounted so that it moves
along the gage sections. A weight is attached to the streamward end
of the chain, and an index marker (M in fig. 13) is attached near the
other end at a distance from the weight that is appropriate for read-ing
the gage height of low flows. Additional index markers can be
attached to the chain at appropriate intervals to read gage heights
greater than those directly obtainable from the mounted gage sec-tions.
Stage is determined by lowering the weight until the bottom of the
Scale
FIGURE 13.-Chain gage (cantilevered mount not shown).

weight just touches the water surface. The gage height then is read
from the mounted gage plate at the location of the appropriate chain
index marker.
RECORDING STREAM-GAGING STATIONS
METHODS OF SENSING STAGE FOR AUTOMATIC
RECORDING
Stage is sensed for automatic recording by a float in a stilling well,
or by a gas-purge system that transmits the pressure head of water in
a stream to a manometer. The latter system, which does not require a
stilling well, is known as a bubble gage.
FLOAT SENSOR
The float sensor consists of a tape or cable passing over a pulley,
with a float in a stilling well attached to one end of the tape or cable
and a counterweight attached to the other end. (See fig. 11.) The float
follows the rise and fall of the water level, and the water level can be
read by using an index and graduated tape, or the pulley can be
attached to a water-stage recorder to transmit the water level to the
recorder.
BUBBLE-GAGE SENSOR
The bubble-gage sensor (Barron, 1963) consists of a gas-purge sys-tem,
a servomanometer assembly, and a servocontrol unit. (See fig.
14.) The gas-purge system transmits the pressure head of water in the
stream to the manometer location. A gas, usually nitrogen, is fed
through a tube and bubbled freely into the stream through an orifice
at a fixed elevation in the stream. The gas pressure in the tube is
equal to the piezometric head on the bubble orifice at any gage height.
The servomanometer converts the pressure in the gas-purge system
to a shaft rotation for driving a water-stage recorder. Mercury is used
as the manometer liquid to keep the overall manometer length to a
minimum. The manometer has a sensitivity of 0.005 ft (0.0015 m) of
water and can be built to record ranges in gage height in excess of 120
ft (36 m). The use of mercury in the manometer permits positioning of
the pressure reservoir to maintain the float-switch contacts in null
position. In this position, the vertical distance between mercury sur-faces
will be 1113.6 times the head of water. A change in pressure at
the reservoir displaces the mercury which in turn activates the float
switch. This causes movement of the pressure reservoir until the
distance of head of water divided by 13.6 is again maintained. This
motion, in turn, is translated to the recorder.
The servocontrol unit provides the relay action necessary to permit
the sensitive float switch to control the operation of the servomotor;

the unit also provides an appropriate time delay between the closing
of the float switch and the starting of the motor.
Several bubble-gage sensors, differing in minor detail from that
described above, are commercially available. Also commercially
available is another type of bubble-gage sensor in which the nitrogen
bubble tubing transmits the river-stage pressure to a bellows; the
bellows, through a mechanical linkage, actuates a recording pen.
The proper placement of the orifice is essential for an accurate
stage record. The orifice should be located where the weight of water
above it represents the stage in the river. If the orifice is partly buried
in sand or mud, the recorded stage will be greater than that in the
river. An orifice preferably should not be installed in swift currents. If
this is unavoidable, the orifice must be kept at right angles to the
direction of flow. A recommended mounting for high-velocity flow is
one in which the orifice is installed flush with the wall of the mount-ing
structure. Care should also be taken to keep the orifice out of
highly turbulent flow.
In unstable streambeds it is sometimes advantageous to place the
bubble orifice in a vented well point driven into the unstable bottom.
FIGURE 14.-Major units of the bubble gage.

If oil (generally kerosene) is to be added to prevent freezing in the
vent pipe, the top of the well screen should be a sufficient distance
below the minimum expected stream stage to retain the required
depth of oil (fig. 15). To prevent variations in the depth of oil from
affecting the manometer reading, the bubble orifice should be below
the top of the screen so that the bubbles emerge into the water.
It is emphasized that for satisfactory operation of the well point the
streambed material should not be so finely grained as to unduly im-pede
the passage of river water to the well point and thereby cause
lag in the recorded stage. To prevent clogging of the well-point screen,
the screen should be made of material that will inhibit chemical
reaction with substances in the water and (or) in the bed material. A
stainless-steel screen set 1 to 3 ft (0.3 to 1.0 m) below the streambed is
recommended.
The bubble gage is used primarily at sites where it would be expen-sive
to install a stilling well. It is also used on sand-channel streams
because the gas tends to keep the orifice from being covered with sand
and the tube may be easily extended to follow a stream channel that
shifts its location. However, the float stilling-well installation is
cheaper to install at many sites, and its performance is usually more
reliable than that of the bubble gage. The two systems have about the
same accuracy--+O.Ol ft (0.003 m). The choice of systems thus de-pends
on the characteristics of the gage site.
WATER-STAGE RECORDERS
A water-stage recorder is an instrument for producing a graphic or
punched-tape record of the rise and fall of a water surface with re-spect
to time. It consists of a time element and a gage-height element
which, when operating together, produce on a chart or on a tape a
record of the fluctuations of the water surface. The time element is
controlled by a clock that is driven by a spring, by a weight, or by
electricity. The gage-height element is actuated by a float or a bubble
gage.
If a float sensor is used, the float pulley is attached to the recorder.
The float and counterweight are suspended on a perforated steel tape
or on a plain or beaded cable. Cone-shaped protrusions on the circum-ference
of the float-tape pulley match performations in the tape. As
the float rises or falls the float pulley rotates in proportion to the
change in stage; the rotation of the pulley is transmitted to the re-corder
and the appropriate gage height is thereby recorded. A copper
float 10 in (0.25 m) in diameter is normally used, but other sizes are
also used depending on the type of recorder, gage-height scale, and
accuracy requirements.

4. STAGE MEASUREMENT
If a bubble-gage sensor is used, the stage is translated to the
corder by a chain and sprocket arrangement. (See fig. 14.)
Stage recorders are either digital or graphic. Both types may
35
re-be
instrument
r level only
pipe can extend to
ter or to high-water
oint
FIGURE .&-Installation of bubble orifice in unstable streambed.

used with the float or bubble gage. Digital recorders are gradually
replacing strip-chart (graphic) recorders at gaging stations in the
United States. The two recorders are about equal in accuracy, relia-bility,
and cost, but the digital recorder is compatible with the use of
electronic computers in computing discharge records. This automated
system offers greater economy and flexibility in the computation-publication
process than do manual methods associated with graphic
recording. However, the use of graphic recorders should be continued
at those sites where a graphic record is necessary to detect ice effects,
backwater, or frequent malfunctions of the recording system.
DICI’I‘AL KECORDEK
The digital recorder used by the U.S. Geological Survey (Isherwood,
1963) is a battery-operated slow-speed paper-tape punch which re-
FIGURE 16.-Dlgital recorder

cords a 4-digit number on a 16-channel paper tape at preselected time
intervals. (See fig. 16.)
Stage is recorded by the instrument in increments of a hundredth of
a foot from zero to 99.99 ft (30.5 m) and is transmitted to the instru-ment
by rotation of the input shaft. Shaft rotation is converted by the
instrument into a coded punch-tape record that is simple enough to be
read directly from the tape. The code consists of four groups of four
punches each. In each group, the first punch represents “1,” the sec-ond
“2,” the third “4,” and the fourth %” Thus a combination of up to
three punches in a group represents digits from 1 to 9, with a blank
space for 0, and the four groups of punches represent all numbers
from 1 to 9,999. (See fig. 17.)
Coding is done by means of two discs containing raised ridges in
accordance with the punch code outlined above. One disc is mounted
directly on the input shaft. The second code disc is connected to the
first by a 1OO:l worm gear so that one hundred revolutions of the
input shaft rotate the second, or high-order disc, one complete revolu-tion.
A paper tape is moved upward through a punch block which is
mounted on a movable arm hinged at the base of the recorder. The
punch block contains a single row of 18 pins, 16 pins for the informa-tion
punches and 2 for punching feed holes.
The tape i-s punched when the punch block with its protruding pins
is forced against the code discs by spring action. Those pins, which
strike the raised ridges of the discs, punch through the paper tape and
record the position of the discs at that instant. The readout cycle
begins with an impulse from the timer that causes a 6-volt motor to
turn a sequencing camshaft. The sequence of operations for one read-ing
includes punching the paper, advancing the paper, and compress-ing
the punch spring for the next readout cycle.
The timers (fig. 18) used on the digital recorders are electro-mechanical
timing devices that are powered by the same 7%volt
battery that operates the 6-volt motor. The timers provide contact
closure for actuating the digital recorder at preselected time intervals
of 5, 15, 30, or 60 minutes by using a different cam for each different
time interval.
The cam on the timer corresponds to the minute hand on a clock;
that is, it makes one revolution per hour in a clockwise direction. If
the cam has one dropoff point, the recorder will punch hourly; if it has
two dropoff points, it will punch every 30 minutes; and if it has four
dropoff points, it will punch every 15 minutes. The timer in figure 18
has four dropoff points. The arm positioned by the cam operates a
single-pole double-throw switch. When the cam dropoff point passes
the arm, the switch initiates the major part of the readout cycle which
includes punching of the tape. A preset action returns the switch to

the initial position prior to the next readout cycle. Alternating-current
timers can be used with the digital recorders at places where
Sprocket drwe holes
1 Tens 1 Units i Tenths
I Direction
of
tape
travel
-00.96
Clock
time
I
Translator alinement holes
FIGURE 17.-Sample digital-recorder tape.

reliable alternating-current power is available.
Digital recorders may miss the absolute peak stage especially on
flashy streams. However, a measure of the maximum peak that occurs
between inspections of the recorder can be obtained by attaching a wire
clip (similar to a paper clip) or small magnet to the float tapejust below the
instrument shelf in such a manner that it will slide along the tape as the
stage rises but remain in a fixed position as the stage declines. (See p.
60-61).
Mechanically punched tape is the most practical for field use under
widely varying conditions of temperature and moisture. Electronic
translators are used to convert the 16-channel punch-tape records to a
tape suitable for input into a digital computer for computation of a
daily mean gage height and daily mean discharge.
In the metric version of the digital recorder, stage is recorded in
increments of 1 millimeter from 0 to 9.999 m.
GRAPHIC RECORDER
The graphic, or analog, recorder furnishes a continuous trace of
water stage, with respect to time, on a chart. Usually the gage-height
element moves the pen or pencil stylus and the time element moves
the chart, but in some recorders those actions are reversed. In the
U.S.A. the common range of available gage-height scales is from 10
in=1 ft (10:12) to 10 in=20 ft (1:24). The width of strip charts is
usually 10 in (0.25 m). The range of available time scales is from 0.3
to 9.6 in (0.0076 m to 0.244 m) per day. Normally the gage-height
FIGURE l&-Digital-recorder timer.

scale of 10 in=5 ft (1:6) or 10 in=10 ft (1:12) is used with a time scale
of 1.2, 2.4, or 4.8 in per day.
Most graphic recorders can record an unlimited range in stage by a
stylus-reversing device or by unlimited rotation of the drum.
Most strip-chart recorders will operate for several months without
servicing. Drum recorders require attention at weekly intervals. Fig-ure
19 shows a commonly used continuous strip-chart graphic re-corder,
and figure 20 a horizontal-drum recorder that must be ser-viced
at weekly intervals. Attachments are available for the recorder
FIGURE 19.-Continuous strip-chart recorder.

shown in figure 19 to record water temperature or rainfall on the
same chart with stage. Figure 21 is a section of a typical strip chart
whose gage-height scale is 5: 12 and whose time scale is 4.8 in per day.
STILLING WELLS
The stilling well protects the float and dampens the water-surface
fluctuations in the stream caused by wind and turbulence. Stilling
wells are made of concrete, reinforced concrete block, concrete pipe,
steel pipe, and occasionally wood. They are usually placed in the bank
of the stream (figs. 22-261, but often are placed directly in the stream
and attached to bridge piers or abutments. (See figs. 27 and 28.) The
FIGURE 20.-Horizontal-drum recorder.

stilling well should be long enough for its bottom to be at least 1 ft
(0.3 m) below the minimum stage anticipated, and its top preferably
should be high enough so that the recording instrument will be above
the level of the loo-year flood.
The inside of the well should be large enough to permit free opera-tion
of all the equipment to be installed. Usually a pipe 4 ft (1.2 m) in
diameter or a well with inside dimensions 4 by 4 ft (1.2 by 1.2 m) is of
satisfactory size, but pipes 1.5 ft (0.5 m) in diameter have been used
for temporary installations where a conventional water-stage re-corder
was the only equipment to be installed. The 4 by 4 ft well
provides ample space for the hydrographer to enter the well to clean it
or to repair equipment. The smaller metal wells and the deep wells
1200 1800 2400 0600 1200
February 4,1972 February 5, 1972
FIGURE 21.-Section of a typical strip chart.

should have doors at various elevations to facilitate cleaning and
repairing. (See figs. 22 and 25.)
When placed in the bank of the stream the stilling well should have
a sealed bottom so that ground water cannot seep into it nor stream
water leak out.
Water from the stream enters and leaves the stilling well through
the intake so that the water in the well is at the same elevation as the
water in the stream. If the stilling well is in the bank of the stream,
the intake consists of a length of pipe connecting the stilling well and
the stream. The intake should be at an elevation at least 0.5 ft (0.15
m) lower than the lowest expected stage in the stream, and at least
0.5 ft above the bottom of the stilling well to prevent silt buildup from
plugging the intake. In cold climates the intake should be below the
FIGURE 22.-Reinforced concrete well and shelter. (Note clean-out door.)

frostline. If the well is placed in the stream, holes drilled in the
stilling well may act as an intake, taking the place of a length of pipe.
Some wells placed in the stream have a cone-shaped hopper bottom
that serves as an intake and is self cleaning.
Two or more pipe intakes are commonly installed at vertical inter-vals
of about 1 ft (0.3 m). During high water, silt may cover the
streamward end of the lower intakes while the higher ones will con-tinue
to operate. The intakes should be properly located and sized to
minimize surge.
Most stations that have intakes subject to clogging are provided
with flushing systems (see fig. 29) whereby water under several feet
of head can be applied to the gage-well end of an intake. Ordinarily a
pump raises water from the well to an elevated tank. The water is
then released through the intake by the operation of a valve. Intakes
without flushing systems may be cleaned with a plumber’s snake or
rod, or by building up a head of water in the well with a portable
pump to force an obstruction out of the intakes.
The intakes for stations placed in the bank of the stream are
usually galvanized-steel pipe. The most common size used is 2-in
(0.05 ml-diameter pipe, but for some wells pipe diameters as large as
4 in (0.1 m) are used. After the size and location of the well have been
decided upon, the size and number of intakes should be determined.
FIGURE 23.-Concrete well and wooden shelter with asphalt-shingle siding.

The intake pipe should be large enough for the water in the well to
follow the rise and fall of stage without significant delay. The follow-
FIGURE 24.-Corrugated-galvanized-steel-pipe well and shelter.

ing relation may be used to predict the lag for an intake pipe for a
given rate of change of stage:
Ah = 0.01 L A,
-yB (;i;>2(sy
in which
Ah = lag, in feet (or meters),
g = acceleration of gravity, in feet (or meters) per second per
second,
FIGURE 25.-Concrete-pipe well and shelter. (Note clean-out door, staff gage, and
upper intake pipe.)

L = intake length in feet (or meters),
D = intake diameter, in feet (or meters),
A, = area of stilling well, in square feet (or square meters),
A,, = area of intake pipe, in square feet (or square meters), and
dh - dt = rate of change of stage, in feet (or meters) per second.
Smith, Hanson, and Cruff (1965) have studied intake lag in
stilling-well systems, relating it to the rate of change of stage of the
stream and to the various types and sizes of components used in the
stilling-well intake system.
The intake pipe should be placed at right angles to the direction of
flow, and it should be level. If the stream velocity at the end of the
intake is high, either drawdown or pileup may affect the water level
in the stilling well, depending on the angle of the flow at the intake
opening. Drawdown causes the water level in the stilling well to be
lower than that in the stream; pileup has the opposite effect. Draw-down
commonly occurs at high velocities even when the intake pipe is
at an angle of 90” with the flow. To reduce or possibly eliminate
drawdown or pileup, a static tube should be attached to the
streamward end of the intake pipe. A static tube is a short length of
pipe attached to an elbow or tee on the end of the intake pipe and
extending horizontally downstream. (See fig. 30.) The end of the static
tube is capped, and water enters or leaves through holes drilled in the
tube.
The usual means of preventing the formation of ice in the well
FIGURE 26.-Concrete-block shelter.

during cold weather are: (1) subfloors, (2) heaters, and (3) oil. Sub-floors
are effective if the station is placed in the bank and has plenty
of fill around it. If the subfloor is built in the well below the frostline
in the ground, ice will seldom form in the well as long as the stage
remains below the subfloor. Holes are cut in the subfloor for the re-corder
float and weights to pass through, and removable covers are
placed over the holes. Subfloors prevent air circulation in the well and
the attendant heat loss.
An electric heater or heat lamps with reflectors may be used to keep
the well free of ice. The cost of operation and the availability of elec-tric
service at the gaging station are governing factors. Heating ca-bles
are often placed in intake pipes to prevent ice from forming.
Oil is used in two ways: (1) Where the well is small and leakproof,
the oil may be poured into the well; and (2) where the well is large or
not leakproof, the oil-usually kerosene, fuel oil, or diesel oil-is
poured into an oil tube. The oil tube, which is open ended and of
sufficiently large diameter to accommodate the recorder float, is sup-ported
in the well in a vertical position with its lower end just above
FIGURE 27.-Steel-pipe well and look-in shelter attached to bridge abutment.

FIGURE 28.-Corrugated-steel-pipe well and wooden shelter attached to
bridge pier.

FIGURE 29.-Flushing system for intakes.
FIGURE JO.-Static tube for intakes. (Note outside reference gage.)

the floor of the well. The oil tube should be long enough to contain the
oil throughout the range in stage expected during the winter. When
oil is put in a well, the oil surface stands higher than the water
surface in the stream. A correction must therefore be made to obtain
the true river stage. The depth of oil required usually ranges from 0.5
to 2.0 ft (0.15 to 0.6 m) depending on the severity of the climate and
the exposure of the well.
Stilling wells often fill with sediment, expecially those located in
arid or semiarid regions. If a well is located on a stream carrying
heavy sediment loads, it must be cleaned often to maintain a continu-ous
record of stage. In those locations sediment traps are helpful in
reducing the frequency and labor of sediment removal. A sediment
trap is a large boxlike structure that occupies a gap in the lower
intake line, streamward from the stilling well. The bottom of the
sediment trap is usually about 3 ft (1.0 m) below the elevation of the
intake. Inside the trap are one or more baffles to cause suspended
sediment to settle in the trap, rather than pass into the well. A re-movable
top to the trap provides access to the interior of the trap for
the removal of trapped sediment.
The operation of type of recording stream-gaging station requires
the installation of one or more nonrecording gages for use as auxil-iary
or reference gages. Reference gages are discussed on pages
53- 54.
INSTRUMENT SHELTERS
Shelters are made of almost every building material available and
in various sizes depending on local custom and conditions. (See figs.
22-28.) The most convenient type of shelter is one that the hydrog-rapher
can enter standing. A shelter with inside dimensions 4 by 4 ft
(1.2 by 1.2 m) and with ceiling height 7 ft (2.2 m) above the floor is
usually of adequate size, unless the shelter is also to be used to store
sediment-sampling equipment and (or) house telemetry equipment
(p. 54-59). Look-in shelters (fig. 27) are also used at sites where a
limited amount of equipment is to be installed and a portable and
inexpensive shelter is desired.
In humid climates, shelters are well ventilated and have a tight
floor to prevent entry of water vapor from the well. Screening and
other barriers are used over ventilators and other open places in the
well or shelter to prevent the entry of insects, rodents, and reptiles.
The bubble gage does not require a stilling well. The instrument
shelter for a bubble gage may be installed at any convenient location
above the reach of floodwaters. This gage may be used to take advan-tage
of existing natural or artificial features in a stream without
costly excavation for well or intake and without need for any external

structural support. The bubble gage is especially well suited for
short-term installations because the entire station is readily disman-tled
and relocated with practically no loss of investment.
A shelter with inside dimensions 4 by 4 by 7 ft (1.2 by 1.2 by 2.2m)
is needed to accommodate the equipment for a bubble gage. Shelters
similar to those in figures 22, 23, and 26 would be adequate. The
shelter can be placed on a concrete slab or other suitable foundation.
The bubble orifice is placed at least 0.5 ft (0.15 m) below the lowest
expected stage in the stream. The plastic tube connecting the orifice
and the instrument is encased in metal pipe or conduit, or buried to
protect it from the elements, animals, and vandalism. A typical
bubble-gage installation is shown in figure 31. The streamward end of
the metal pipe should be flush with the streamward face of the pier
shown in figure 31 to prevent disturbance of the streamlines of river
flow in the vicinity of the orifice. The streamward end of the orifice
line should also have a downward slope, as shown in the figure. It
has been found that if the end of the orifice line is installed in a
horizontal position, water tends to run up the bubble tube after each
bubble is formed, and the induced surge is recorded by the stage
recorder.
FIGURE 31.-Typical bubble-gage installation.

REFERENCE AND AUXILIARY GAGES AT RECORDING GAGING STATIONS
Nonrecording gages, which were discussed on pages 24-32, are
used both as reference and auxiliary gages at recording stream-gaging
stations. As used in this manual a reference gage is the gage
to which the recording instrument is set; it is the base gage for the
recording station. All other nonrecording gages at the recording sta-tion
are considered to be auxiliary gages. A detailed discussion fol-lows.
Outside gage-At bubble-gage stations a nonrecording gage, estab-lished
in close proximity to the bubble orifice, acts as the base or
reference gage for checking and resetting the gage height indicated
by the water-stage recorder.
At stations equipped with a stilling well for the operation of a
float-operated stage recorder, there is always the possibility that the
stage in the stilling well may not be representative of the stage of the
stream. For example, intakes can become plugged, floats can spring a
leak, or oil can leak out of wells or oil tubes. Consequently, a non-recording
auxiliary gage is installed outside the stilling well so that
the water level of the stream can be determined directly for compari-son
with the stage in the stilling well. It is not necessary that the two
observed stages agree precisely; hydraulic conditions at the station
may be such that precise agreement is not possible. If a reading of the
outside auxiliary gage indicates that an unsatisfactory record is
being obtained by the recording gage, the trouble is rectified im-mediately.
If immediate repairs are not feasible, or if there has been
an instrument failure, the outside auxiliary gage is used as a tempo-rary
substitute for the recording gage. The outside auxiliary gage can
be read as needed by a local observer to continue the record of stage
until the malfunction of the recording station is rectified.
Staff or wire-weight gages are usually used as outside auxiliary
gages. Outside staff gages located in the pools near the gage struc-tures
are visible in figures 5, 6, 22, 25, and 30; a wire-weight auxil-iary
gage on the parapet wall of the bridge is visible in figure 1, and
another is seen in figure 27.
Inside gage-At gaging stations equipped with a stilling well a
nonrecording gage inside the structure is used to indicate the water-surface
elevation in the stilling well. Readings on this inside gage are
compared with readings on the outside auxiliary gage to assure that
the stilling-well intakes are functioning properly. If the intakes are
functioning properly, the inside gage is used for checking and reset-ting
the gage height indicated by the water-stage recorder. In short,
the inside gage is the base or reference gage for the station. Float- or
electric-tape gages, or vertical staff gages, are the inside reference
gages most commonly used in stilling wells.

On occasion a reference mark or reference point of known eleva-tion,
with respect to gage datum, is used in place of either a reference
or auxiliary gage. The stage is then determined by measuring from
the reference mark or point down to the water surface either in the
stream or in the stilling well, as the case may be. While the practice of
using a reference mark or point is acceptable, it is not nearly as
convenient as the practice of using a standard nonrecording gage.
(The distinction between a reference mark and reference point should
be noted here: Both have elevations that are known, but a reference
point is a point on the gage structure itself; a reference mark is a
point that is not on the gage structure, and whose elevation is there-fore
unaffected by any movement of the gage structure.)
The practice described above of using the inside gage, rather than
the outside gage, as the reference or base gage for a recorder equipped
with a stilling well is followed in the U.S.A. and in many other coun-tries.
The reasoning behind that practice is that recorded (inside)
gage heights will be used to determine discharge, and if differences
exist between inside and outside stages, those differences will be
known only for those times when both gages are read. If the outside
gage is used as the base gage, corrections, known or assumed, must be
applied to all recorded gage heights to convert them to outside stages.
Furthermore, outside gages are often difficult to read with precision
because of the action of wind and waves. In other countries the out-side
gage is used as the reference gage for the reasons that (1) river
stage is often as important as discharge to the user of the record and
(2) a stage-discharge relation is dependent on river stage, rather than
on the stage inside a stilling well. The validity of both those reasons is
recognized in the U.S.A. Therefore outside high-water marks are ob-tained
for each flood event, and where the elevation of the marks
differs significantly from the peak inside stage, both inside and out-side
stages are published. Also, where there is significant difference
between inside and outside gage readings, the stage-discharge rela-tion
is first developed on the basis of outside-gage readings observed
at the times when discharge is measured. The relation is then ad-justed
to correspond with inside-gage readings observed at the times
of discharge measurement.
TELEMETERING SYSTEMS
Telemetering systems are used when current information on
stream stage is needed at frequent intervals and it is impractical to
visit the gaging station each time the current stage is needed.
Current stage information is usually necessary for reservoir opera-tion,
flood forecasting, prediction of flows, and for current-data report-ing.
The types of telemetering systems are:

1. Those that continuously indicate or record stage at a distance from
the gage site. Examples of this type are the position-motor and
impulse telemetering systems.
2. Those that report instantaneous gage readings on call or at pre-determined
intervals. Examples of this type are the Telemark
and resistance telemetering systems, and the experimental
satellite data-collection systems.
POSITION-MOTOR SYSTEM
The position-motor system provides remote registering of water
levels on graphic recorders or on counter or dial indicators over dis-tances
up to 15 mi (25 km). This system employs a pair of self-synchronizing
motors-one on the transmitter, whose rotor is ac-tuated
by a float-tape gage or a bubble gage, and the other on the
receiving unit, whose rotor follows the rotary motion of the transmit-ting
motor to which it is electrically connected. Alternating current is
used to operate the system, and a five-wire transmission line is
required-two excitation wires and three line wires.
IMPULSE SYSTEM
The impulse system provides remote registering of water levels on
graphic recorders or on counter and dial indicators over longer dis-tances
than does the position-motor system. This system will operate
over leased telephone lines or other metallic circuits. The impulse
sender at the gaging station is actuated by a float-tape gage or a
bubble gage and sends electrical impulses over the line connecting it
to the receiver. This system usually has a battery for the power source
at the sender and alternating current at the receiver, though direct
current or alternating current may be used at both ends. The advan-tage
of this system over the position-motor system is that it will
operate over long distances.
TELEMARK SYSTEM
The Telemark system codes instantaneous stage and signals this
information either audibly over telephone circuits or by coded pulses
for transmission by radio. The distance of transmission is unlimited
because signals can be sent over long-distance telephone circuits or
by radio. Telemark response to a telephone ring is automatic. When
used in radio transmission, the signals are started by a timing device
set for a predetermined broadcast schedule, or the Telemark may be
interrogated by radio channel to start the signal.
The Telemark consists of (1) the positioning element which is ac-tuated
by a float-tape gage or a bubble gage (fig. 32) and (2) the
signaling element which, when signaled, drives a contact across the

signaling drums that are positioned in correspondence with the stage.
The Telemark may be operated by either alternating current or by
batteries.
A Telemark that operates directly off a digital recorder is available
and will probably be increasingly used. This Telemark does not need
its own stage sensor; it uses that of the digital recorder. A memory
system is used so that when the Telemark is signaled, the last gage
height recorded on the digital recorder is transmitted.
Telemarks for radio reporting are equipped with an auxiliary
switch and coding bar for transmitting identifying radio station call
letters and numbers in international Morse code, in addition to
transmitting the stage.
FIGURE 32.-Telemark gage.

RESISTANCE SYSTEM
The resistance system, as used in the U.S.A., was developed by the
U.S. Weather Bureau. It provides remote indications of water level
for distances up to about 40 mi (about 65 km). Two models are avail-able,
one for distances of about a mile (1.6 km) and the other for
longer distances. The system consists of two potentiometers in a
wheatstone-bridge circuit with a microammeter null indicator. One of
the potentiometers is located in the gage house and is actuated by a
float and pulley assembly. (See fig. 33.) The other potentiometer and
the null indicator are housed at the observation site. (See fig. 34.) By
adjusting this potentiometer for a null balance on the meter, the gage
height can be read directly to tenths of a foot from a dial coupled to
the potentiometer shaft. This system operates on batteries, and three
wires connect the unit.
SATELLITE DATA-COLLECTION SYSTEM
The U.S. Geological Survey has been experimenting for several
years with the collection of stream-stage data by use of an orbiting
satellite which receives radio transmissions of stage and transmits
FIGURE 33.-Resistance system transmitter unit.

the data to central receiving stations. An operational system of that
kind would make stage data continuously available for use by the
managers of water projects who require current (“real time”) infor-mation
for project operation. Because the system is still in the exper-imental
stage it will be described only briefly.
Experimental work on the system began soon after the launch of
the Earth Resources Technology Satellite (ERTS) in July 1972. At
numerous stream-gaging stations that are dispersed over a wide geo-graphic
area, inexpensive battery-operated radios, called data-collection
platforms (DCP), are used to transmit stage data through
ERTS to the National Aeronautics and Space Administration (NASA)
receiving stations at Goldstone, California, and at Greenbelt, Mary-land.
The data are processed and distributed to experimenters from
the ERTS Operations and Control Center in Greenbelt.
Data can be provided to a DCP either directly from a digital water-stage
recorder or through an intermediate memory device. In the
FIGURE 34.-Resistance system indicator unit.

direct communication the most recently recorded digital stream stage
is continuously available to the DCP for inclusion in a 0.03%second
radio message that is transmitted every 3 minutes. Several times
daily the ERTS passes within 1,800 mi of the DCP, and the data are
at that time relayed to the receiving stations. Where the intermediate
memory device is used, the data are formatted efficiently in the device
for inclusion in the periodic DCP message. By use of the memory
device virtually all 24 of the hourly stream stages collected daily at
North American stream-gaging stations can be accumulated and re-layed,
as opposed to the 5 or 6 hourly stages that are relayed daily
when the DCP is directly connected to the digital-stage recorder.
Tests of the satellite data-collection system have been successful to
date (1980) and indicate that the satellite relay of environmental
data from widely dispersed and remotely located gaging stations can
be effectively and reliably performed.
OPERATION OF A RECORDING STREAM-GAGING STATION
Strip-chart or digital recorders are designed to give a continuous
record of stage, but careful attention to details is necessary at each
visit to the station to ensure a reliable and uninterrupted record
during the period (commonly 4-6 weeks) that usually elapses be-tween
such visits. This section of the manual presents only general
instructions for servicing recording stream-gaging stations. It is not
practical to attempt to provide detailed instructions here for servicing
stage-recorders because of the large numbers of such instruments of
varying design that are available. For detailed instructions concern-ing
any particular stage-recorder, it is necessary that the hydrog-rapher
consult the service manual prepared by the manufacturer of
the instrument or prepared by the stream-gaging agencies that use
the particular instrument.
The first thing done by the hydrographer on his visit to the record-ing
station is to determine if the clock or timer is running. If it is a
strip-chart recorder that is being serviced, the point at which the pen
or pencil is resting is then circled; if it is a digital recorder that is
being serviced, the instrument is caused to punch the digital tape and
the set of punched holes is circled. The time by the hydrographer’s
watch is noted and the base nonrecording reference gage is read.
Those observations are written on the chart or digital tape in prox-imity
to the circled gage height. The hydrographer then reads all
gages and notes the chart position or digital-tape position, with re-spect
to time and gage height, of the circled pen mark or punched
holes. All that information is also written on the chart or digital tape.
The various gage readings and the recorded gage heights are com-pared
to determine if intakes are functioning properly or if there is a

malfunction in the gas-purge system of the bubble gage. The time
indicated by the chart or digital tape is compared with the time indicated
by the hydrographer’s watch to determine if the instrument
clock or timer is operating satisfactorily. The section of chart or digi-tal
tape bearing the gage-height record is next removed and is exam-ined
to determine if there has been any recorder malfunction since
the previous servicing of the station.
The clock is then wound, or if the clock is battery driven, the
battery voltage is checked and the chart or digital tape is rethreaded
into the take-up roll. The pen or punch mechanism is next set to agree
with the gage height indicated by the base reference gage, and the
chart or digital tape is advanced to give agreement with the hydrog-rapher’s
watch time. By resetting the recorder at this point, before
completing his inspection of the station facilities, the hydrographer
gives himself another opportunity to check the operation of the re-corder
after his work is completed and the instrument has been
operating for a period of time.
If the station has a float-operated recorder, the hydrographer in-spects
the float to determine if it leaks and checks the float-clamp
screw to make sure there can be no slippage of the float tape where it
joins the float. He also checks the stilling well to be sure there is no
unduly large accumulation of sediment in the well. If the well is
equipped with an oil tube for winter operation he uses a point on the
top of the tube to measure down to the oil surface within the tube and
to the water surface outside the tube. The differential between the
two measurements, when divided by a value equal to 1.0 minus the
specific gravity of the oil, equals the depth of oil in the oil tube. The
hydrographer can decide from that computation whether oil has
leaked from the tube and the additional amount of oil, if any, to be
added. If the stilling well is equipped with a flushing device, the
intakes should be flushed as a matter of course. If no flushing device
has been provided, and there are indications that the intakes are
lagging, the intakes should be cleaned by forcing a plumber’s snake
through them.
If a high discharge has occurred since the previous visit to a
stilling-well-equipped station, high-water marks should be sought
both in the stilling well and outside the well, as a check on the peak
stage shown by the stage recorder. After making that check, the
high-water mark should be cleaned from the inside of the well to
prevent confusion with high-water marks that will be left by sub-sequent
peak discharges.
Another means of checking recorded peak stages is by having a
wire clip (similar to a paper clip) or magnet attached to the float tape
immediately below the shelf through which the tape passes. As the

stage rises, the wire clip or magnet, being too large to pass through
the hole in the shelf, retains its position at the bottom of the shelf, and
the moving float tape slides past it. When the stage recedes, the clip
or magnet remains attached to the tape and moves downward as the
float moves downward. Any one of several alternative methods may
be used to determine the peak stage that had been attained. In one
method the peak stage is obtained by subtracting a correction con-stant
from the tape reading at the top of the wire clip. That correction
constant is equal to the difference in elevation between the index
pointer for the float gage and the bottom of the shelf. In a second
method the visiting hydrographer computes the difference between
readings on the float tape at the bottom of the shelf and at the top of
the wire clip or magnet. He adds that difference to the current gage
height to obtain the peak stage attained. A third method of determin-ing
the peak stage is to raise the float until the wire clip or magnet is
at the bottom of the shelf; the corresponding tape-gage reading is the
peak stage that had been attained. Regardless of the method used,
after determining the peak stage the wire clip or magnet should be
moved back to the bottom of the shelf for subsequent indication of
peak stage.
If an indicator of minimum stage is desired, a similar device-wire
clip or magnet-can be attached to the float tape immediately below
the instrument shelf, but on the counterweight side of the float
sheave. The operation of the minimum-stage indicator is similar to
that described above for the peak-stage indicator.
If the station has a bubble-gage sensor, the bubble orifice should be
inspected to make sure that it has not been buried by a deposit of
sediment. A log of gas-feed rate, gas consumption, and gas-cylinder
replacement (fig. 35) should be kept to insure a continuous supply of
gas and to help in checking for leakage in the system. There can be no
serious leak in the gas-purge system if (1) the manometer operates to
indicate stage correctly and (2) the gas consumption based on the
average bubble rate over a period of time corresponds with the gas
consumption computed from the decrease in cylinder pressure. If a
gas leak is evident, its location can be determined by isolating var-ious
parts of the gas-purge system by the sequential closing of valves
in the system. If a high discharge has occurred since a previous visit
to the station, a high-water mark should be sought in the vicinity of
the base reference gage, as a check on the peak stage shown by the
stage recorder.
After the hydrographer has completed his inspection of the station
facilities, he returns to the stage recorder and repeats the first steps
he had taken in servicing the recorder. He determines that the clock
or timer is running; circles the point at which the pen is resting on the

MEASUREMENT OF STAGE AND DISCHARGE
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strip chart; observes his watch time; reads all gages, and writes his
observations on the strip chart or digital tape. He does not leave the
station without assuring himself that: the recorded gage height and
time agree with the gage height of the base reference gage and his
watch time: the clock is running; all necessary valves are open; the
float wheel (if any) is engaged; the pen (if any) is marking.
A few generalities may be stated concerning the maintenance of
recording stream-gaging stations to increase the accuracy and im-prove
the continuity of the stage record. Malfunctions of the recorder
can be reduced by the periodic cleaning and oiling of the recorder and
clock or timer. Each year intakes, stilling wells, and sediment traps
should be thoroughly cleaned. Excessive humidity and temperatures
in the gage house should be reduced to a minimum by proper ventila-tion,
and if feasible, extremely cold temperatures in the gage house
should be modified by the use of heating units or insulation. Humid-ity
and temperature control reduce the errors associated with paper
expansion and contraction. Experience in the U.S.A. has shown that a
program of careful inspection and maintenance will result in a com-plete
gage-height record about 98 percent of the time.
FACTORS AFFECTING THE ACCURACY OF THE STAGE
RECORD
Continuous records of discharge at a gaging station are computed
from the record of stage and the stage-discharge relation. For that
purpose stage records having an accuracy of kO.01 ft (kO.003 m) are
generally required. That accuracy can usually be attained by use of
the continuous stage-recording systems previously described. The
record obtained by sketching a continuous-stage graph through the
plotted points representing periodic observations of a nonrecording
gage cannot attain such accuracy, of course, but with care the
individual gage observations can usually have an accuracy within
10.01 ft.
In the discussions that follow, nonrecording gages will be treated
first and then recording gages will be discussed. A remark appropri-ate
to a discussion of the accuracy of any gage concerns the mainte-nance
of the gage datum to the accuracy criterion of 0.01 ft. That is
achieved by running levels to reference marks for the gage (p. 24)
and, if necessary, adjusting the gage to restore the original datum.
Levels should be run at least once every 2-3 years, and oftener if
conditions are known to be unstable. If a nonrecording gage is used
only as an outside auxiliary gage for a stilling well, a larger error in
gage datum may be tolerated, and adjustment to the gage need not be

made for datum discrepancies that do not exceed 0.02 ft (0.006 m).
That is so because seldom will inside and outside gages agree exactly
even when both are set precisely to the same datum. The inside refer-ence
gage, as explained earlier (p. 54) is the base gage for the station;
the primary purpose of the outside gage at a station equipped with a
stilling well is to indicate whether or not the intakes are operating
properly. (As mentioned on page 54, in some countries the outside
gage is used as the reference or base gage.)
NONRJXORDING GAGES
STAFF GAGE
Settlement or uplift of the structure(s) supporting the staff gage
may disturb the gage datum. Where levels from a reference mark
show that the datum of an inclined staff gage (p. 26) has been dis-turbed,
the gage is recalibrated by removing the staples used for the
graduations and replacing them at the proper elevations. Vertical
staff gages are usually made up of several porcelain-enameled iron
sections, each about 3.4 ft (1.04 m) long and bearing permanent
graduations. Where levels from a reference mark show disturbance of
the datum of a vertical staff gage, it is necessary to reset the individ-ual
gage sections. The graduations of the manufactured gage plates
often have minor discrepancies, and therefore if the gage plates must
be reset, they should be reset so that a graduation near the center of
each gage plate is at the proper datum.
It is often difficult to accurately detect the water line when making
staff-gage observations under the conditions of poor light and (or)
clear water. Under those conditions it is helpful to float a matchstick
or some similar floatable material against the gage and thereby
define the water line. When the water surface is surging rapidly as a
result of wave action, the stage to be recorded is the mean of the
elevations of the peak and trough of the waves.
WIKE-WEIGHT GAGE
Wire-weight gages (p. 26) are usually mounted on bridges, and
changes in gage datum often result from the settlement of bridge
abutments or piers, or from changes in the deflection of the bridges
resulting either from differences in traffic loading at the times of
observation or from seasonal changes in air temperature. In addition
to errors attributable to datum changes, erroneous readings of the
type A wire-weight gage may also be caused by slippage of the
graduated disc of the gage; that slippage results from insecure tight-ening
of the disc screws. The latter condition can be detected if a

reading of the gage height of the horizontal checking bar is always
made prior to lowering the weight to the water surface.
In checking the datum of the type A wire-weight gage by levels
from a reference mark, the elevation of the horizontal checking bar
and that of the bottom of the weight at various heights above the
water surface are compared with gage readings. When necessary,
adjustment of the gage to give accurate readings is made by loosening
the graduated disc, rotating the disc to the true gage height of the
bottom of the weight as determined from levels, and then retighten-ing
the disc screws.
Reliable observations are difficult to obtain by wire-weight gage
when the water surface is disturbed by waves; the stage sought under
those circumstances is the mean of the elevations of the peak and
trough of the waves. On the other hand, it is also difficult to sense the
water surface from a high bridge when the water is quiescent. The
ideal condition for sensing the water surface occurs when a slow-moving
water current is present under the weight. When observa-tions
are made on a windy day, the wire that supports the weight will
bow rather than hang vertically, thereby causing the gage to under-register.
The error introduced will depend on the intensity of the wind
and on the height of the gage above the water surface. The combina-tion
of a high wind and high bridge may cause appreciable underreg-istration
of the gage.
Another source of error, and one that also increases with height
above the water surface, is in the tendency of the weight to rotate
about its vertical axis as the weight is being lowered. The rotation
twists the wire, and sequences of untwisting and twisting of the wire
follow. During each period of twisting the wire shortens and the
weight ascends; during each period of untwisting the wire lengthens
to its full length and the weight descends. Observation of the gage
height of the water surface should not be made until the weight has
ceased to rotate.
FLOAl‘-I-APE GAGE
Change in the datum of a float-tape gage (p. 26) may result from
movement of the structure supporting the gage or from slippage of the
adjustable index. A float-tape gage will also read incorrectly if the
tape has slipped in the clamp connecting the tape and float (gage will
overregister) or if the float has sprung a leak and has taken in water
(gage will underregister). The first steps in checking a float-tape gage
therefore are to make sure that the clamp screw bears tightly on the
tape and to shake the float for indications of water sloshing within the
float.

Where levels from a reference mark show the elevation of the ad-justable
index to be in error, the screw holding the index is loosened,
the index is raised or lowered to its proper position, and the index
screw is retightened. The elevation of the water surface in the stilling
well is next obtained by measuring with a steel tape to the water
surface from the index or other suitable point of known elevation.
Any further adjustment that is needed to make the gage height agree
with the water-surface elevation is made by adjusting the length of
tape at the float clamp. After all adjustments are complete, a record
should be made for future reference of the tape graduation at which
the tape enters the tape clamp. If the stage of the stream is changing,
the valves on the stilling-well intakes should be closed while adjust-ments
to the float-tape gage are being made in order to maintain a
constant water level in the stilling well.
ELECTRIC-TAPE GAGE
Change in the datum of an electric-tape gage (p. 28) can only result
from movement of the structure supporting the gage, because the
position of the index of the gage is permanent with respect to the
instrument. An electric-tape gage may also read incorrectly (overreg-ister)
if the tape and weight are insecurely clamped together and
slippage of the tape has occurred. Where levels from a reference mark
show the gage index to be in error, nothing can be done about moving
the index, but its new (and true) gage height is made a matter of
record. The original datum of the gage can be maintained, however,
by adjusting the effective length of the tape, that is, by changing the
length of tape that is inserted and clamped in the gage weight (fig.12).
In other words, when the tape is unreeled so that the bottom of the
weight is, for example, 1.00 ft (0.3 m) below the index, the tape gage
should read 1.00 ft (0.3 m) less than the gage height of the index.
After the adjustment is completed, a record should be made, for future
reference, of the tape graduation at which the tape enters the weight.
If the stage of the stream is changing rapidly at the time a reading is
to be taken in the stilling well, it is helpful to close the valves on the
stilling-well intakes in order to obtain a constant water level in the
stilling well.
Use of the electric-tape gage as the inside reference gage is practi-cally
a necessity where a small diameter stilling well is used in a cold
climate. In that situation oil must be added to prevent freezing, and
because the stilling well is too small to accommodate an oil tube (p.
48), the oil must be added in the well itself. Because the oil is lighter
than water, the surface of the floating oil in the stilling well will be
higher than the water level at the streamward end of the stilling-well

intakes. It is the gage height of the water level (GH) that is sought,
and it may be computed by either of two equations:
GH = [gage height of oil surface] - [(l.O- specific gravity
of oil) x (depth of oil)] (1)
or
GH = [gage height of interface of oil and water] + [(specific
gravity of oil) x (depth of oil)]. (2)
Use of an electric-tape gage makes it a simple matter to measure
the distances needed in equation 2. That part of the tape above the
weight is rubbed with carpenter’s chalk for a distance of about 1.5 ft
(0.5 m) above the weight, and the weight is then lowered until a
signal is received on the voltmeter. At that point the electric-tape
gage reading obtained will be that of the oil-water interface (p. 28).
The tape is then reeled up and the lower end inspected. The oil will
have wetted the chalk on the tape leaving a sharp demarcation be-tween
the wet and dry lengths of tape. The depth of oil is equal to the
distance between the demarcation line and the bottom of the weight.
If the depth of the oil is less than the length of the weight, the oil will
not reach the tape. In that event, the weight is lowered a known
distance below the oil-water interface-say, 1.0 ft (0.3 m)-and the
apparent oil depth that is determined is reduced by 1.0 ft (0.3 m), the
additional distance that the weight was lowered. The computed oil
depth and the observed gage height of the oil-water interface are used
in equation 2 to compute the true gage height.
CHAIN GAGE
Change in the datum of a chain gage (p. 31) can result from move-ment
of the structure on which the gage is mounted, but there are
many other sources of error. They include stretching of the chain,
foreign material between chain links, wear of the chain links, and
wear of the pulley wheel. For that reason the chain length between
the bottom of the weight and the chain index markers should be
measured at each visit by the hydrographer, using a 4-lb (2-kg) pull
on the chain. A small spring balance is usually used to put the proper
tension on the chain when measuring its length. If the chain length
differs by more than 0.02 ft (0.006 m) from the “true” value estab-lished
the last time the datum was checked by levels, the length of the
chain is adjusted at the point where the chain is attached to the
weight. The adjustment is easily made because the chain and weight
are attached by means of a cotter pin through one of a series of holes

in the neck of the weight, the spacing between holes being about 0.02
ft (0.006 m).
In checking the gage datum by levels from a reference mark, the
gage height of a point of known elevation on the supporting structure
(reference point) is first checked. Next, the elevation of the bottom of
the weight at one or more heights above the water surface, as deter-mined
by levels from a reference mark, is compared with gage read-ings
When necessary, adjustment of the chain length to give accurate
gage readings is made in the manner indicated above. The length of
the chain is measured and recorded before and after the adjustment.
The reliability of gage readings of the water surface is affected by
wind, waves, and water current, in a manner similar to that discussed
for the wire-weight gage (p. 65). There is no tendency, however, for
the weight to rotate when lowered, as described in the discussion of
the wire-weight gage.
ACCURACY OF FLOAT-OPERATED RECORDERS
This section of the report discusses the inaccuracies inherent in any
float-operated instrument; the discussion is not concerned with such
sources of error as datum changes, faulty intake operation, float leak-age,
float-tape slippage, and paper expansion, which were discussed
in the preceding sections. The principal sources of error inherent in a
float-operated instrument are float lag, line shift, and submergence of
the counterweight (Stevens, 1921). With regard to the algebraic sign
of the errors discussed below, a positive (+) sign indicates that the
instrument shows a stage higher than the true stage, and a negative
(-) sign indicates that the instrument underregisters.
Float lag.-If the float-operated recorder is set to the true water
level while the water level is rising, it will thereafter show the correct
water level, as far as float lag is concerned, for all rising stages. For
falling stages, however, the recorded stage will be above the true
water level (positive error) by the amount of float lag or change in
flotation depth of the float. A reverse effect occurs if the original gage
setting is made when the water level is falling. Float lag varies di-rectly
with the force (F) required to move the mechanism of the re-corder
and inversely as the square of the float diameter (0). F com-monly
ranges from 1 to 5 oz (0.03 to 0.15 kg) depending on the type
and condition of the instrument.
The equation for maximum float-lag error (MFLE) is
MFLE = 0.37 F/D* (English units),
where MFLE is expressed in feet, D is expressed in inches, and F is
expressed in ounces. The equation is

MFLE = (0.00256) F/D2 (metric units), (4)
where MFLE and D are expressed in meters, and F is expressed in
kilograms.
If we assume a value of 3 oz (0.08 kg) for F and a value of 8 in (0.2
m) for D, MFLE equals 0.017 ft (0.005 m). If the recorder was set to
the true water level while the float was rising, the record on a falling
stage will be in error by +0.017 ft. If however, the index were set at
the true level at a stationary stage-that is, at the peak or trough of a
changing stage, or when the valves in a stilling well were closed-then
the error will be halved on a changing stage. The error will be
+0.0085 ft for falling stages and -0.0085 for rising stages.
Line &ft.-With every change of stage a part of the float tape
passes from one side of the float pulley to the other, and the change in
weight changes the depth of flotation of the float. The magnitude of
change depends on the change in stage (AH) since the last correct
setting of the recorder, the unit weight (U) of the tape, and the float
diameter (D). The error will be positive (+) for a rising stage and a
negative (-) for a falling stage.
The equation for line-shift error (LSE) is
LUY (English units), (5)
where U is expressed in ounces per foot, D is in inches, and LSE and
AH are in feet.
The equation is
LSE = (0.00256) AH (metric units), (6)
where U is expressed in kilograms per meter, and LSE, D, and AH are
expressed in meters.
If we assume a value of 0.14 ozlft (0.013 kg/m) for U, a value of 50 ft
(15 m) for AH, and a value of 8 in (0.2 m) for D, LSE equals 0.04 ft
(0.012 m).
Submergence of the counterweight.-When the counterweight and
any part of the float line become submerged as the stage rises, the
pull on the float is reduced and its depth of flotation is increased. The
converse is true when the submerged counterweight emerges from
the water on a falling stage. Thus, the error caused by submergence
or emergence is opposite to that of the line-shift error and tends to

compensate for the line-shift error. The submergence error is depen-dent
on the weight of the counterweight (c) and the float diameter CD).
The equation for submergence error (SE) is
SE = 0.017 $(English units), (7)
where SE is expressed in feet, c is in ounces, and D is in inches.
The equation is
SE = (0.000118) s(metric units), (8)
where SE and D are expressed in meters and c is expressed in kilo-grams.
If we assume a value of 1.25 lb (0.57 kg) for c and a value of 8 in (0.2
m) for D, SE = 0.0053 ft (0.0016 m).
Although not related to errors inherent in a float-operated stage
recorder, it might be mentioned here that error in recorded stage may
be caused by expansion or contraction of the stilling well of a tall gage
structure that is exposed to large temperature changes. For example,
a steel well 80 ft (24 m) high, exposed to an increase in temperature of
4O”C, will have its instrument shelf raised 0.04 ft (0.012 m), assum-ing,
of course, that the instrument shelter is attached to the well.
Summary.-The errors inherent in a float-operated stage recorder
will affect computed discharges. The effect of float lag can be reduced
to any desired level by the use of an appropriately large float, and
that accuracy level may then be maintained by keeping the instru-ment
cleaned and oiled to reduce friction. The recorder should be set
to the gage height in the stilling well when the stage in the well is
constant, because the float-lag error in subsequent recorded gage-height
will then be only half as large as it would be if the recorder
setting were made during a period of changing stage in the stilling
well. Even if the stage of the stream is changing, the stage in the well
may be kept constant by keeping the intake valves closed while the
recorder is being set.
The error resulting from caunterweight submergence is a constant
function of stage and becomes an integral part of the stage-discharge
relation. The same would be true of line-shift error if the recorder
settings were made only when the stage is low, but that practice is
usually impractical. Line shift can be a significant source of error
only at gaging stations that experience a wide range of stage.

ACCURACY OF BUBBLE-GAGE RECORDERS
This section of the report discusses the inaccuracies inherent in any
bubble-gage system for sensing stage; the discussion is not concerned
with such sources of error as datum corrections, sediment deposition
on the bubble orifice, and leaks in the system, which were discussed
in the preceding sections. The principal sources of error inherent in a
bubble-gage recorder are variation in gas friction, variation in re-quired
bubble-feed rate with rate of increase in stage, and variation
in weight of gas column with stage.
Variation in gas friction.-Friction created by the flow of gas
through the bubble tubing results in the pressure at the manometer
being slightly higher than that at the orifice. If the bubble-feed rate
could be kept constant and temperature did not vary, the friction
would remain constant and the accuracy of the gage would be unaf-fected,
because the manometer is always set to agree with the water-surface
elevation. However, changes in gas-feed rates cause variation
in the friction of the gas flowing through the tube, and where long
bubble tubes are used, the variation in friction can produce
significant error in recorded gage height.
Inaccuracies due to variation in gas friction can be eliminated by
using two gas tubes-one to feed gas to the bubble orifice, the other to
act as a static pressure tube to transmit pressure from a point at or
near the orifice back to the manometer.
As a conservative criterion for determining when the use of dual
tubing is desirable, it is suggested that variations in gas friction be
limited to 0.01 ft (0.003 m). If, for a given length of orifice line, an
error no greater than 0.01 ft results from a 100 percent increase in
bubble rate, a single bubble tube will be satisfactory. Figure 36, based
on laboratory tests using the standard U.S. Geological Survey bubble
gage shows the relation between the length of bubble tubing and a
loo-percent variation in bubble rate for a gas-friction error of 0.01 ft.
To illustrate the use of figure 36, assume that a loo-percent variation
in bubble rate represents a change from 40 bubbles per minute to 80
bubbles per minute. The corresponding length of bubble tubing indi-cated
by the diagram is 370 ft (113 m). Thus any length of single
tubing up to 370 ft could be used in this particular case without
introducing a friction error in excess of 0.01 ft. If more than 370 ft of
tubing is required at this particular site, and a gage-height error
greater than 0.01 ft cannot be tolerated, two gas tubes should be used.
When two tubes are used, they should be joined at a T-connector, from
whose vertical leg a single tube extends to the orifice. The
T-connector should be located above the normal high-water elevation
to prevent the entry of water into both legs of the system if pressure

loss occurs. Additional valves must also be provided so that the static
pressure tube can be separately purged, if necessary.
Variation in required bubble-feed rate with rate of increase in
stage.-During rapid rises in stage the instrument will lag if the
450 ,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,11 ,,,,lll,
FRICTION TEST
Polyethylene tubing
H-inch diameter
20 40 60 80 100
VARIATION IN BUBBLE RATE (BUBBLES PER MINUTE)
FOR 0.01 FOOT ERROR
FIGURE 36.-Diagram for determining allowable length of bubble tubing for maximum
friction error of 0.01 ft.

bubble-feed rate is too low. Laboratory tests on the standard U.S.
Geological Survey bubble gage indicate that figure 37 may be used to
28
I I I I I I I YI I I/I
26
22
I I I I I I I I I I I I I/I I I/I 1x1 I
20
18
16
8
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
BUBBLES PER MINUTE PER FOOT OF TUBE
FIGURE 37.-Diagram for determining required bubble rate.
1 .o

determine the bubble rate required for the maximum expected rate of
increase of stage, where the minimum expected stage above the
orifice will be less than 10 ft (3.0 m) for long periods of time. For
periods when a minimum stage of more than 10 ft is expected to
prevail, a lower bubble rate should be used to conserve gas, because
the rate of increase of stage that a given bubble rate will support
increases directly with stage. It was found that for installations
where the minimum stage will continuously be higher than 10 ft, the
maximum expected rate of increase of stage should be divided by
HCminj + 33
33 before entering figure 37. (Hc,i”, is the minimum ex-pected
stage above the orifice.) For example, for a given expected rate
of increasing stage, the adequate bubble rate for a minimum stage of
100 ft (30.0m) will be one-fourth of that for a minimum stage of 10
100 + 33
f&the factor 33
equals 4.
Variation in weight of gas column with stage.-At installations
where the manometer is high above the bubble orifice, and large
fluctuations in stage occur, the variation in weight of the gas column
with stage will cause the manometer to read low (underregister) at
high stages. The error varies almost linearly with stage and for that
reason the manometer readout in that situation can be corrected
without too much difficulty. Depending on the type of instrument
used, either the inclination of the manometer is adjusted or a change
is made in the gearing between the servosystem and the recording
equipment.
As a matter of fact any source of error that varies linearly with
stage-for example, the density of the water may increase with stage
as a result of increased sediment load-may be compensated for by
the adjustments mentioned above. Changes in temperature are
usually a negligible source of error, except in high-head installations
having large fluctuations in stage. In that situation it is recom-mended
that the bubble-gage system be equipped with a
temperature-compensated servomanometer to minimize the error at-tributable
to temperature changes.
SPECIAL PURPOSE GAGES
MODEL T RECORDER
The model T recorder (fig. 38) is a graphic recorder that has a 1:6
gage-height scale and a time scale of 2,4 in. per day. Use of the recorder
is limited to a 3-ft (0.9 m) range in stage and it should be serviced
weekly, although it will record more than one trace on the 7-day
chart. The model T recorder is operated by a motor-wound spring-

driven timer, and power is supplied to the timer by a 4?&volt battery.
A timer is also available that operates on a l%-volt battery. The
housing of the recorder is designed to fit on the top of a vertical 3-in
(0.076 ml-diameter pipe that can be used as the stilling well. This
recorder is much cheaper and more compact than the conventional
graphic recorders and is well suited for temporary installations for
low-flow studies, particularly those concerned with diurnal fluctua-tion
in discharge during low-flow periods. The model T recorder is not
used at continuous-record gaging stations.
FIGURE 38.-Model T recorder.

SR RECORDER
The model SR recorder (fig. 39) is a graphic recorder that records
flood stages and rainfall. A 5-in (O.l27m)-diameter flat circular disc is
rotated by a battery-wound clock. The power source is a 1%volt
battery. The chart is circular and turns one revolution in 24 hr. Three
ranges in stage are available for the effective chart width of 2 in (0.05
m): 5, 10, or 20 ft. The recorder sits on a 2-in-diameter pipe that
serves as the stilling well (similar to that for the model T). Five
inches of rainfall can also be recorded on the effective width of the
chart, but the rainfall reservoir can be equipped with a siphon that
will allow an unlimited amount of rainfall to be recorded. The rainfall
reservoir is a separate 2-in-diameter pipe that fills at the rate of 1 ft
(0.3 m) for each 1 in (0.025 m) of rainfall. After the pipe has filled to a
height of 5 ft (1.52 m), the siphon is tripped to empty the pipe.
The SR recorder is much cheaper and more compact than the con-ventional
graphic recorders and is used for studying rainfall-runoff
FIGURE 39.-Model SR recorder

relations for isolated storms on small watersheds. The SR recorder is
not used at continuous-record gaging stations.
A word of caution is in order at this point. The SR recorder has not
proven to be an unqualified success, although it has performed satis-factorily
at many installations. Its use is therefore recommended re-servedly.
CREST-STAGE GAGE
The crest-stage gage is a device for obtaining the elevation of the
flood crest of streams. The gage is widely used in the U.S.A. because it
is simple, economical, reliable, and easily installed. Because of those
attributes the crest-stage gage has become a basic instrument in re-gional
studies of flood frequency. For such studies the network of
standard gaging stations is augmented by a network of crest-stage
gages, thereby providing flood-peak information at a great many sites
in the region at reasonable cost.
A crest-stage gage is also a valuable adjunct to the nonrecording
gage at nonrecording gaging stations. It provides a record of the peak
stages of stream rises, and those stages can be used with the ob-server’s
routine readings when sketching the estimated continuous-stage
graph through the plotted points of observed stage.
Many different types of crest-stage gages have been tested by the
U.S. Geological Survey. (See, for example, Friday, 1965, and Carter
and Gamble, 1963.) The one found most satisfactory is a vertical piece
of 2-in (0.05 m) galvanized pipe containing a wood or aluminum staff
held in a fixed position with relation to a datum reference. (See fig.
40.) The bottom cap has six intake holes located as shown in figure 40
to minimize nonhydrostatic drawdown or superelevation inside the
pipe. Tests have shown this arrangement of intake holes to be effec-tive
with velocities up to 10 ft/s (3 m/s) and at angles up to 30 degrees
with the direction of flow. The top cap contains one small vent hole.
The bottom cap, or a perforated tin cup or copper screening in cup
shape attached to the lower end of the staff, contains regranulated
cork. As the water rises inside the pipe the cork floats on the water
surface. When the water reaches its peak and starts to recede the cork
adheres to the staff inside the pipe, thereby retaining the crest stage
of the flood. The gage height of a peak is obtained by measuring the
interval on the staff between the reference point and the floodmark.
Scaling can be simplified by graduating the staff. The cork should be
cleaned from the staff before replacing the staff in the pipe to prevent
confusion with high-water marks that will be left by subsequent peak
discharges.
The datum of the gage should be checked by levels run from a
reference mark to the top of the staff, the graduated staff being of

2-M pipe ) I
; I k
i ;
I I
I
I I I
I
i
I
I
%-in by l+in i I
measuring stick , I
Perforated tin cup
for reeranulated
r
hole
Note-Set g-penny nail
top of measuring stick
flush fit with cap
at
for
Section A -A’
FIGURE 40.-Crest-stage gage.
known length. The gage itself should be serviced on a regular basis.
However, the staff should not be removed from the pipe for any reason
when the stage is high. If, after such removal, the staff is reinserted
when water stands high in the pipe, the resulting surge of the water
displaced by the staff will leave an artificial “high-water mark” on
the staff.
SELECTED REFERENCES
Barron, E. G., 1963, New instruments for surface-water investigations, in Mesnier, G.
N., and Iseri, K. T., Selected techniques in water-resources investigations: U.S.
Geol. Survey Water-Supply Paper 1669-2, 64 p.

5. DISCHARGE-CURRENT-METER METHOD 79
Buchanan, T.J., and Somers, W. P., 1968, Stage measurement at gaging stations: U.S.
Geol. Survey Techniques Water-Resources Investigations, Book 3, Chap. A-7,28p.
Carter, J. R., and Gamble, C. R., 1963, Tests of crest-stage gage intakes: U.S. Geol.
Survey open-file report, Water-Resources Division, Washington, D.C.
Corbett, D. M., and others. 1943, Stream-gaging procedure: U.S. Geol. Survey Water-
Friday, John, 1965, Tests of crest-stage intake systems: U.S. Geol. Survey open-file
report.
International Standards Organization, 1969, Liquid flow measurement in open
Channels-Establishment and operation of a gauging station and determination of
the stage-discharge relation: IS0 Recommendation RllOO, Geneva, p. 9-11.
Isherwood, W. L., 1963, Digital water-stage recorder, in Mesnier, G. N., and Iseri, K.
T., Selected techniques in water-resources investigations: U.S. Geol. Survey
Water-Supply Paper 1669-2, 64 p.
Mesnier, G. N., and Iseri, K. T., 1963, Selected techniques in water-resources investi-gations:
U.S. Geol. Survey Water-Supply Paper 1669-Z, 64 p.
Smith, Winchell, Hanson, R. L., and Cruff, R. W., 1965, Study of intake lag in con-ventional
stream-gaging stilling wells: U.S. Geol. Survey open-file report, Water-
Resources Division, Menlo Park, Calif.
Stevens, J. C., 1921, The accuracy of water level recorders and indicators of the float
type: American Society Civil Engineers Transactions, v. 83 (1919-201, p. 894-903.
World Meteorological Organization, 1962, Field methods and equipment used in hy-drology
and hydrometeorology: Flood Control Series no. 22, p. 18-24.
CHAPTER 5.-MEASUREMENT OF DISCHARGE BY
CONVENTIONAL CURRENT-METER METHOD
INTRODUCTION
Streamflow, or discharge, is defined as the volume rate of flow of
water, including any substances suspended or dissolved in the water.
Discharge is usually expressed in cubic feet per second or cubic me-ters
per second.
Discharge measurements are made at each gaging station to de-termine
the discharge rating for the site. The discharge rating may be
a simple relation between stage and discharge or a more complex
relation in which discharge is a function of stage, slope, rate of change
of stage, or other factors. Initially the discharge measurements are
made with the frequency necessary to define the station rating, as
early as possible, over a wide range of stage. Measurements are then
made at periodic intervals, usually monthly, to verify the rating or to
define any changes in the rating caused by changes in stream-channel
conditions.
Discharge measurements may he made by any one of the methods
discussed in chapters 5-8. However, the conventional current-meter
method is most commonly used in gaging streams. When using this

method, observations of width, depth, and velocity are taken at inter-vals
in a cross section of the stream, while the hydrographer is wad-ing
or supported by a cableway, bridge, ice cover, or boat. A current
meter is used to measure velocity. This chapter describes the con-ventional
current-meter method.
GENERAL DESCRIPTION OF A CONVENTIONAL
CURRENT-METER MEASUREMENT
OF DISCHARGE
A current-meter measurement is the summation of the products of
the subsection areas of the stream cross section and their respective
average velocities. The formula
Q = Zu u) (9)
represents the computation, where Q is total discharge, a is an indi-vidual
subsection area, and u is the corresponding mean velocity of
the flow normal to the subsection.
In the midsection method of computing a current-meter measure-ment,
it is assumed that the velocity sample at each vertical repre-sents
the mean velocity in a rectangular subsection. The subsection
area extends laterally from half the distance from the preceding ob-servation
vertical to half the distance to the next, and vertically from
the water surface to the sounded depth. (See fig. 41.1
The cross section is defined by depths at verticals 1,2,3,4, . . . n. At
each vertical the velocities are sampled by current meter to obtain
the mean velocity for each subsection. The subsection discharge is
then computed for any subsection at vertical x by use of the equation,
4s = u.r [
2 2 1 &
a- - h-1,) + (b,+,, - b.I-)
2 1 d s (10)
= u, (s+l) - be,,
where
qx = discharge through subsection x,
u,r = mean velocity at vertical x,
b, = distance from initial point to vertical x,
b,,.-,, = distance from initial point to preceding vertical,
bm+,, = distance from initial point to next vertical, and
d,. = depth of water at vertical x.
Thus, for example, the discharge through subsection 4 (heavily
outlined in fig. 41) is

q4 = u4 [b -s 6 1s
2 d 4.
The procedure is similar when x is at an end section. The “preced-ing
vertical” at the beginning of the cross section is considered coinci-dent
with vertical 1; the “next vertical” at the end of the cross section
is considered coincident with vertical n. Thus,
4=1U [Ib -b1, d
2 1
and
bn
b-1)
I
EXPLANATION
1,2,3 . . . . . . . . n Observation verticals
bl.bz,tq, . . ..b. Distance, in feet or meters, from the
initial point to the observation vertical
dl,dz,dg. . . ..d. Depth of water, in feet or meters, at the
observation vertical
Dashed lines Boundaries of subsections; one
heavily outlined is discussed in text
FIGURE 41.-Definition sketch of midsection method of computing cross-section area
for discharge measurements.

For the example shown in figure 41, q, is zero because the depth at
observation point 1 is zero. However, when the cross-section bound-ary
is a vertical line at the edge of the water as at vertical n, the depth
is not zero and velocity at the end vertical may or may not be zero.
The formula for q, or q,t is used whenever there is water only on one
side of an observation vertical such as at piers, abutments, and is-lands.
It is necessary to estimate the velocity at an end vertical,
usually as some percentage of the adjacent vertical, because it is
impossible to measure the velocity accurately with the current meter
close to a boundary. There is also the possibility of damage to the
equipment if the flow is turbulent. Laboratory data suggest that the
mean vertical velocity in the vicinity of a smooth sidewall of a
rectangular channel can be related to the mean vertical velocity at a
distance from the wall equal to the depth. The tabulation below gives
values that define the relation.
Lhstance porn lmll, as a Mean uertrcal uelm1ty, as
ram of the depth related to V,,
0.00
.25
O:g;$J
.50 .95v::
1.00 LOOV,,
NOTE-V, IS the mean vertrcal velocity at a distance from the vertical wall equal to the depth.
The summation of the discharges for all the subsections-usually
25 to 30 in number-is the total discharge of the stream. An example
of the measurement notes used by the U.S. Geological Survey is
shown in figure 42.
The mean-section method, used by the U.S. Geological Survey prior
to 1950, differs from the midsection method, described above, in com-putation
procedure. In the older method discharges are computed for
subsections between successive observation verticals. The velocities
and depths at successive verticals are each averaged, and each sub-section
extends laterally from one observation vertical to the next.
Subsection discharge is the product of the average of two mean veloci-ties,
the average of two depths, and the distance between observation
verticals. In both methods total discharge is the sum of the subsection
discharges. A study by Young (1950) concluded that the midsection
method is simpler to compute and is a slightly more accurate proce-dure
than the mean-section method.
Current-meter meaurements are usually classified in terms of the
means used to cross the stream during the measurement, such as
wading, cableway, bridge, boat, or ice cover.
INSTRUMENTS AND EQUIPMENT
Current meters, timers, and a means of counting meter revolutions
are needed for the measurement of discharge, along with additional

FIGURE 42.-Computation notes of a current-meter measurement by the midsection
method.

equipment that depends on the manner in which the measurement is
to be made-that is, whether by wading, cableway, bridge, boat, or
from ice cover. Instruments and equipment used in making the
current-meter measurements are described in this section of the
manual under the following categories: current meters, sounding
equipment, width-measuring equipment, equipment assemblies, and
miscellaneous equipment.
CURRENT METERS
A current meter is an instrument used to measure the velocity of
flowing water. The principle of operation is based on the pro-portionality
between the velocity of the water and the resulting angu-lar
velocity of the meter rotor. By placing a current meter at a point
in a stream and counting the number of revolutions of the rotor dur-ing
a measured interval of time, the velocity of water at that point is
determined.
The number of revolutions of the rotor is obtained by an electrical
circuit through the contact chamber. Contact points in the chamber
are designed to complete an electrical circuit at selected frequencies
of revolution. Contact chambers can be selected having contact points
that will complete the circuit twice per revolution, once per revolu-tion,
or once per five revolutions. The electrical impulse produces an
audible click in a headphone or registers a unit on a counting device.
The intervals during which meter revolutions are counted are timed
with a stopwatch. A discussion of the required time interval follows.
Turbulent flow, which is ordinarily found in natural streams and in
artificial channels, is always accompanied by local eddying, which
results in pulsations in the velocity at any point. Figure 43, taken
from a study by Pierce (19411, shows the pulsations observed in a
laboratory flume for two different mean velocities. The greater mag-nitude
of the pulsations, relative to the mean, at the lower velocity
explains why current-meter observations at a point should cover a
longer period when low velocities are being measured than when
higher velocities are being measured. At high velocities, pulsations
have only minor effect on the current-meter observations. In the
U.S.A. it is customary to observe velocity at a point by current meter
for a period that ranges from 40 to 70 s. It is recognized that the use of
a period of from 40 to 70 s is not long enough to insure the accuracy of
a single point-observation of velocity. However, because the pulsa-tions
are random and because velocity observations during a dis-charge
measurement are made at 25 to 30 verticals, usually with two
observations being made in each vertical, there is little likelihood
that the pulsations will bias the total measured discharge of a stream.
(See p. 181-182.) Longer periods of current-meter observation at a

point are not used, because it is desirable to complete a discharge
measurement before the stage changes significantly and because the
use of longer observation periods may add significantly to the operat-ing
cost of a large number of gaging stations.
Current meters generally can be classified with respect to two main
types: those meters having vertical-axis rotors and those having
horizontal-axis rotors. The comparative characteristics of these two
types are summarized below:
1. Vertical-axis rotor with cups or vanes.
a. Operates in lower velocities than do horizontal-axis meters.
b. Bearings are well protected from silty water.
c. Rotor is repairable in the field without adversely affecting the
rating.
d. Single rotor serves for the entire range of velocities.
2. Horizontal-axis rotor with vanes.
a. Rotor disturbs flow less than do vertical-axis rotors because of
axial symmetry with flow direction.
b. Rotor is less likely to be entangled by debris than are vertical-axis
rotors.
c. Bearing friction is less than for vertical-axis rotors because
bending moments on the rotor are eliminated.
VERTICAL-AXIS CURRENT METERS
A common type of vertical-axis current meter is the Price meter,
type AA. (See fig. 44.) This meter is used extensively by the U.S.
Geological Survey. The standard Price meter has a rotor 5 in (0.127
mrvation = 34 seconds
Mean velocity = 0.10 ft 1s
z +30
Average length of an individual ot
z9 +20
0’ +10
E
0
Z-10 ’ ’ ’ ’ ’ ’ ’ ’
v -- II Ir
.
. I ’
k! ---. I
g -20 0 100 200 300 400 500 600 700 800 900
i2i Mean velocity = 1.00 ft 1s
Average length of an individual observation = 23 seconds
z +10
5
! 0 -.r -a* ‘. .-.’ ‘* .- 3 P”
.H 4, .J
t ..~ -, -.
-loo 100 200 300 400 500 600 700
TIME. IN SECONDS FROM BEGINNING OF OBSERVATIONS
FIGURE 43.-Comparison of pulsations for two different mean velocities measured in a
laboratory flume, 12 ft wide.

m) in diameter and 2 in (0.05 m) high with six cone-shaped cups
mounted on a stainless-steel shaft. A pivot bearing supports the rotor
shaft. The contact chamber houses both the upper part of the shaft
and a slender bronze wire (cat’s whisker) attached to a binding post.
With each revolution an eccentric contact on the shaft makes contact
with a bead of solder at the end of the cat’s whisker. A separate
reduction gear (pentagear), wire, and binding post provide a contact
each time the rotor makes five revolutions. A tailpiece keeps the
meter pointing into the current.
In addition to the standard type AA meter for general use there is a
type AA meter for low velocities. No pentagear is provided. This
modification reduces friction. The shaft usually has two eccentrics
making two contacts per revolution. The low-velocity meter normally
is rated from 0.2 to 2.5 ft/s (0.06 to 0.76 m/s) and is recommended for
use when the mean velocity at a cross section is less than 1 ft/s (0.3
m/s).
In addition to the type’AA meters, the U.S. Geological Survey uses
a Price pygmy meter in shallow depths. (See fig. 44.) The pygmy
meter is scaled two-fifths as large as the standard meter and has
neither a tailpiece nor a pentagear. The contact chamber is an inte-gral
part of the yoke of the meter. The pygmy meter makes one
contact per revolution and is used only with rod suspension.
The U.S. Geological Survey has recently developed a four-vane
vertical-axis meter. (See fig. 45.) This meter is useful for meas-urements
under ice cover because the vanes are less likely to fill with
slush ice and because it requires a much smaller hole for passage
through the ice. One yoke of the vane meter is made to be suspended
at the end of a rod and will fit holes made by an ice drill. Another yoke
FIGURE 44.-Price type AA meter, top; Price pygmy meter, bottom.

is made for regular cable or rod suspension. (See fig. 45.) The vane
meter has the disadvantage of not responding as well as the Price
type AA meter at velocities less than 0.5 ft/s (0.15 m/s).
A new contact chamber has been designed by the U.S. Geological
Survey to replace the wiper contact of the type AA and vane meters.
The new contact chamber contains a magnetic switch, glass enclosed
in a hydrogen atmosphere and hermetically sealed. The switch as-sembly
is rigidly fixed in the top of the meter head just above the tip
of the shaft. The switch is operated by a small permanent magnet
rigidly fastened to the shaft. The switch quickly closes when the
magnet is alined with it and then promptly opens when the magnet
moves away. The magnet is properly balanced on the shaft. Any type
AA meter can have a magnetic switch added by replacing the shaft
and the contact chamber. The magnetic switch is placed in the special
contact chamber through the tapped hole for the binding post. The
rating of the meter is not altered by the change. An automatic
counter (p. 130) is used with the magnetic-switch contact chamber. If
a headphone is used, arcing may weld the contacts.
A Price meter accessory that indicates the direction of flow is de-scribed
on page 129.
Vertical-axis current meters do not register velocities accurately
when placed close to a vertical wall. A Price meter held close to a
right-bank vertical wall will underregister because the slower water
velocities near the wall strike the effective (concave) face of the cups.
The converse is true at a left-bank vertical wall. (The terms “left
bank’ and “right bank” designate direction from the center of a
stream for an observer facing downstream.) The Price meter also
FIGURE 45.-Vane ice meter, top; vane meter with cable suspension yoke, bottom.

underregisters when positioned close to the water surface or close to
the streambed.
HORIZONTAL-AXIS CURRENT iMETERS
The types of horizontal-axis meters most commonly used are the
Ott, Neyrpic, Haskell, Hoff, and Braystoke. The Ott meter is made in
Germany, the Neyrpic meter in France, and both are used extensively
in Europe. The Haskell and Hoff meters were developed in the United
States, where they are used to a limited extent. The Braystoke meter
is used extensively in the United Kingdom. The Ott meter (fig. 46) is
a precision instrument but is not widely used in the U.S.A. because it
is not as durable as the Price meter under extreme conditions. The
makers of the Ott meter have developed a component propeller that
in oblique currents automatically registers the velocity component at
right angles to the measuring section for angles as great as 45” and
FIGURE 46.-Ott current meter.
FIGURE 47.-Velocity components measured by Ott and Price current meters.

for velocities as great as 8 ft/s (2.4 m/s). For example, if this compo-nent
propeller were held in the position AB in figure 47 it would
register V cos a rather than V, which the Price meter would register.
The Neyrpic meter is used rarely in the U.S.A. for the same reason
that the Ott meter is rarely used there.
The Haskell meter has been used by the U.S. Lake Survey, Corps of
Engineers, in streams that are deep, swift, and clear. By using propel-lers
with a variety of screw pitches, a considerable range of velocity
can be measured. The Haskell meter is more durable than most other
horizontal-axis current meters.
The Hoff meter (fig. 48) is another current meter used in the U.S.A.
The lightweight propeller has three or four vanes of hard rubber. The
meter is suited for the measurement of low velocities but is not suited
for rugged use.
COMPARISON OF PERFORMANCE OF VERTICAL-AXIS AND
HOKIZONTAL-AXIS CURRENT METERS
Comparative tests of the performance of vertical-axis and
horizontal-axis current meters, under favorable measuring condi-tions,
indicate virtually identical results from use of the two types of
meter. That was the conclusion reached in 1958 by the U.S. Lake
Survey, Corps of Engineers, after tests made with the Price, Ott, and
Neyrpic current meters (Townsend and Blust, 1960). The results of
one of their tests is shown in figure 49.
Between the years 1958 and 1960, the U.S. Geological Survey made
19 simultaneous discharge measurements on the Mississippi River
using Price and Ott meters. The average difference in discharge be-tween
results from the two meters was -0.15 percent, using the
measurements made with the Price meter as the standard for com-parison.
The maximum differences in discharge measured by the two
meters was -2.76 and +1.53 percent.
FIGURE 48.-Hoff current meter.

I . I I I
ClN033S kl3d 1333 NI ‘All3OJ3A

OPI‘ICAL CURRENT METER
In recent years the U.S. Geological Survey has developed an optical
current meter (fig. 50). The meter and its use have been described by
Chandler and Smith (1971). The optical current meter is designed to
measure surface velocities in open channels without immersing
equipment in the stream. However, because it measures only surface
velocity, the optical meter is not considered a substitute for con-ventional
equipment in those situations where good measurements
can be made by standard techniques. It is a device that has extended
the capability of making discharge measurements to a range of situa-tions
under which standard current-meter techniques cannot be used.
Those situations include flood velocities that are too high to be meas-ured
by conventional meter-for example, supercritical velocities in
floodways-or the presence of a debris load during flood periods that
makes it hazardous to immerse a current meter.
Basically, the meter is a stroboscopic device consisting of a low-power
telescope, a single oscillating mirror driven by a cam, a
variable-speed battery-operated motor, and a tachometer. The water
surface is viewed from above through the meter, while gradually
changing the speed of the motor to bring about synchronization of the
FIGURE 50.-Optical current meter.

angular velocity of the mirror and the surface velocity of the water.
Synchronization is achieved when the motion of drift or disturbances
on the water surface, as viewed through the meter, is stopped. A
reading of the tachometer and height of the meter above the water
surface are the only elements needed to compute the surface velocity.
The velocity measurement may be made from any bridge, walkway,
or other structure that will support the optical meter. The vertical
axis of the meter must be perpendicular to the water surface. Surface
velocity (Vs,) is computed from the equation
V, = KRD,
where K is the constant for the meter, R is the readout from the
tachometer, and D is the distance to the water surface in feet. The
tachometer is scaled to produce a value of K equal to 1.00. The surface
velocity computed from the above equation must be corrected by an
appropriate coefficient to obtain the mean velocity in the vertical. The
precise coefficient applicable is, of course, unique to the particular
stream and to the location of the vertical in the stream cross section.
However, data abstracted from conventional current-meter meas-urements
show that application of a coefficient of 0.90 will not intro-duce
errors of more than 25 percent in concrete-lined channels. For
natural channels a coefficient of 0.85 has been used.
A unique feature of the optical current meter is the automatic
correction that is made for variations in the direction of the
streamlines of flow. If the flow approaches the cross section at an
angle other than the perpendicular, and if the axis of the oscillating
mirror in the meter is parallel to the cross section, then at the null
point of observation, the water will appear to move laterally across
the field of view. The meter measures only the velocity vector normal
to the cross section, and there is no need to apply horizontal angle
corrections.
The range of velocities that can be measured with the optical
current meter is limited at the lower end by the accuracy of the
tachometer and at the upper end by the physical limitations of the
human eye. Table 1 shows the range of velocities that can be meas-
TABLE l.-Range of velocities that can be measured with optical current meter
Observatmn heqht CD) MaxImum velocity Mmmwm velocity for
z5 percent resolution
(it) (m) m/s) (m/s) Ws) (m/s)
5 1.52 25 7.62 1.6 0.49
10 3.05
B8 46.5170 1700”:
15.2 3.2 .98
2302.59 46.48 1.4956

ured from various heights above the water surface with the U.S.
Geological Survey model of the meter. The minimum velocities shown
in column 3 of the table can be measured with an error of 25 percent;
the higher velocities at the various observation heights will be meas-ured
with lesser error.
CARE OF -fHE CURRENT MIXER
To insure reliable observations of velocity it is necessary that the
current meter be kept in good condition. The care of conventional
meters will be discussed first.
Before and after each discharge measurement the meter cups or
vanes, pivot and bearing, and shaft should be examined for damage,
wear, or faulty alinement. Before using the meter its balance on the
cable-suspension hanger should be checked, the alinement of the
rotor when the meter is on the hanger or wading rod should also be
checked, and the conductor wire should be adjusted to prevent inter-ference
with meter balance and rotor spin. During measurements, the
meter should periodically be observed when it is out of the water to be
sure that the rotor spins freely.
Meters should be cleaned and oiled daily when in use. If meas-urements
are made in sediment-laden water, the meter should be
cleaned immediately after each measurement. For vertical-axis me-ters
the surfaces to be cleaned and oiled are the pivot bearing, pen-tagear
teeth and shaft, cylindrical shaft bearing, and thrust bearing
at the cap.
After oiling, the rotor should be spun to make sure that it operates
freely. If the rotor stops abruptly, the cause of the trouble should be
sought and corrected before using the meter. The duration of spin
should be recorded on the field notes for the discharge measurement.
A significant decrease in the duration of spin indicates that the bear-ings
require attention. In vertical-axis current meters the pivot re-quires
replacement more often than other meter parts, and it there-fore
should be examined after each measurement. The pivot and pivot
bearing should be kept separated, except during measurements, by
use of the raising nut provided in the Price meter or by replacing the
pivot with a brass plug in the pygmy meter. Fractured, worn, or
rough pivots should be replaced.
Meter repairs by the hydrographer should be limited to minor
damage only. That is particularly true of the rotor, where small
changes in shape can significantly affect the meter rating. In
vertical-axis meters, minor dents in the cups can often be
straightened to restore the original shape of the cups, but in case of
doubt, the entire rotor should be ‘replaced with a new one. Badly
sprung yokes, bent yoke stems, misalined bearings and tailpieces

should be reconditioned in shops equipped with the specialized
facilities needed.
There are only few details connected with care of the optical
current meter. The meter should be transported in a shock-proof car-rying
case and the battery should be checked periodically. Field per-formance
of the tachometer should also be checked periodically.
Three steps are involved in the checking process. First, a cam speed is
measured by counting and timing mirror oscillations with a stop-watch,
and the corresponding dial reading of the tachometer is ob-served.
Next, a tachometer dial readout is computed from the meas-ured
cam speed and the known scale factor of the tachometer dial. In
the final step the observed dial reading and the computed dial readout
are compared.
RATING OF CURRENT METERS
To determine the velocity of the water from the revolutions of the
rotor of a conventional current meter, ti relation must be established
between the angular velocity of the rotor and the velocity of the water
that spins the rotor. That relation is known as the rating of the
current meter. The rating is established by first towing the meter at a
constant velocity through a long water-filled trough, and then relat-ing
the linear and rotational velocities of the current meter. The
following paragraphs describe the rating of meters by the U.S.
Geological Survey at the Hydrologic Instrumentation Facility in
Mississippi.
The rating trough used is a sheltered concrete tank 450 ft (137 m)
long, 12 ft (3.7 m) wide, and 12 ft (3.7 m) deep. An electrically driven
car rides on rails extending the length of the tank. The car carries the
current meter at a constant rate through the still water in the basin.
Although the rate of travel can be accurately adjusted by means of an
electronic regulating gear, the average velocity of the moving car is
determined for each run by making an independent measurement of
the distance it travels during the time that the revolutions of the
rotor are electrically counted. Eight pairs of runs are usually made
for each current meter. A pair of runs consists of two traverses of the
basin, one in each direction, at the same speed. Practical consid-erations
usually limit the ratings to velocities ranging from 0.1 to
about 15 ft/s (0.03 to about 4.6 m/s), although the car can be operated
at lower speeds. Unless a special request is made for a more extensive
rating, the lowest velocity used in the rating is about 0.2 ft/s (0.06
m/s), and the highest is about 8.0 ft/s (2.5 m/s).
For convenience in field use, the data from the current-meter rat-ings
are reproduced in tables, a sample of which is shown in figure 51.

The velocities corresponding to a range of 3 to 350 revolutions of the
rotor within a period of 40 to 70 s are listed in the tables. This range
in revolution and time has been found to cover general field require-ments.
To provide the necessary information for extending a table for
the few instances where extensions are required, the equations of the
rating table are shown in the spaces provided in the heading. The
term, R, in the equations refers to revolutions of the rotor per second.
The equation to the left of the figure in parentheses (2.20 in fig. 51) is
the equation for velocities less than 2.20 ft./s (0.67 m/s), and the equa-tion
to the right is for velocities greater than 2.20 ft/s. The velocity
2.20 ftls is common to both equations.
It should be noted that the equations given are those of the rating
table and not necessarily those of the actual rating. If a rating table
already on file matches a rating within close tolerances, that table is
selected in preference to preparing a new one. The tolerances are
listed below:
Reuolutxms of rotor Tolerance, zn
per second (RI percent
Lessthan 1.0~---------------------------------------- 1.0
1.0 and greater----___----______________________----- .5
Because of the rigid control in the manufacture of the Price meter,
virtually identical meters are now being produced, and their rating
equations tend to be identical. Therefore, the U.S. Geological Survey
now feels no need to calibrate the meters individually. Instead, an
average standard rating is established by calibrating a large number
of meters that have been constructed to U.S. Geological Survey
specifications, and that rating is then supplied with each meter. To
insure that all meters are virtually identical, the dies and fixtures for
the construction of Price meters are supplied to the manufacturer.
Price meters that have been first rated using a wading-rod suspen-sion,
and then rated using a cable suspension with U.S. Geological
Survey Columbus-type weights and hangers, have not shown
significant differences in rating. Therefore, no suspension coefficients
are needed, and none should be used, if Columbus-type weights and
hangers are properly used. Tests that compared meters were dis-cussed
on pages 89-90. In those tests Columbus-type weights were
used with all meters. The close agreement of results for all meters
indicate that no suspension coefficients are required when
horizontal-axis current meters are used with Columbus-type weights.
The rating of the optical current meter is relatively simple. Its
operation is based on precise mathematical principles, and, given an
accurate tachometer, meter accuracy is dependent only on the config-uration
of the cam that oscillates the mirror. A master cam is used in

the manufacture of the individual meter cams. The meter is rated by
observation of a long endless belt driven at constant speed. That
known belt speed is checked against the speed computed by multiply-ing
the height of the meter above the belt by the tachometer reading.
If the comparison of known and computed speeds shows a lack of
agreement, the tachometer scaling is changed to bring about agree-ment.
SOUNDING EQUIPMENT
Sounding (determination of depth) is usually done mechanically,
the equipment used being dependent on the type of measurement
being made. Depth and position in the vertical are measured by a
rigid rod or by use of a sounding weight suspended from a cable. The
cable length is controlled either by a reel or by a handline. A sonic
sounder is also available, but it is usually used in conjunction with a
reel and a sounding weight.
Sounding equipment used by the U.S. Geological Survey is de-scribed
in the following categories: wading rods, sounding weights,
sounding reels, handlines, and sonic sounder.
WADING RODS
The two types of wading rods commonly used are the top-setting rod
and the round rod. The top-setting rod is preferred because of the
convenience in setting the meter at the proper depth and because the
hydrographer can keep his hands dry in the process. The round rod
can be used in making ice measurements as well as wading meas-urements
and has the advantage that it can be disassembled to 1-ft
(0.3-m) lengths for storing and transporting.
The top-setting wading rod has a l/2-in (12.7-mm) hexagonal main
rod for measuring depth and a 3%in (9.5mm) diameter round rod for
setting the position of the current meter (fig. 52).
The rod is placed in the stream so the base plate rests on the
streambed, and the depth of water is read on the graduated main rod.
When the setting rod is adjusted to read the depth of water, the meter
is positioned automatically for the 0.6-depth method. (See p. 134.)The
0.6-depth setting might also be described as the 0.4-depth position
measured up from the streambed. When the depth of water is divided
by 2 and this new value is set, the meter will be at the 0.2 depth
position measured up from the streambed. When the depth of water is
multiplied by 2 and this value is set, the meter will be at the 0.8-
depth position measured up from the streambed. These two positions
represent the conventional 0.2- and O.&depth positions. (See p. 134.)
The round wading rod consists of a base plate, lower section, three
or four intermediate sections, sliding support, and a rod end (not
essential). The parts are assembled as shown in figure 53. The meter

FIGURE 52.-Top-setting wading rod with
meter attached.

FIGURE 53.-Round wading rod with meter attached.

is mounted on the sliding support and is set at the desired position on
the rod by sliding the support.
The round rod is also used in making ice measurements. Inter-mediate
sections of the round rod are screwed together to make an ice
FIGURE 54.-Lower section of ice rod for
use with vane ice meter.

rod of desired length (fig. 54). The most convenient length for an ice
rod is about 3 ft (1 m) longer than the maximum depth of water to be
found in a cross section. About 12 ft (4 m) is the maximum practical
length for an ice rod; depths greater than 10 ft (3 m) are usually
measured with a sounding weight and reel. The base plate, sliding
support, and lower section are not used on an ice rod. Instead, a
special lower section is screwed directly into the top of the contact
chamber of the vane ice meter. (See fig. 54.) If a Price meter is used
under ice cover, another special lower section is used to hold the
meter by means of the hanger screw. (See fig. 55.) All lower sections
for ice rods are now made so that the center of the vanes or cups is at
the 0-ft point on the rod.
SOUNDING WEIGHTS AND ACCESSORIES
If a stream is too deep or too swift to wade, the current meter is
suspended in the water by cable from a boat, bridge, or cableway. A
sounding weight is suspended below the current meter to keep it
FIGURE 55.-Lower section of ice rod for use with Price meter.

stationary in the water. The weight also prevents damage to the
meter when the assembly is lowered to the streambed.
The sounding weights now used in the U.S.A. are the Columbus
weights, commonly called the C type. (See fig. 56.) The weights are
streamlined to offer minimum resistance to flowing water. Each
weight has a vertical slot and a drilled horizontal hole to accommo-date
a weight hanger and securing pin.
The weight hanger (fig. 57) is attached to the end of the sounding
line by a connector. The current meter is attached beneath the con-nector,
and the sounding weight is attached to the lower end of the
hanger by means of the hanger pin.
In addition to the weights shown in figure 56, weights of 150, 200
and 300 lb (68, 91, and 136 kg) are used for measuring the discharge
of deep, swift rivers. The sounding-weight hangers shown in figure 57
are designed to accommodate the weights of the various sizes. The
height of the meter rotor above the bottom of the sounding weight
must be considered in calculations to position the meter for velocity
observations at various percentages of the stream depth.
SOUNDING REELS
A sounding reel has a drum for winding the sounding cable, a crank
and ratchet assembly for raising and lowering the weight or holding
it in any desired position, and a depth indicator. The U.S. Geological
Survey has five types or sizes of sounding reel in common use, the
choice of reel being dependent on the depth of water to be measured
and on the weight required for sounding. The lightest of the reels,
known as the Canfield reel (fig. 581, can be used with either single- or
two-conductor cable; the other four reels use two-conductor cable,
whose diameter ranges from 0.084 in to 0.125 in (2.13 to 3.18 mm),
FIGURE 56.-Columbus 15-, 30-, 50-, 75, and loo-lb sounding weights.

depending on the weight to be handled. The three smaller reels have
a hand crank for raising and lowering the meter and weight (fig. 58);
FIGURE 57.-Sounding-weight hangers and hanger pins.

the largest of the five reels is operated by a battery-powered unit but
has a handcrank for emergency use; the second largest reel (fig. 59)
may be operated either by a hand crank or a power unit. Specially
designed connectors are used to join the end of the reel cable to the
sounding-weight hanger.
The two smaller reels (Canfield and A-pack reels) are equipped
with counters for indicating depth (fig. 58); the three larger reels are
equipped with computing depth indicators (figs. 59 and 60). On the
computing depth indicator, depth is indicated by a pointer. Tens of
feet are read on a numbered dial through an aperture near the top of
the main dial. The main dial also has a graduated spiral to indicate
directly the O.&depth position (p. 134) for depths up to 30 ft (9.15 m).
HANDLINES
When discharge measurements that are to be made from a bridge
require light sounding weights-15 or 30 lb (6.8 or 13.6 kg&the
weight and meter are often suspended on a handline (figs. 61 and 62).
Handlines can also be used from cable cars, but they seldom are
because a sounding reel mounted on the cable car is much more con-venient
to use.
FIGURE 58.-Canfield reel.

Measurement and Computation of Streamflow: Volume 1 Measurement of Stage and DischargePaper 2175 1982

The handline is made up of two separate cables that are electrically
connected at a reel (fig. 63). The upper or hand cable is that part of the
handline that is used above the water surface. It is a heavy-duty
two-conductor electric cable, whose thick rubber protective covering
makes the cable comfortable to handle. At its upper end is a connec-tion
for the headphone. The lower or sounding cable is a light
reverse-lay steel cable with an insulated core. A connector joins the
lowerend of the sounding cable to the hanger that is used as a mount
for the current meter and sounding weight. Sounding cable in excess
of the length needed to sound the stream being measured is wound on
FIGURE 61.-Handline

the reel. The sounding cable is tagged at convenient intervals with
streamers of different colored binding tapes, each colored streamer
being a known distance above the current-meter rotor. The use of
these tags in determining depth is described on page 150.
The advantages of the handline are ease in assembling the equip-ment
for a discharge measurement and relative ease in making dis-charge
measurements from certain types of bridges, particularly
truss bridges that do not have cantilevered sidewalks. The disadvan-tages
of the handline are a lesser degree of accuracy in depth deter-mination
than that obtained with a sounding reel, more physical
exertion is required in making the discharge measurement, and the
handline can seldom be used for high-water measurements of large
FIGURE 62.-Handline in use from a bridge.

streams because of the heavy sounding weights needed for such
measurements,
SONIC SOIJNDER
A commercial, compact, portable sonic sounder has been adopted by
the U.S. Geological Survey to measure stream depth. (See figs. 64 and
65.)
The sounder is powered by either a 6- or 12-volt storage battery and
will operate continuously for 10 hr on a single battery charge. Three
recording speeds are available, 36, 90, or 180 in (0.91, 2.29,4.57 m)
per hr. Four operating ranges, O-60,60-120, 120-180, and 180-240
ft (O-18.3, 18.3-36.6, 36.6-54.9, and 54.9-73.2 m) allow intervals of
60 ft (18.3 m) of depth to be recorded. The sounder is portable, weigh-ing
only 46 lb (20.9 kg). The transducer has a narrow beam angle of 6”
which minimizes errors on inclined streambeds and allows the hy-drographer
to work close to piers or other obstructions.
In swift debris-laden streams measurements can be made with this
equipment without lowering the meter and weight to the streambed.
As soon as the weight is in the water, the depth will be recorded. The
meter can then be set at the 0.2 depth or just below the water surface
for a velocity observation. The observed velocity can be converted to
mean velocity in the vertical by applying an appropriate coefficient.
(See p. 135-137.)
FIGURE 63.-Handline reels; Lee-Au (top) and Morgan (bottom).

Temperature change affects the sound-propagation velocity, but
error from that source is limited to about -c2 percent in fresh water.
That error can be eliminated completely by adjusting the sounder to
FIGURE 64.-Sounding weight with compass and sonic transducer ready for assembly.
FIGURE 65.-Sonic measuring assembly.

read correctly at an appropriate average depth determined by other
means.
WIDTH-MEASURING EQUIPMENT
The distance to any point in a cross section is measured from an
initial point on the bank. Cableways and bridges used regularly for
making discharge measurements are commonly marked at 2-, 5-, lo-,
or 20-ft (0.61-, 1.52-, 3.05-, or 6.10-m) intervals by paint marks. Dis-tance
between markings is estimated, or measured with a rule or
pocket tape.
For measurements made by wading, from boats, or from unmarked
bridges, steel or metallic tapes or tag lines are used. Tag lines are
made of l/32-, l/16-, 3/32-, or l/B-in (0.79-, 1.59-, 2.38-, or 3.18-mm)-
diameter galvanized steel aircraft cord having solder beads at meas-ured
intervals to indicate distances. The standard arrangement of
solder beads or tags used by the U.S. Geological Survey is as follows:
one tag every 2 ft for the first 50 ft of tag line;
one tag every 5 ft for stations between 50 and 150 ft on the tag
line;
one tag every 10 ft for stations between 150 ft and the end of the
tag line.
For identifying the stationing of the tags, an additional tag (total of
two tags) is used at stations 0, 10, 20, 30, 40, 50, 150, 250, 350, and
450 ft. Two additional tags (total of three tags) are used at stations
100,200,300, 400, and 500 ft.
The standard lengths of tag line are 300, 400 and 500 ft (91.4, 122,
and 152m), but other sizes are available.
Three types of tag-line reels in use are Lee-Au, Pakron, and Co-lumbus
type A (fig. 66). Larger reels designed particularly for use
with boats are described on page 120. It is practically impossible to
string a tag line for discharge measurements from a boat when the
width of the stream is greater than 2,500 ft (750 m). The methods
used to determine width at such sites are described on pages 156- 157.
EQUIPMENT ASSEMBLIES
Special equipment is necessary for each type of current-meter
measurement. The meters, weights, and reels used have already been
described. The additional equipment needed is described in this sec-tion.
The special equipment assemblies have been divided into five basic
groups: cableway, bridge, boat, ice, and velocity-azimuth-depth as-sembly
(VADA) equipment.
The cableway provides a track for the operation of a cable car from
which the hydrographer makes a current-meter measurement. Cable

cars aIso support the sounding reel and other necessary equipment.
Both sitdown and standup types of cable cars are used in stream
gaging. (See figs. 67 and 68). Pierce (1947) describes plans for both
types. Normally, sitdown cars are used for cableway spans less than
400 ft (122 m) and for those spans where the lighter sounding weights
are used. The standup car is used on the longer spans and where
heavy sounding weights are needed.
The cars are moved from one point to another on the cableway by
means of cable-car pullers. (See fig. 69.) The standard car puller is a
cast aluminum piece with a snub attached to act as a brake. The snub,
usually four-ply belting, is placed between one of the car sheaves and
the cable to prevent movement of the car along the cable. A second-type
puller is used when a car is equipped with a follower brake (fig.
69). A third type, the Colorado River cable-car puller, is the same in
principle as the puller used on cars equipped with a follower brake.
Power-operated cable cars are available for extremely long spans or
other special situations. (See fig. 70.)
Sitdown cable cars have a variety of means of supporting the sound-ing
reel. A-pack and Canfield reels are designed to clamp on the side
of the car (fig. 71). Permanent or portable reel seats are attached to
the cable cars for larger reels. (See figs. 67 and 72.)
FIGURE 66 -Tag-line reels: top left, Pakron; top right, Lee-Au with removable hub in
front; bottom, Columbus type A.

FIGURE 67.-Sitdown cable car.
FIGURE 68.-Standup cable car.

FIGURE 69.-Cable-car puller for follower-brake cable cars, left; for stan-dard
cars, right.

FIGURE ‘IO.-Power-operated cable cars. (A ) battery-powered car; (B) gasoline-powered
car.

Standup cable cars have reel seats attached to the structural mem-bers
of the car (fig. 68). A sheave attached to the structural members
carries the sounding line so that the sounding weight and current
meter will clear the bottom of the car. Power reels can also be used on
standup cable cars.
Carrier cableways are sometimes used on the smaller streams for
measuring discharge as well as for sediment sampling. They are used
in areas where it is impossible to wade, where no bridges are avail-
FIGURE 71.-Sitdown cable car with Canfield reel clamped to side of car.

able, and where it has been impractical to build a complete cableway.
The assembly is operated from the shore (fig. 73). Carrier cables are
FIGURE 72.-Portable reel seat on sitdown-type cable car. (Note tags on sounding
cable.)

more widely used in Europe, particularly in the United Kingdom,
than they are in the U.S.A.
BRIDGE EQUIPMENT
When one measures from a bridge, the meter and sounding weight
can be supported by a handline, or by a sounding reel mounted on a
crane, or by a bridge board. The handline has been described on pages
104- 108.
Two types of hand-operated portable cranes are the type A (figs. 74
and 75) for use with weights up to 100 lb (45.4 kg) and the type E for
heavier weights.
All cranes are designed so that the superstructure can be tilted
FIGURE 73.-Carrier (bank-operated) cableway. Two reels are used; one moves the
meter assembly laterally, and the other moves the current meter vertically.

forward over the bridge rail far enough for the meter and weight to
clear most rails. Where bridge members obstruct the movement of the
crane from one vertical to the next, the weight and meter can be
brought up, and the superstructure can be tilted back to pass by the
obstruction. (See figs. 74 and 75.)
Cast-iron counterweights weighing 60 lb (27.2 kg) each are used
with four-wheel-base cranes. (See fig. 75.) The number of such
weights needed depends upon the size of the sounding weight being
supported, the depth and velocity of the stream, and the amount of
debris being carried by the stream.
A protractor is used on cranes to measure the angle the sounding
line makes with the vertical when the weight and meter are dragged
downstream by the water. The protractor is a graduated circle
clamped to an aluminum plate. A plastic tube, partly filled with col-ored
antifreeze, fitted in a groove between the graduated circle and
FIGURE 74.-Type-A crane with three-wheel base. (During soundings and velocity
observations the crane is tilted against the bridge rail. An A-55 reel is mounted on
the crane.)

the plate, is the protractor index. A stainless-steel rod is attached to
the lower end of the plate to ride against the downstream side of the
sounding cable. The protractor will measure vertical angles from
-25” to +90”. The cranes in figures 74 and 75 are equipped with
protractors at the outer end of the boom.
Bridge boards may be used with an A-pack or A-55 sounding reel
and with weights up to 50 lb (22.7 kg). A bridge board is usually a
plank about 6 to 8 ft (1.8 to 2.4 m) long with a sheave at one end over
which the meter cable passes and a reel seat near the other end. The
board is placed on the bridge rail so that the force exerted by the
sounding weight suspended from the reel cable is counterbalanced by
the weight, of the sounding reel (fig. 76). The bridge board may be
hinged near the middle to allow one end to be placed on the sidewalk
or roadway.
Many special arrangements for measuring from bridges have been
FIGURE 75.-Type-A crane with four-wheel base with boom in retracted position. (A
B-56 reel is mounted on crane. Note fluid protractor on outer end of boom.)

devised to suit particular purposes. Truck-mounted cranes are often
used for measuring from bridges over the larger rivers. (See fig. 77.)
Monorail stream-gaging cars have been developed for large rivers.
The car is suspended from the substructure of the bridge by means of
an I-beam. The car is attached to the I-beam track by trolleys and is
propelled by a forklift motor having a wheel in contact with the bot-tom
of the beam. The drive mechanism and sounding equipment are
powered by a 430-ampere-hour, 450-lb (204-kg), 12-volt battery.
BOAT EQUIPMENT
Measurements made from boats require special equipment not used
for other types of measurement. Extra-large tag-line reels are used on
wide streams. Three different tag-line reels are used by the U.S.
Geological Survey for boat measurements:
1. A heavy duty horizontal-axis reel without a brake and with a
capacity of 2,000 ft (610 m) of %-in (3.1%mm)-diameter cable
(fig. 78).
FIGURE 76.-Bridge board in use.

2. A heavy-duty horizontal-axis reel with a brake and with a ca-pacity
of 3,000 ft (914 m) of %-in-diameter cable (fig. 79).
3. A vertical-axis reel without a brake and with a capacity of 800 ft
(244 m) of ?&in-diameter cable (fig. 80).
A utility line of 30 ft (9 m) of 3/32-in (2.38-mm&diameter cable with
a harness snap at one end and a pelican hook at the other is connected
to the free end of the boat tag line and fastened around a tree or post,
thereby preventing damage to the tag line. After the tag line is
strung across the stream, the reel is usually bolted to a plank and
chained to a tree. The tag line has station markers at appropriate
intervals.
Special equipment is necessary to suspend the meter from the boat
when the depths are such that a rod suspension cannot be used. A
crosspiece reaching across the boat is clamped to the sides of the boat
and a boom attached to the center of the cross piece extends out over
the bow. (See fig. 81.) The crosspiece is equipped with a guide sheave
and clamp arrangement at each end to attach the boat to the tag line
and make it possible to slide the boat along the tag line from one
station to the next. A small rope can be attached to these clamps so
FIGURE 77.-Truck-mounted crane used on the Mississippi River.

that in an emergency a tug on the rope will release the boat from the
tag line. The crosspiece also has a clamp that prevents lateral move-ment
of the boat along the tag line when readings are being made.
The boom consists of two structural aluminum channels, one tele-scoped
within the other to permit adjustments in length. The boom is
equipped with a reel plate on one end; on the other end is a sheave
over which the meter cable passes. The sheave end of the boom is
designed so that by adding a cable clip to the sounding cable, a short
distance above the connector, the sheave end of the boom can be
retracted when the meter is to be raised out of the water. The raised
FIGURE 78.-Horizontal-axis boat tag-line reel without a brake.

meter is easy to clean and is in a convenient position when not being
operated.
All sounding reels fit the boat boom except the A-pack and the
Canfield reels, which can be made to fit by drilling additional holes in
the reel plate on the boom.
In addition to the equipment already mentioned, the following
items are needed when making boat measurements:
1. A stable boat big enough to support the hydrographers and equip-ment.
2. A motor that can move the boat with ease against the maximum
current in the stream.
3. A pair of oars for standby use.
4. A life preserver for each hydrographer.
5. A bailing device.
Figure 82 shows the equipment assembled in a boat.
FIGURE 79.-Horizontal-axis boat tag-line reel with a brake.

ICE EQUI P.MENT
Current-meter measurements made under ice cover require special
equipment for cutting holes in the ice through which to suspend the
meter.
Cutting holes through the ice on streams to make discharge meas-urements
has long been a laborious and time-consuming job. The
development of power ice drills, however, has eliminated many of the
difficulties and has reduced considerably the time required to cut the
holes. Holes are often cut with a commercial ice drill that cuts a 6-in
(0.15-m) diameter hole (fig. 83). The drill weighs about 30 lb (13.6
FIGURE SO.-Vertical-axis boat tag-line reel (when in use the axis of the reel is vertl-
Cal).

kg) and under good conditions will cut through 2 ft (0.6 m) of ice in
about a minute.
Where it is impractical to use the ice drill, ice chisels are used to cut
the holes. Ice chisels used are usually 4 or 4% ft (about 1.3 m) long
and weigh about 12 lb (5.5 kg). The ice chisel is used when first
crossing an ice-covered stream to determine whether the ice is strong
enough to support the hydrographer. If a solid blow of the chisel blade
does not penetrate the ice, it is safe to walk on the ice, providing the
ice is in contact with the water.
Some hydrographers supplement the ice chisel with a Swedish ice
auger. The cutting blade of this auger is a spadelike tool of hardened
steel that cuts a hole 6-8 in (0.15-0.20 m) in diameter. The auger is
operated by turning a bracelike arrangement on top of the shaft.
When holes are cut in the ice the water, which is usually under
pressure because of the weight of the ice, rises in the hole. To deter-mine
the effective depth of the stream (p. 153-154), ice-measuring
sticks are used to measure the distance from the water surface to the
FIGURE 81.-Boom and crosspiece for use on boats. (A, retractable end of boom; B,
guide sheave and clamp for attaching to’tag line; C, clamp to prevent movement of
the boat along the tag line; D, plate to accomodate reel; E, rope to release clamps (Z3)
to free boat from tag line; and F, clamps to attach crosspiece to boat.)

bottom of the ice. This is done with a bar about 4 ft long (1.2 m), made
of strap steel or wood, which is graduated in feet and tenths of a foot
and has an L-shaped projection at the lower end. The horizontal part
of the L is held on the underside of the ice, and the depth to that point
FIGURE 82.-Measuring equipment set up in a boat.

is read at the water surface on the graduated part of the stick. The
horizontal part of the L is at least 4 in (0.1 m) long so that it may
FIGURE 83.-Gasoline-powered ice drill. (Photograph by permission of General Equip-ment
Co.)

extend beyond any irregularities on the underside of the ice.
When the total depth of water under ice cover is greater than 10 or
12 ft (3.0 or 3.6 m), a sounding reel or handline is usually used. The
sounding reel is mounted on a collapsible support set on runners. (See
fig. 84.)
A special ice-weight assembly is used for sounding under ice be-
FIGURE %-Collapsible reel support and ice-weight assembly.

cause a regular sounding weight will not fit through the hole cut by
the ice drill (fig. 84). The weights and meter are placed in a
framework that will pass through the drilled hole.
VELOCITY-AZIMUTH-DEPTH ASSEMBLY
The velocity-azimuth-depth assembly, commonly called VADA,
combines a sonic sounder with a remote-indicating compass and Price
current meter to record depth, indicate the direction of flow, and
permit observations of velocity at any point.
In figure 85, the azimuth-indicating unit is shown mounted on a
four-wheel crane. Incorporated within the remote-indicator box is the
battery for the current-meter circuit, the headphone jacks, and the
two-conductor jack for the sonic sounder. A switch allows the remote-indicating
unit to be used separately or in conjunction with the sonic
sounder. The sonic sounder is described on page 108. This assembly is
useful in tidal investigations and in other special studies, as well as
at regular gaging stations, where it is desirable to determine the
FIGURE 85.-Velocity-azimuth-depth assembly.

direction of flow beneath the water surface, because of the possibility
that it may differ from that at the surface.
MISCELLANEOUS EQUIPMENT
Several miscellaneous items that have not been described are nec-essary
when current-meter measurements are made. Three
classifications of this equipment are timers, counting equipment, and
waders and boots.
In order to determine the velocity at a point with a current meter, it
is necessary to count the revolutions of the rotor in a measured inter-val
of time, usually 40-70 s. The velocity is then obtained from the
meter-rating table (fig. 51). The time interval is measured to the
nearest second with a stopwatch.
The revolutions of the meter rotor during the observation of veloc-ity
are counted by an electric circuit that is closed each time the
contact wire touches the single or penta eccentric of the current me-ter.
A battery and headphone are part of the electrical circuit, and a
click is heard in the headphone each time the contact wire touches.
(See fig. 86.) Compact, comfortable hearing-aid phones have been
adapted by some to replace the headphones.
A magnetic-switch contact chamber has been developed to replace
the contact-wire chamber (p. 87). An automatic electric counter has
also been developed for use with the magnetic contact chamber (fig.
86). The counter can register up to 999 and has a reset button. A
metal clip is attached to the counter so that it may be easily carried
on the hydrographer’s belt. The electric counter should not be used
with the contact-wire chamber, because at low velocities the contact
wire wipes irregularly thereby sending several signals to the counter
for each revolution.
FIGURE 86.-Automatic counter (left) and headphone (right).

Waders or boots are needed when wading measurements are made.
Waders should be loose fitting even after allowance has been made for
heavy winter clothing. Ice creepers strapped on the shoe of boots or
waders should be used on steep or icy streambanks and on rocky or
smooth and slippery streambeds. (See fig. 87.)
MEASUREMENT OF VELOCITY
The current meter measures velocity at a point: The method of
making discharge measurements at a cross section requires determi-nation
of the mean velocity in each of the selected verticals. The mean
velocity in a vertical is obtained from velocity observations at many
points in that vertical, but it can be approximated by making a few
velocity observations and using a known relation between those ve-locities
and the mean in the vertical. The more commonly used
methods of determining mean vertical velocity are:
FIGURE 87.-Ice creepers for boots and waders.

1. Vertical-velocity curve.
2. Two-point.
3. Six-tenths-depth.
4. Three-point.
5. Two-tenths depth.
6. Subsurface-velocity.
7. Surface-velocity.
8. Integration.
Less commonly used are the following multipoint methods of deter-mining
mean vertical velocity:
9. Five-point.
10. Six-point.
VERTICAL-VELOCITY CURVE METHOD
In the vertical-velocity curve met.hod a series of velocity observa-tions
at points well distributed between the water surface and the
streambed are made at each of the verticals. If there is considerable
curvature in the lower part of the vertical-velocity curve, it is advis-able
to space the observations more closely in that part of the depth.
Normally, the observations are taken at O.l-depth increments be-tween
0.1 and 0.9 of the depth. Observations are always taken at 0.2,
0.6, and 0.8 of the depth so that the results obtained by the vertical-velocity
curve method may be compared with those obtained by the
more commonly used methods of velocity observation. Observations
are made at least 0.5 ft (0.15m) below the water surface and above the
streambed when the Price AA meter or the vane meter is used and
are made at least 0.3 ft (0.09 m) from those boundaries when the Price
pygmy meter is used; those meters underregister velocity when
placed closer to the water surface or streambed.
The vertical-velocity curve for each vertical is based on observed
velocities plotted against depth (fig. 88). In order that vertical-velocity
curves at different verticals may be readily compared, it is
customary to plot depths as proportional parts of the total depth. The
mean velocity in the vertical is obtained by measuring the area be-tween
the curve and the ordinate axis with a planimeter, or by other
means, and dividing the area by the length of the ordinate axis.
The vertical-velocity curve method is valuable in determining co-efficients
for application to the results obtained by other methods but
is not generally adapted to routine discharge measurements because
of the extra time required to collect field data and to compute the
mean velocity.
Intensive investigation of vertical-velocity curves by Hulsing,
Smith, and Cobb (1966) resulted in table 2 which shows average
ordinates of the vertical-velocity curve.

0
60
l-b-
8C
WI 4TI ER SURFACE
0.40 0.60 0.80 1.00
VELOCITY, IN FEET PER SECOND
1.2 0
100 L
0.20
FIGURE 88.-Typical vertical-velocity curve.
TABLE 2.-coefficients for standard verticahelocity curve
Ratio of pomt velocity
Ratlo of observatmnd epth to meanv elocityI n
to depth of water the vertical
0.05 ___________ ---------- _______ - _-------- 1.160
.l ______----------_-__------------------ 1.160
.2 __________--_--------------~---------- 1.149
.3 ____________---------------~---------- 1.130
.4 _________________--------------------- 1.108
.5 ________________---------------------- 1.067
.6 _________________---__________________ 1.020
.7 ________________---------------------- .953
.8 __________---------___________________ .871
.9 _-----------------_------------------- .746
.95 ________________ -------- ____~~~~~~-~~~ ,648

TWO-POINT METHOD
In the two-point method of measuring velocities, observations are
made in each vertical at 0.2 and 0.8 of the depth below the surface.
The average of those two observations is taken as the mean velocity
in the vertical. This method is based on many studies involving ac-tual
observation and mathematical theory. Experience has shown
that this method gives more consistent and accurate results than any
of the other methods listed, other than the five-point, six-point, and
vertical-velocity curve methods. The two-point method is the one
generally used by the U.S. Geological Survey. Table 2 indicates that
the two-point method, on the average, gives results that are within 1
percent of the true mean velocity in the vertical.
The two-point method is not used at depths less than 2.5 ft (0.76 m)
when measuring with a Price current meter, because the meter would
then be too close to the water surface and to the streambed to give
dependable results.
The vertical-velocity curve will be distorted by overhanging vege-tation
that is in contact with the water or by submerged objects, such
as large rocks and aquatic growth, if those elements are in close
proximity, either in the upstream or downstream direction, to the
vertical in which velocity is being measured. Where that occurs the
two-point method will not give a reliable value of the mean velocity in
the vertical, and an additional velocity observation at 0.6 of the depth
should be made. The three observed velocities should then be used in
the three-point method (p. 135). A rough test of whether or not the
velocities at the 0.2 and 0.8 depths are sufficient for determining
mean vertical velocity is given in the following criterion: the 0.2-
depth velocity should be greater than the O.&depth velocity but less
than twice as great.
SIX-TENTHS DEPTH METHOD
In the 0.8depth method, an observation of velocity made in the
vertical at 0.6 of the depth below the surface is used as the mean
velocity in the vertical. Actual observation and mathematical theory
have shown that the 0.6-depth method gives reliable results. (See
table 2.) The U.S. Geological Survey uses the 0.6-depth method under
the following conditions:
1. Whenever the depth is between 0.3 ft (0.09 m) and 1.5 ft (0.46 m)
and a Price pygmy meter is being used, or between 1.5 ft (0.46
m) and 2.5 ft (0.76 m) and a Price type AA (or type A) meter is
being used. (See table 3 for depth and velocity limitations of
each meter.)
2. When large amounts of slush ice or debris make it impossible to

observe the velocity accurately at the 0.2 depth. That condition
prevents the use of the two-point method.
3. When the distance between the meter and the sounding weight is
too great to permit placing the meter at the 0.8 depth. That
circumstance prevents the use of the two-point method.
4. When the stage in a stream is changing rapidly and a measure-ment
must be made quickly.
Although, the preceding paragraph states that the 0.6-depth
method may be used with a pygmy meter when water depths are as
shallow as 0.3 ft (0.09 m), strictly speaking, the O.&depth method
should not be used when depths are less than 0.75 ft (0.23 m). This
follows from the fact that the pygmy meter underregisters when set
closer to the streambed than 0.3 ft (p. 132). From a practical
standpoint, however, when it is necessary to measure velocities
where water depths are as shallow as 0.3 ft, the 0.6-depth method is
used. It is recognized, however, that the results obtained in that situ-ation
are only approximate values that underestimate the true veloc-ity.
Efforts made to date to define shallow-depth coefficients for natu-ral
streams have been unsuccessful.
THREE-POINT METHOD
In the three-point method velocities are observed at 0.2,0.6, and 0.8
of the depth, thereby combining the two-point and 0.6-depth methods.
The mean velocity is computed by averaging the 0.2- and 0.8-depth
observations and then averaging that result with the 0.6-depth ob-servation.
When more weight to the 0.2- and 0.8-depth observations is
desired, the arithmetical mean of the three observations may be used.
The first procedure is usually followed, however.
The three-point method is used when the velocities in the vertical
are abnormally distributed, as explained on page 134. When a Price
type AA (or type A) current meter is used, the three-point method
cannot be applied unless the depths are greater than 2.5 ft (0.76 m).
(See table 3.)
TWO-TENTHS-DEPTH METHOD
In the 0.2-depth method the velocity is observed at 0.2 of the depth
below the surface and a coefficient is applied to the observed velocity
to obtain the mean in the vertical. The method is principally used for
measuring flows of such high velocity that it is not possible to obtain
depth soundings or to position the meter at the 0.8 or 0.6 depth.
A standard cross section or a general knowledge of the cross section
at a site is used to compute the 0.2 depth when it is impossible to
obtain soundings. A sizable error in an assumed 0.2 depth is not
critical in the determination of velocity because the slope of the

vertical-velocity curve at this point is usually nearly vertical. (See fig.
88.) The 0.2 depth is also used in conjunction with the sonic sounder
for flood measurements. (See p. 108.)
The measurement made by the O.%-depth method is normally com-puted
by using the 0.2-depth velocity observations without coeffi-cients,
as though each observation were a mean in the vertical. The
approximate discharge thus obtained divided by the area of the
measuring section gives the weighted mean value of the 0.2-depth
velocity. Studies of many measurements made by the two-point
method show that for a given measuring section the relation between
the mean 0.2-depth velocity and the true mean velocity either re-mains
constant or varies uniformly with stage. In either circum-stance,
this relation may be determined for a particular 0.2-depth
measurement by recomputing measurements made at the site by the
two-point method using only the 0.2-depth velocity observation as the
mean in the vertical. The plotting of the true mean velocity versus
the mean 0.2-depth velocity for each measurement will give a
velocity-relation curve for use in adjusting the mean velocity for
measurements made by the 0.2-depth method.
If at a site too few measurements have been made by the two-point
method to establish a velocity-relation curve, vertical-velocity curves
are needed to establish a relation between the mean velocity and the
0.2-depth velocity. The usual coefficient to adjust the 0.2-depth veloc-ity
to the mean velocity is about 0.87. (See table 2.)
The 0.2-depth method is not as reliable as either the two-point
method or the 0.8depth method when conditions are equally favor-able
for a current-meter measurement by any of the three methods.
SUBSURFACE-VELOCITY METHOD
In the subsurface-velocity method the velocity is observed at some
arbitrary distance below the water surface. That distance should be
at least 2 ft (0.6 m), and preferably more for deep swift streams to
avoid the effect of surface disturbances. The subsurface-velocity
method is used, in the absence of an optical current meter, when it is
impossible to obtain soundings and the depths cannot be estimated
with sufficient reliability to even approximate a 0.2-depth setting for
a conventional current-meter measurement. Coefficients are neces-sary
to convert the velocities observed by the subsurface-velocity
method to the mean velocity in the vertical. A prerequisite in obtain-ing
those coefficients is to determine the depths during the measure-ment
from soundings made after the stage has receded enough for
that purpose. Those depths are used with the known setting of the
current meter below the water surface to compute ratios of depth of
observation to total depth during the measurement. The coefficients

to be used with the subsurface-velocity observations can then be com-puted
either by use of the data in table 2 or by obtaining vertical-velocity
curves at the reduced stage of the stream.
SURFACE-VELOCITY METHOD
If an optical current meter (p. 91-93) is available, the surface-velocity
method is used in preference to the subsurface-velocity
method described above. In a natural channel a surface-velocity coeffi-cient
of 0.85 or 0.86 is used to compute mean velocity on the basis of
the data in table 2. In a smooth artificial channel a surface-velocity
coefficient of 0.90 is used. If the artificial channel has smooth vertical
walls, the coefficients shown in figure 89 are used in the vicinity of
the walls. Figure 89 is based on data obtained in a laboratory study.
The fact that the coefficients close to the wall are greater than unity
is explained by the fact that the secondary currents that form near
0.85;
DISTANCE
I
FROM
2 3
VERTICAL WALL OF CHANNEL,
RATIO OF DEPTH OF FLOW
EXPRESSED AS A
FIGURE 89.-Relation of surface-velocity coefficient to distance from vertical wall of a
smooth rectangular channel.

the walls depress the position of the filaments of maximum velocity;
that is, the maximum velocity in a vertical close to the wall does not
occur at the water surface.
INTEGRATION METHOD
In the integration method the meter is lowered in the vertical to the
bed of the stream and then raised to the surface at a uniform rate.
During this passage of the meter the total number of revolutions and
the total elapsed time are used with the current-meter rating table to
obtain the mean velocity in the vertical. The integration method can-not
be used with a vertical-axis current meter because the vertical
movement of the meter affects the motion of the rotor; consequently,
the method is not used in the U.S.A., where the Price meter is the
standard current meter. However, the integration method is used to a
degree in European countries where horizontal-axis meters are the
standard current meters. The accuracy of the measurement is depen-dent
on the skill of the hydrographer in maintaining a uniform rate of
movement of the meter. A disadvantage of the method is the inability
of the meter to measure streambed velocities because the meter can-not
be placed that low. Coefficients smaller than unity are therefore
required to correct the observed integrated velocity.
FIVE-POINT METHOD
The five-point method is rarely used in the U.S.A. Velocity observa-tions
are made in each vertical at 0.2, 0.6, and 0.8 of the depth below
the surface, and as close to the surface and to the streambed as practi-cal.
The European criteria for surface and bottom observations state
that the horizontal axis of the current meter should not be situated at
a distance less than 1% times the rotor height from the water surface,
nor should it be situated at a distance less than 3 times the rotor
height from the streambed. In addition, no part of the meter should
break the surface of the water.
The velocity observations at the five meter positions are plotted in
graphical form, and the mean velocity in the vertical is determined by
the use of a planimeter, as explained on page 132. As an alternative,
the mean velocity may be computed from the equation
V ITICI"= 0. wsurhx + 3v, 2 + 3v,,, + 2v,,., + Vbed).
SIX-POINT METHOD
The six-point method is rarely used in the U.S.A., but is sometimes
used in European countries in situations where the existence of a
distorted vertical-velocity distribution is known or suspected; for
example, in the presence of aquatic growth or under ice cover. Veloc-

ity observations are made in each vertical at 0.2, 0.4, 0.6, and 0.8 of
the depth below the surface, and also close to the surface and to the
streambed. The criteria for surface and streambed observations are
those given in the discussion above.
The velocity observations at the six meter positions are plotted in
graphical form and the mean velocity in the vertical is determined by
planimetering the area bounded by the vertical-velocity curve and
the ordinate axis, as explained on page 132. The mean velocity may
also be computed mathematically from the equation,
V IlEa” = 0. UVsurface + 2vo.2 + 2v,.‘l + 2V” 6 + 2VO.8 + Vbed.
PROCEDURE FOR CONVENTIONAL CURRENT-METER
MEASUREMENT OF DISCHARGE
The first step in making a conventional current-meter measure-ment
of discharge is to select a measurement cross section of desirable
qualities. If the stream cannot be waded, and high-water meas-urements
are made from a bridge or cableway, the hydrographer has
no choice with regard to selection of a measurement cross section. If
the stream can be waded, the hydrographer looks for a cross section of
channel with the following qualities:
1. Cross section lies within a straight reach, and streamlines are
parallel to each other.
2. Velocities are greater than 0.5 ftls (0.15 m/s) and depths are
greater than 0.5 ft (0.15 m).
3. Streambed is relatively uniform and free of numerous boulders
and heavy aquatic growth.
4. Flow is relatively uniform and free of eddies, slack water, and
excessive turbulence.
5. Measurement section is relatively close to the gaging-station con-trol
to avoid the effect of tributary inflow between the measure-ment
section and control and to avoid the effect of storage be-tween
the measurement section and control during periods of
rapidly changing stage.
It will often be impossible to meet all of the above criteria, and when
that is the case, the hydrographer must exercise judgment in select-ing
the best of the sites available for making the discharge meas-urement.
If the stream cannot be waded and the measurement must be made
from a boat, the measurement section selected should have the attri-butes
listed above, except for those listed in item 2 concerning depth
and velocity. Depth is no consideration in a boat measurement; if the
stream is too shallow to float a boat, the stream can usually be waded.
However, velocity in the measurement section is an important con-

sideration. If velocities are too slow, meter registration may be af-fected
by an oscillatory movement of the boat, in which the boat, even
though fastened to the tag line, moves upstream and downstream as a
result of wind action; or, where a vertical-axis meter is used, meter
registration may be affected by vertical movement of the boat as a
result of wave action (p. HO- 181). If velocities are too fast, it becomes
difficult to string the tag line across the stream.
Regardless of the type of measurement that is to be made, if the
gaging station is downstream from a hydroelectric powerplant, the
stage will be changing too rapidly, most of the time, to assure a
satisfactory discharge measurement. The hydrographer should ob-tain
a schedule of operations from the powerplant operator, or deter-mine
the operating schedule from the gage-height chart, and plan to
make his discharge measurements near the crest or trough of the
stage hydrograph, or during periods of near-constant discharge from
the powerplant.
After the cross section has been selected, the width of the stream is
determined. A tag line or measuring tape is strung across the meas-urement
section for measurements made by wading, from a boat,
from ice cover, or from an unmarked bridge. Except where a bridge is
used, the line is strung at right angles to the direction of flow to avoid
horizontal angles in the cross section. For cableway or bridge meas-urements,
use is made of the graduations painted on the cable or
bridge rail as described on page 110. Next the spacing of the verticals
is determined to provide about 25 to 30 subsections. If previous dis-charge
measurements at the site have shown uniformity of both the
cross section and the velocity distribution, fewer verticals may be
used. The verticals should be so spaced that no subsection has more
than 10 percent of the total discharge. The ideal measurement is one
in which no subsection has more than 5 percent of the total discharge,
but that is seldom achieved when 25 subsections are used. (The dis-charge
measurement notes in figure 42 show that the subsection with
the greatest discharge had 6.2 percent of the total discharge.) It is not
recommended that all observation verticals be spaced equally unless
the discharge is evenly distributed across the stream. The spacing
between verticals should be closer in those parts of the cross section
that have the greater depths and velocities.
After the stationing of the observation verticals has been deter-mined,
the appropriate equipment for the current-meter measure-ment
is assembled and the measurement note sheets for recording
observations are prepared. (See fig. 42.) The following information
will be recorded for each discharge measurement:
1. Name of stream and location to correctly identify the established
gaging station; or name of stream and exact location of site for a
miscellaneous measurement.

2. Date, party, type of meter suspension, and meter number.
3. Time measurement was started using military time (24-hr clock
system).
4. Bank of stream that was the starting point.
5. Control conditions.
6. Gage heights and corresponding times.
7. Water temperature.
8. Other pertinent information regarding the accuracy of the dis-charge
measurement and conditions which might affect the
stage-discharge relation.
The streambank is identified by the letters LEW or REW (left edge
of water or right edge of water, respectively, when facing
downstream). The time is recorded periodically in the notes during
the course of the measurement. If the gaging station is equipped with
a digital recorder it is advantageous to synchronize the time observa-tions
with the punch cycle of the recorder. (See fig. 42.) The time
observations are important for computing the mean gage height of
the discharge measurement, if the measurement is made during a
period of appreciable change in stage. (See p. 170-173.) When the
discharge measurement is completed, the time is recorded along with
the streambank (LEW or REW) where the measurement ended.
We have digressed somewhat in discussing the measurement notes
and now return to the details of the discharge measurement. After
the note sheet is readied, the meter assembly is checked. The meter
should balance on the hanger used and should spin freely; the electric
circuit through the meter should operate satisfactorily; and the stop-watch
should check satisfactorily in a comparison with the hydrog-rapher’s
watch. After recording on the note sheet the station (distance
from initial point) of the edge of water, the actual measurement is
ready to be started.
Depth (if any) at the edge of water is measured and recorded. The
depth determines the method of velocity measurement to be used,
normally the two-point method (p. 134) or the 0.6-depth method (p.
134). The setting of the meter for the particular method to be used is
then computed, and the meter position is recorded, using a designa-tion
such as 0.8 or 0.6 or 0.2, as the case may be. After the meter is
placed at the proper depth and pointed into the current, the rotation
of the rotor is permitted to become adjusted to the speed of the current
before the velocity observation is started. The time required for such
adjustment is usually only a few seconds if velocities are greater than
1 ft/s (0.3 m/s), but for slower velocities, particularly if the current
meter is suspended on a cable, a longer period of adjustment is
needed. After the meter has become adjusted to the current, the
number of revolutions made by the rotor is counted for a period of 40
to 70 s. The stopwatch is started simultaneously with the first signal

or click, which is counted as “zero,” and not “one.” The count is ended
on a convenient number coinciding with one of those given in the
column headings of the meter rating table. The stopwatch is stopped
on that count and is read to the nearest second or to the nearest even
second if the hand of the stopwatch is on a half-second mark. That
number of seconds and the number of revolutions are then recorded.
If the velocity is to be observed at more than one point in the
vertical, the meter setting for the additional observation is deter-mined,
the revolutions are timed, and the data are recorded. The
hydrographer moves to each of the observation verticals and repeats
the above procedure until the entire cross section has been traversed.
For each vertical he records distance from initial point, water depth,
meter-position depth, revolutions of the meter, and the time interval
associated with those revolutions (fig. 42).
Consideration must be given to the direction of flow, because it is
the component of velocity normal to the measurement section that
must be determined. The discussion that follows concerns currents
that approach the measurement section obliquely, at angle a (fig. 47).
If, in a wading measurement, the meter used is a horizontal-axis
meter with a component propellor, such as the Ott meter, the propel-lor
should be pointed upstream at right angles to the cross section,
but only if (Y is less than 45”. Such a meter will register the desired
component of velocity normal to the cross section, when (Y is less than
45”. If (Y is greater than 45”, the component meter should be pointed
into the current. All other meters on a wading-rod suspension should
likewise be pointed into the current. Any meter on a cable suspen-sion,
as is used for the higher stages, will automatically point into the
current because of the effect of the meter vanes. When the meter is
pointed into an oblique current the measured velocity must be mul-tiplied
by the cosine of the angle (a) between the current and a per-pendicular
to the measurement section in order to obtain the desired
normal component of the velocity.
In the U.S.A., either of two methods is used to obtain cosine (Y (fig.
47). In the first method, use is made of the field notes which have a
point of origin (0) printed on the left, margin and cosine values on the
right margin (fig. 42). The cosine of the angle of the current is meas-ured
by holding the note sheet in a horizontal position with the point
of origin on the tag line, bridge rail, cable rail, or any other feature
parallel to the cross section (fig. 90). With the long side of the note
sheet parallel to the direction of flow, the tag line or bridge rail will
intersect the value of cosine a on the top, bottom, or right edge of the
note sheet. The direction of the current will be apparent from the
direction of movement of floating particles. If the water is clear of
floating material, small bits of floating material are thrown into the

stream and the edge of the note sheet is alined parallel to the direc-tion
of movement. If no such material is available, the inelegant, but
time-honored method of spitting into the stream is used to obtain an
indicator of the direction of flow. The measured velocity is multiplied
by the cosine of the angle to determine the velocity component normal
to the measurement section.
The second, and more reliable, method of obtaining cosine a in-volves
the use of a folding foot-rule. These rules, which are either 3 or
6 ft long, are graduated in hundreths of a foot and are jointed every
half foot. The first 2 ft of the rule is extended, the 2.00-ft marker is
placed on the tag line or bridge rail (fig. 91), and the rule is alined
with the direction of the current. The rule is folded at the 1-ft mark so
that the first foot of the rule is normal to the tag line or bridge rail.
That reading, subtracted from 1.00, is cosine o. For example, if the
reading on the rule is 0.09 ft, cosine (Y equals 0.91.
Details peculiar to each of the various types of current-meter
measurement are described in the sections of the manual that follow.
CURRENT-METER MEASUREMENT BY WADING
Current-meter measurements are best made by wading, if condi-tions
permit. (See fig. 92.) Wading measurements have a distinct
advantage over measurements made from cableways or bridges in
that it is usually possible to select the best of several available
cross sections for the measurement. The type AA or pygmy meter
is used for wading measurements in the U.S.A. Table 3 lists the
type of meter and velocity method to be used for wading measure-ments
at various depths.
Some departure from table 3 is permissible. For example, if a type
Meter m stream
Tag line, edge of cable
car, or bridge rail
-
FIGURE 90.-Measurement of horizontal angle with measurement-note sheet.

AA meter is being used in a measurement section that has almost all
its depths greater than 1.5 ft (0.46 ml, the pygmy meter should not be
substituted for the few depths that are less than 1.5 ft, or vice versa.
With regard to the use of the type AA meter in depths less than 1.5 ft,
strictly speaking, that meter should not be used in depths less than
1.25 ft (0.38 m). A depth of 1.25 ft will accommodate the 0.6-depth
method without causing the meter to be set closer than 0.5 ft from the
streambed; if the meter is set any closer to the streambed it will
underregister the velocity (p. 132). However, if the hydrographer is
using the type AA meter in a measurement section that has only few
verticals shallower than 1.25 ft, he may use that meter for depths
that are even as shallow as 0.5 ft (0.15 m) without changing to a
pygmy meter. The hydrographer must make a judgment decision. He
knows that his meter is underregistering the velocity by some un-known
percentage in the depths shallower than 1.25 ft, but if that
shallow-depth flow represents less than 10 percent of the total dis-charge,
his total measured discharge should not be too greatly in
error.
Neither the type AA meter nor the pygmy meter should be used for
measuring velocities slower than 0.2 ft/s, unless absolutely necessary.
If depths or velocities under natural conditions are too low for a
dependable current-meter measurement, the cross section should be
modified, if practical, to provide acceptable conditions. It is often pos-
Tag line, edge of cable
/ car, or bridge rail
Folding foot-rule
FIGURE 91.-Measurement of horizontal angle with folding foot-rule.

sible to build temporary dikes to eliminate slack water or shallow
depths in a cross section, or to improve the cross section by removing
rocks and debris within the section and in the reach of channel im-
FIGURE 92.-Wading measurement using top-setting rod.
TABLE 3.-Current-meter and velocity-measurement method for various depths (wading
measurement)
Depth Meter Velcclty method
(iv (ml
2.5 or more 0.76 or more Type AA (or type A) 0.2 and 0.8
1.5-2.5 0.46-0.76 ____ do --__ .6
.3-1.5 .09- .46 Pygmy’ .6
‘Used when velocltlss are less than 2 5 Otis (0 76 m/s)

mediately upstream and downstream from the section. After the cross
section has been modified, the flow should be allowed to stabilize
before starting the discharge measurement.
The hydrographer should stand in a position that least affects the
velocity of the water passing the current meter. That position is
usually obtained by facing the bank so that the water flows against
the side of the leg. The wading rod is held at the tag line by the
hydrographer who stands about 3 in (0.07 m) downstream from the
tag line and at least 1.5 ft (0.46 m) from the wading rod. He should
avoid standing in the water if his feet and legs occupy a significantly
large percentage of a narrow cross section. In small streams where
the width permits, the hydrographer stands on an elevated plank or
other support, rather than in the water.
The wading rod should be held in a vertical position with the meter
parallel to the direction of flow while the velocity is being observed. If
the flow is not at right angles to the tag line, the angle coefficient
should be carefully measured (figs. 90 and 91).
When measuring streams having shifting beds, the soundings or
velocities can be affected by the scoured depressions left by the hy-drographer’s
feet. For such streams, the meter should be placed ahead
of and upstream from the feet. For such streams, too, the hydrog-rapher’s
notes should accurately describe the configuration of the
streambed and water surface. (See p. 376-379.)
A measurement should be made of the depth of water over the
lowest point of the control, either before or after the discharge meas-urement.
The gage height corresponding to this lowest point (gage
height of zero flow) is very useful in analyzing the stage-discharge
relation for the gaging station. (See p. 333-334).
When the flow is too low for a reliable measurement of discharge by
current meter, the discharge is determined by use of (1) a volumetric
method of measurement, (2) a portable Parshall flume, or (3) a porta-ble
weir plate. Those three methods of discharge determination are
discussed in chapter 8.
CURRENT-METER MEASUREMENTS FROM CABLEWAYS
The equipment assemblies for use on cableways are described on
pages 110-117.
The size of the sounding weight used in current-meter meas-urements
depends on the depth and velocity in the measurement
cross section. A rule of thumb generally used is that the size of the
weight (lb) should be greater than the maximum product of velocity
(ft/s) and depth (ft) in the cross section. If insufficient weight is used,
the meter assembly will be dragged downstream. If debris or ice is
flowing or if the stream is shallow and swift, the weight used should

5. DISCHARGE-CURRENT METER METHOD 147
be appreciably heavier than that indicated by the above rule. The
rule is not rigid, but it does provide a starting point for deciding on
the size of weight required at various stages.
The Price type AA current meter is generally used in the U.S.A.
when making discharge measurements from a cableway. The depth is
measured by use of a sounding reel, and the velocity is measured by
setting the meter at the proper position in the vertical. (See table 4.)
Table 4 is designed so that no velocity observations will be made with
the meter closer than 0.5 ft (0.15 m) to the water surface. In the zone
from the water surface to a depth of 0.5 ft, the current meter is known
to give erroneous results.
Some sounding reels are equipped with a computing depth indi-cator.
To use the computing spiral, the indicator is set at zero when
the center of the current-meter rotor is at the water surface. The
sounding weight and meter are then lowered until the weight touches
the streambed. If, for example, a 30 C .5 (see table 4) suspension is
used and if the indicator reads 18.5 ft when the sounding weight
touches the bottom, the depth would be 19.0 ft (18.5 ft + 0.5 ft). To
move the meter to the 0.8-depth position (0.8~ 19.0 ft), the weight and
meter are raised until the hand on the indicator is over the 19-ft mark
on the graduated spiral (fig. 60); the hand will then be pointing to
15.2 on the main dial. To set the meter at the 0.2-depth position
(0.2~ 19.0 ft), the weight and meter are raised until the hand on the
indicator is pointing to 3.8 ft on the main dial.
One problem found in observing velocities from a cableway is that
movement of the cable car from one station to the next causes the car
to oscillate for a short time after coming to a stop. The hydrographer
should wait until this oscillation has been dampened to the extent
that it is negligible before counting meter revolutions.
Tags can be placed on the sounding line at known distances above
the center of the meter cups as an aid in determining depths. Fur-thermore,
the use of tags allows the meter to be kept submerged
throughout the discharge measurement to prevent freezing in cold air
during the winter measurements. The tags, which are usually
streamers of different colored binding tape, are fastened to the sound-ing
line by solder beads or by small cable clips. Tags are used for
determining depth in either of two ways.
1. In the procedure that is usually preferred, a tag is set at the
water surface, after which the depth indicator is set at the distance
between that particular tag and the center of the meter cups. This is
equivalent to setting the indicator at zero when the center of the
meter rotor is at the water surface, and the hydrographer then pro-ceeds
with his depth settings as described in a preceding paragraph. If
debris or ice is flowing, this method prevents damage to the meter.

TABLE 4.-Velocity-measurement method for various meter suspensions and depths
Mmmmm depth
Suspension’ 0 6 method 0.2 and 0.8 method
(iI) (In) (f;) (ml
15 c .5,30 c .5 _---------_---------__ ------ 1.2 0.37 2.5 0.76
5oc.55 ________________---_______________ 1.4 .43 2.8 .85
50 c .9 ______________________________ ------ 2.2 .67 1.37
75 C 1.0, 100 C 1.0, 150 C 1.0 ---___-------_ 2.5 .76 t,i 1.52
200 c 1.5,300 c 1.5 ________ ------ _____ ----- 23.8 1.16 7.5 2.29
‘Suspensions shown mdicate the size of the sounding weight and the d&%vx fmm the bottom of the weight to the
current-meter axs. Thus “50 C .9” refers to B 50.pound Columbus-type weight, the suspensmn for which puts the
meter 0.9 R above the bottom of the weight.
‘Use O.&depth method for depths between 2.5 and 3 7 ft, and apply appropriate coefficient (usually 0.87 from table
2).
2. In the second method the sounding weight is first lowered to the
streambed, and the depth is then determined by raising the weight
until the first tag below the water surface appears at the surface. The
total depth is then sum of (a) the distance the weight was raised to
bring the tag to the water surface, (b) the distance the tag is above the
center of the meter cups, and (c) the distance from the bottom of the
weight to the center of the cups. This method is usual1.y used with
handlines, and it is also used to simplify the measurement of deep,
swift streams (p. 159-163).
If large quantities of debris are carried by the stream, the meter
should be periodically raised to the cable car for inspection during the
measurement to be certain that the pivot and rotor of the meter are
free of debris. However, the meter should be kept in the water during
the measurement if the air temperature is well below freezing. The
hydrographer should carry a pair of lineman’s side-cutter pliers when
making measurements from a cableway. These can be used to cut the
sounding line to insure safety if the weight and meter become caught
on a submerged object or on heavy floating debris and it is impossible
to release them. Sometimes the cable car can be pulled to the edge of
the water where the entangling debris can be removed.
When a measurement of a deep, swift stream is made firom a cable-way,
the meter and weight do not hang vertically but tare dragged
downstream. The vertical angle, that is, the angle between the
meter-suspension cable and the vertical, should be measured by pro-tractor
in order to correct the soundings to give the actual vertical
depth. The procedure used to correct soundings is described on pages
159- 168.
If a handline is used to suspend the current meter and sounding
weight, the measurement procedure to be followed is that described in
the section on bridge measurements (p. 150-151).

CURRENT-METER MEASUREMENTS FROM BRIDGES
Bridges are often used for making discharge measurements of
streams that cannot be waded. Measurement cross sections under
bridges are often satisfactory for current-meter measurements, but
cableway sections are usually superior.
No set rule can be given for choosing between the upstream or
downstream side of the bridge for making a discharge measurement.
The advantages of using the upstream side of the bridge are:
1. Hydraulic characteristics at the upstream side of bridge open-ings
usually are more favorable.
2. Approaching drift can be seen and thus can be more easily
avoided.
3. The st,reambed at the upstream side of the bridge is not likely to
be scoured as badly as the downstream side.
The advantages of using the downstream side of the bridge are:
1. Vertical angles are more easily measured because the sounding
line will move away from the bridge.
2. The flow lines of the stream may be straightened by passing
through a bridge opening with piers.
Whether to use the upstream side or the downstream side of a
bridge for a current-meter measurement should be decided individ-ually
for each bridge after considering the above factors. Other perti-nent
factors relate to physical conditions at the bridge, such as loca-tion
of the walkway, traffic hazards, and accumulation of trash on
pilings and piers.
In making the discharge measurement either a handline, or a
sounding reel supported by a bridge board or by a portable crane, is
used to suspend the current meter and sounding weight from the
bridge. The velocity is measured by setting the meter at positions in
the vertical as indicated in table 4. If velocities are high, the equip-ment
is used no closer than several feet from piers and abutments. In
that situation depths and velocities at the pier or abutments are
estimated on the basis of observations in the vertical nearest the pier.
(See p. 82.)
Where piers are in the measuring section, it is usually necessary to
use more than 25-30 subsections to obtain results as reliable as those
obtained with a similar measuring section that has no piers. Piers not
only affect the horizontal distribution of velocities, but they
frequently affect the direction of the current, causing horizontal an-gles
that must be carefully measured.
Whether or not to exclude the area of a bridge pier from the area of
the measurement cross section depends primarily on the relative lo-cations
of the measurement section and the end of the pier. If meas-

urements are made from the upstream side of the bridge, it is the
relative location of the upstream end (nose) of the pier that is rele-vant;
for measurements made from the downstream side it is the
location of the downstream end (tail) of the pier that is relevant. If
any part of the pier extends into the measurement cross section, the
area of the pier is excluded. However, bridges quite commonly have
cantilevered walkways from which discharge measure’ments are
made. In that case the measurement cross section lies beyond the end
of the pier-upstream from the nose or downstream from the tail,
depending on which side of the bridge is used. In that situation it is
the position and direction of the streamlines that determines whether
or not the pier area is to be excluded. The hydrographer, if’he had not
previously noted the stationing of the sides of the pier when projected
to the measurement cross section, does so now. If there is negligible or
no downstream flow in that width interval (pier subsection)-that is,
if only stagnation and (or) eddying exists upstream from the nose or
downstream from the tail, whichever is relevant-the area of the pier
is excluded. If there is significant downstream flow in the pier subsec-tion,
the area of the pier is included in the area of the measurement
cross section. The horizontal angles of the streamlines in and near the
pier subsection will usually be quite large in that circumstance.
Footbridges are sometimes used for measuring the discharge of
canals, tailraces, and small streams. Often a rod suspension can be
used for the meter when measuring from a footbridge. In low veloci-ties
the procedure for determining depth when using a rod suspension
is the same as that used for wading measurements. For higher veloci-ties
depth is obtained from the difference in readings at an index
point on the bridge when the base plate of the rod is at the water
surface and when it is on the streambed. The measurement of depth
by that method eliminates errors in reading the depth caused by the
fast-moving water piling up on the upstream face of the rod. Hand-lines,
bridge cranes, and bridge boards are also used from footbridges.
When using a sounding reel, depths and velocities are measured by
the methods described in the preceding section of the manual on
cableway measurements (p. 146- 148). When using a handline, depth
is determined by first lowering the sounding weight to the streambed
and then raising the weight until one of the tags is at the water
surface. The distance that the weight is raised is measured along the
rubber-covered cable (p. 106) with either a steel or metallic tape, a
folding foot-rule, or a graduated rod. The total depth of water is then
the summation of (1) the distance the particular tag is above the
meter cups, (2) the measured distance the meter and weight were
raised, and (3) the distance from the bottom of the weight to the meter
cups.

Another, less widely used, method of determining depth requires
that the meter cups be set at the water surface, after which the sound-ing
weight is lowered to the streambed while measuring, with tape or
rule, the length of line that is let out. This measured distance, plus
the distance from the bottom of the sounding weight to the meter
cups, is the depth of water.
When using a handline, enough cable is unwound from the hand-line
reel to keep the reel out of water when the sounding weight is on
the streambed at the deepest part of the measuring section. That
prevents submergence of the reel and thick rubber-covered cable and
attendant drag on the equipment in high-velocity flow, and unless the
bridge is relatively close to the water surface, it still permits the
hydrographer to raise and lower the meter by means of the rubber-covered
cable rather than the bare-steel cable. When the meter is set
for a velocity observation, the hydrographer stands on the rubber-covered
cable or ties it to the handrail to hold the meter in place. By
doing so his hands are free to operate the stopwatch and record the
data.
If the bridge has vertical truss members in the plane of the meas-urement
cross section, the handline can be disconnected from the
headphone wire and passed around the truss member with the sound-ing
weight on the bottom. This eliminates the need for raising the
weight and meter to the bridge each time a move is made from one
vertical to another and is the principal advantage of a handline.
CURRENT-METER MEASUREMENTS FROM ICE-COVER
Discharge measurements under ice cover (fig. 93) are usually made
under conditions that range from uncomfortable to severe, but it is
extremely important that they be made, because the reliability of a
large part of the computed discharge record for a winter period may
depend on one such measurement.
Cross sections for possible use for measuring under ice cover should
be selected during the open-water season when channel conditions
can ,be observed and evaluated. Commonly the most desirable meas-urement
section will be just upstream from a riffle because slush ice
that collects under the ice cover is usually thickest at the upstream
end of the pools created by riffles. The equipment used for cutting or
drilling holes in the ice was described on pages 124-129.
The danger of working on ice-covered streams should never be un-derestimated.
When crossing the stream, the hydrographer should
test the strength of the ice with solid blows using a sharp ice chisel.
Ice thickness may be irregular, especially late in the season when a
thick snow cover may act as an insulator. Water just above freezing
can slowly melt the underside of the ice, creating thin spots. Ice

FIGURE 93.-Ice rod being used to support current meter for a discharge
measurement, top; ice drill being used to cut holes, bottom’.

bridged above the water may be weak, even though relatively thick.
At the cross section selected for measurement three holes, one at
each quarter point of the width, are cut to check on the possible
presence of slush ice or possible maldistribution of flow. If poor condi-tions
are found, other cross sections are similarly investigated to find
one that is free of slush ice and has a favorable horizontal distribution
of flow. After finding a favorable cross section, at least 20 holes are
cut for the current-meter measurement of discharge. The holes should
be spaced so that no subsection carries more than 10 percent of the
total discharge. On narrow streams it may be simpler to remove all
the ice in the cross section.
The effective depth of the water (fig. 94) is the total depth of water
minus the distance from the water surface to the bottom of the ice.
The vertical pulsation of water in the holes in the ice sometimes
causes difficulty in determining the depths. The total depth of water
is usually measured with an ice rod or with a sounding weight and
reel, depending on the depth.
The distance from the water surface to the bottom of the ice is
measured with an ice-measuring stick (p. 1251, unless slush is present
at the hole. In that situation the effective depth is the total depth
b
Streambed ‘I ”
a= Water surface to bottom of ice 0.2-depth setting=a+0.2c
b= Total depth of water 0.8-depth setting= b - 0.2~
c = Effective depth (C = b -a) 0.6-depth setting = b - 0.4~
FIGURE 94.-Method of computing meter settings for measurements under ice
cover.

minus the distance from the water surface to the interfacle between
water and slush. To locate that interface, the current meter is sus-pended
at a depth below the slush ice where the meter rotor turns
freely. The meter is then slowly raised until the rotor stops; that point
is considered the interface, and its depth below the water’ surface is
measured for determining the effective depth. The effective depth is
then used to compute the proper position of the meter in the vertical.
The vane ice meter is recommended for use under ice cover because
(1) the vanes do not become filled with slush ice as the clups of the
Price meter often do, (2) the yoke of the vane meter will fit in the hole
made by the ice drill, and (3) the yoke and ice rod can serve as an
ice-measuring stick. The contact chamber of the vane meter can be
rotated to any position; its binding post is therefore placed perpen-dicular
to the axis of the yoke to avoid interference when’ using the
top of the yoke as the horizontal leg of an ice-measuring istick.
Because of the roughness of the underside of the ice cover, the
location of the filament of maximum velocity is some distance below
the underside of the ice. Figure 95 shows a typical vertical-velocity
0
20 r
100 1 c
0 0.2 0.4 0.6 0.8 l.CI 1.2
VELOCITY, IN FEET PER SECOND
FIGURE B&-Typical vertical-velocity curve under ice cover

curve under ice cover. In making a discharge measurement the 0.2-
and O.&depth method is recommended in the U.S.A. for effective
depths equal to or greater than 2.5 ft, and the 0.6-depth method for
effective depths less than 2.5 ft. It is also recommended that two
vertical-velocity curves be defined when ice measurements are made
to determine whether any coefficients are necessary to convert the
velocity obtained by the 0.2- and O.&depth method, or by the 0.6-
depth method, to the mean velocity. Normally the average of the
velocities obtained by the 0.2- and 0.8-depth method gives the mean
velocity, but a coefficient of about 0.92 usually is applicable to the
velocity obtained by the 0.6-depth method. In Europe a three-point
method is commonly used in which velocity observations are made at
0.15, 0.5, and 0.85 of the effective depth.
When measuring the velocity, the meter is kept as far upstream as
possible to minimize any effect that the vertical pulsation of water in
the hole might have on the meter registration. The meter is exposed
as little as possible to the cold air so that its operation will not be
impaired by the formation of ice on exposed parts.
If there is only partial ice cover on the measuring section, the
procedure described above is used for the ice-covered observation ver-ticals,
and open-water methods are used for the open-water verticals.
A sample sheet of discharge-measurement notes for a measurement
made under ice cover is shown in figure 96. Vertical-velocity curves
that had been defined for that measurement had indicated that mean
velocity in a vertical was given by the 0.2- and O.&depth method, and
that the 0.6-depth method required a coefficient of 0.92.
CURRENT-METER MEASUREMENTS FROM BOATS
Discharge measurements are made from boats where no cableways
or suitable bridges are available and where streams are too deep to
wade. Personal safety is the limiting factor in the use of boats on
streams having high velocities.
In making a boat measurement the tag line is first strung across
the measurement section by unreeling the line as the boat moves
across the stream. Some tag-line reels are equipped with brakes (fig.
79) to control the line tension during the unreeling. If a tag line
whose reel is unequipped with a brake has been strung across a
stream, the slack is taken up by means of a block and tackle attached
to the reel and to an anchored support on the bank. If there is traffic
on the river, one man must be stationed on the bank to lower and
raise the tag line to allow river traffic to pass. Streamers should be
attached to the tag line so that it may be seen by boat pilots. The
method of positioning the boat for measuring depths and velocities,
by sliding the boat along the tag line from one observation vertical to
another, was described on page 121.

If the flow of traffic on the river is continual or if the width of the
river is too great for a tag line to be used, other means are needed to
position the boat. One method that dispenses with the tag line in-volves
keeping the boat lined up wit,h flags positioned on ‘each end of
FIGURE 96.-Part of notes for discharge measurement under ice cover.

the measurement cross section. Flags on one bank would suffice, but
it is better to have them on both banks. The position of the boat in the
cross section can be determined by means of a transit on the shore and
a stadia rod held in the boat (fig. 97). Another method of determining
the position of the boat is by setting a transit on one bank at a
convenient measured distance from, and at right angles to, the cross
section. The position of the boat is computed by measuring the angle
to the boat, as shown in figure 98. A third method of determining the
position of the boat requires a sextant in the boat. The sextant is used
to read the angle between a flag at the end of the cross section and
another at a known distance perpendicular to the cross section (fig.
98). The boat position can be computed from the measured angle and
the known distance between the flags on the shore. Unless anchoring
is more convenient, the boat must be held stationary by its motor
when readings are being taken.
Boat measurements are not recommended where velocities are
I
Transit
P p f)
/,
Stadia rod
held in boat
FIGURE 97.-Determining position in the cross section, stadia method.
p p
A 6
1
* ‘ . . ‘*
P P
IC D
x
Transit
MC=CE tan & (transit)
MC= * (sextant)
FIGURE 98.-Determining position in the cross section, angular method.

slower than 1 ft/s (0.3 m/s) when the boat is subject to the action of
wind and waves. (See p. 180-181.) If the maximum depth iin the cross
section is less than 10 ft (3 m) and the velocity is low, a rod is usually
used for measuring the depth and supporting the current meter. For
greater depths and velocities, a cable suspension with reel, boat
boom, and sounding weight is used. The procedure for measuring
discharge from a boat using the boat boom and crosspiece (p. 122-
123) is the same as that for measuring from a bridge or’ cableway,
once the special equipment has been set up and the method of po-sitioning
the boat has been established.
A special method of measuring discharge from a boat wi,thout stop-ping
the boat at observation stations-the moving-boat method-is
described in detail in chapter 6.
NETWORKS OF CURRENT METERS
Occasional special measurements require the simultaneous deter-mination
of velocities at several points in a cross section, distributed
either laterally or vertically. For example, it may be nc?cessary to
measure a vertical-velocity profile quickly in unsteady flows and to
check it frequently in order to determine the changes in shape of the
vertical profile as well as the rates of those changes. Another example
is the measurement of tide-affected streams where it is desirable to
measure the total discharge continously during at least a full tidal
cycle (approximately 13 hr). The need for so many simultaneous ve-locity
determinations (one at each vertical in the cross section) for so
long a period can be an expensive and laborious process using con-ventional
techniques of discharge measurement.
A grouping of 21 current meters and special supplemental in-strumentation
has been used by the U.S. Geological Survey to facili-tate
measurements of the types just described. Only a few persons are
required to operate the system. The 21 meters are connected so that
the spacing between any two adjacent meters can be varied to dis-tances
as great as 200 ft (61 m). Furthermore, each meter has suffi-cient
handline cable to be suspended vertically from a bridge for as
much as 200 ft. The meters have a standard calibration. Revolutions
of the rotors are recorded by electronic counters that are grouped
compactly in one box at the center of the bank of meters. The
operator, by flipping one switch, starts all 21 counters simultaneously
and, after an interval of several minutes, stops all counters. The
indicated number of revolutions for the elapsed time interval is con-verted
to a velocity for each meter. The distance between meters is
known; a record of stage is maintained to evaluate depth; prior infor-mation
at the site is obtained to convert point velocities in the verti-cals
to mean velocities in those verticals. All of the information nec-essary
to compute discharge in the cross section is therefore available

and is tabulated for easy conversion to discharge.
Other countries have developed similar equipment; for example, a
grouping of 40 meters is used in the United Kingdom.
SPECIAL PROBLEMS IN CONVENTIONAL CURRENT-METER
MEASUREMENTS
MEASUREMENT OF DEEP, SWIFT STREAMS
The measurement of deep, swift streams by current meter usually
presents no serious problems when adequate sounding weights are
used and when floating ice or drift is not excessive. Normal proce-dures
must sometimes be altered, however, when measuring streams
under particularly adverse conditions, the four most common situa-tions
of that kind being represented by the following cases:
Case A, Possible to sound, but weight and meter drift downstream.
Case B. Not possible to sound, but a standard cross section is avail-able.
Case C. Not possible to sound, and no standard cross section is avail-able.
Case D. Not possible to submerge the meter in the water.
Procedures are described below for discharge measurements made
under those adverse conditions. The procedures for cases B, C, and D
are actually applicable only where channel conditions in the meas-urement
cross section or reach are stable, meaning that no significant
scour or deposition occurs.
CASE A. DEPTH CAN BE SOUNDED
Where it is possible to sound the depth but the weight and meter
drift drownstream, the depths as measured by the usual methods will
be in error? being too large (fig. 99). The correction for the error has
two parts, the air correction and the wet-line correction. The air cor-rection
is shown in figure 99 as the distance cd. The wet-line correc-tion
in figure 99 is shown as the difference betwen the wet-line depth
de and the vertical depth dg.
As shown in figure 99, the air correction depends on the vertical
angle P and the distance ab. The correction is computed as follows:
ab =ac
cosp2L~=~ ab ab
ad ac+cd ab+cd
ab+cd= - ab
cos P
cd=- ab
cos P -ab =ab [A-l]- (11)

The air correction for even-numbered angles between 4” and 36”
and for vertical lengths between 10 and 100 ft is shown in table 5. The
correction is applied to the nearest tenth of a foot; hundredths are
given to aid in interpolation. Table 6 is a similar table in metric units.
The air correction may be near1.y eliminated by using tags at
Q Apex of vertical angle
in sounding line
i I
I
I
I
I I
I I
I
I
I
I
I
I
I
I
I
I I
[ Streambed :
f 9 e h
FIGURE 99.-Position of sounding weight and line in deep, swift water.

selected intervals on the sounding line, and then using the tags to
reference the water surface. This practice is almost equivalent to
moving the reel to a position just above the water surface.
The correction for excess length of line below the water surface is
obtained by using an elementary principle of mechanics. If a known
horizontal force is applied to a weight suspended on a cord, the cord
takes a position of rest at some angle with the vertical, and the tan-gent
of the vertical angle of the cord is equal to the horizontal force
divided by the vertical force of the weight. If several additional hori-zontal
and vertical forces are applied to the cord, the tangent of the
angle in the cord above any point is equal to a summation of the
horizontal forces below that point, divided by the summation of the
vertical forces below the point.
The distribution of total horizontal drag on the sounding line is in
accordance with the variation of velocity with depth. The excess in
length of the curved line over the vertical depth is the sum of the
products of each tenth of depth and the function (llcosP)-1 of the
corresponding angles; the function is derived for each tenth of depth
by means of the tangent relation of the forces acting below any point.
The wet-line correction for even-numbered angles between 4” and
36” and for wet-line depths between 10 and 100 ft is shown in table 7.
(Table 8 is a similar table in metric units.) The correction is applied to
the nearest tenth of a foot. The wet-line correction cannot be deter-mined
until the air correction has been deducted from the observed
depth.
The following assumptions were used in deriving the wet-line cor-rection
tables:
1. The weight will go to the bottom despite the force of the current.
2. The sounding is made when the weight is at the bottom but en-tirely
supported by the line.
3. Drag on the streamlined weight in the sounding position is ne-glected.
4. The table is general and can be used for any size sounding weight
or line that is designed to offer little resistance to the current.
If the direction of flow is not perpendicular to the measuring sec-tion,
the angle of the measuring line as indicated by the protractor
will be less than the true angle of the line. The air correction and
wet-line correction will then be too small. To correct for this it is
necessary to either measure by protractor the horizontal angle be-tween
the direction of flow and a perpendicular to the measurement
section, or determine the horizontal-angle coefficient by the methods
described on pages 142-143.
If the horizontal angle of the direction of flow is called H, the meas-ured
vertical angle P, and the true vertical angle X, the relation

between the angles is expressed by the equation
tan X = tan. (fig. 100).
cos H
(12)
ELEVATION
&lane of orotractor
ran Y=- fi
of H= horizontal angle
P=rneasured vertical angle
X=actual vertical angle
COS H
hfa=90”
ifo=90
fih = 90”
aih=90
-_t-a n P _ fi x & = &
cos Ii af fi of
tanx=fi=tan
of COs H
FIGURE lOO.-Sketch of geometry of relation of actual to measured vertical angle when
flow direction is not normal to measurement section.

Table 9 gives the quantities in tenths of degrees, to be added to
observed vertical angles to obtain the true vertical angles for a range
of horizontal angles between 8” and 28”.
The conditions that cause error in sounding the depth also cause
error in setting the meter at selected depths. The correction tables are
not strictly applicable to the problem of setting the meter for velocity
observations because of the increased horizontal force on the sound-ing
weight caused by higher velocities when the weight is raised from
the streambed. A meter placed in deep, swift water by the ordinary
methods for observations at selected percentages of the depth will be
too high in the water. The use of tables 5-9 will tend to eliminate this
error in the placement of the meter, and although not strictly appli-cable,
their use for this purpose has become general.
For the 0.2-depth position, the curvature of the wet line is assumed
to be negligible, and the length of sounding line from the apex of the
vertical angle to the weight is considered a straight line. The method
used to place the meter at the O.Zdepth position is as follows:
1. Compute the 0.2 value of the vertical depth.
2. Lower the meter this depth into the water and read the vertical
angle.
3. Obtain the air correction from table 5 or 6. The vertical length
used to obtain the air correction is the sum of (a) 0.2 of the
vertical depth, (b) the distance from the water surface to the
apex of the angle, and (c) the distance from the bottom of the
weight to the meter.
4. Let out an additional amount of line equal to the air correction.
5. If the angle increases appreciably when the additional line is let
out, let out more line until the total additional line, the angle,
and the vertical distance are in agreement with figures in the
air-correction table.
To set the meter at the O.&depth position, a correction to the amount
of line reeled in must be made for the difference, if any, between the
TABLE 9.-De
4
rees to be added to observed vertzcal angles to obtain actual vertrcal
an,g es when flow direction LS not normal to measurement section
Observed vertical angle
Horizontal angle
8” 12” 16” 20 24” 28”
cos=o.99 cos=o 98 cos=o 96 cos=o 94 cos=o 91 cos=O.88
8”
_______._____- -------_-__------
12” -------~-----_________________ 0..1l 0.2 0.3 0.5 0.8
::
.5
1::
1.1 ::i
16” -----_-..-----_ -----_-_------__ .l 1.4
20” ----- -----__-_--------- ______ - .2 :i
:! 1.2 1.7 X2
24” -____ --..-----___------- _____ -- .2
1.4 2.0 2.8
28” -----_-------_---------------- .2
::
1:: 1.5 2.2 3.0
32” -_-__ -----____---------__----- .2 1.0 1.6 2.4 3.3
36” _____ - ______- -----_-___------- .2 .6 1.1 1.7 2.5 3.4

air correction for the sounding position and that for the O.&depth
position. This difference is designated as m in table 10. If the angle
increases for,the O.&depth position, the meter must be lowered, if the
angle decreases the meter must be raised.
In setting the O.&depth position of the meter, the wet-line correc-tion
may require consideration if the depths are more than 40 ft and if
the change in vertical angle is more than 5 percent. If the vertical
angle remains the same or decreases, the wet-line correction (table 7
or 8) for the 0.8-depth position is less than the wet-line correction for
the sounding position by some difference designated as n in table 10.
If the vertical angle increases, the difference in correction n de-minishes
until the increase in angle is about 10 percent; for greater
increases in angle, the difference between corrections also increases.
Table 10 summarizes the effect on air- and wet-line corrections
caused by raising the meter from the sounding position to the 0.8-
depth position.
For slight changes in the vertical angle, because of the differences
m and n in the air- and wet-line corrections, the adjustments to the
wet-line length of the 0.8-depth position are generally small and
usually can be ignored. Table 10 indicates, however, that the meter
may be placed a little too low if the adjustments are not made. Be-cause
of this possibility, the wet-line depth instead of the vertical
depth is sometimes used as the basis for computing the 0.8-depth
position, and no adjustments are made for the differences m and n.
CASE B. DEPTH CANNOT BE SOUNDED BUT STANDARD CROSS SECTION
IS AVAILABLE
On occasion it is not possible to sound the bottom, but a standard
measurement cross section at the bridge or cableway may be availa-ble
from previous measurements that were made. Such a cross section
TABLE lO.--Summary table for setting the meter at 0.8-depth position in deep, swift
streams
AIT correctmn Wet-lme correEt1on
Change m vertical angle
Dxectmn of change Correctwn ta meter Dlrectmn of change Correctmn to meter
posltlon posltlon
None -___---__--_ None _-_--__- None __-___---- Decrease -----_ Raise meter
the dis-tance
n.
Decrease ---_---_ Decrease------Raise meter _--- do -__--- Do.
the dis-tance
m.
Increase ________ Increase ______ Lower meter (‘)
the dis-
Decrease, then
increase.
tance m.
‘Etame meter the distance n unless the mcrease m angle IS greater than about 10 percent, then It 1s necessary to
lower the meter the distance n.

5. DISCHARGE CURRENT METER METHOD 169
will be useful only if all discharge measurements use the same per-manent
initial point for the stationing of verticals across the width of
the stream, and if there is an outside reference gage or reference point
on the bank or bridge to which the water-surface elevation at the
measurement cross section may be referred. In the situation de-scribed
above, the following procedure is used:
1. Determine depths at the observation verticals from the standard
cross section and the known water-surface elevation at the
measurement cross section.
2. Measure the velocity at 0.2 of the depth.
3. Compute the measurement in the normal manner using the meas-ured
velocities as though they were the mean velocities in the
vertical, and using the depths from step 1.
4. Determine the coefficient to adjust the 0.2-depth velocity to mean
velocity in the cross section, as explained on pages 135-136.
5. Apply the coefficient from step 4 to the computed discharge from
step 3.
CASE C. DEWH CANNOT BE SOUNDED AND NO STANDARD CROSS SECTION
IS AVAILABLE
When it is not possible to sound the depth and a standard cross
section is not available, the following procedure is used:
1. Refer the water-surface elevation before and after the measure-ment
to an elevation reference point on a bridge, on a driven
stake, or on a tree at the water’s edge. (It is assumed here that
no outside reference gage is available at the measurement cross
section.)
2. Estimate the depth and observe the velocity at 0.2 of the estimated
depth. The meter should be at least 2.0 ft (0.6 m) below the water
surface. Record in the notes the actual depth the meter was
placed below the water surface. If an estimate of the depth is
impossible, place the meter 2.0 ft below the water surface and
observe the velocity there.
3. Make a complete measurement at a lower stage and include some
vertical-velocity curves.
4. Use the complete measurement and difference in stage between
the two measurements to determine the cross section of the first
measurement. To determine whether the streambed has shifted,
the cross section should be compared with one obtained in a
previous measurement at that site.
5. Use vertical-velocity curves, or the relationship between mean
velocity and 0.2-depth velocity, to adjust the velocities observed
in step 2 to mean velocity.
6. Compute the measurement in the normal manner using the
depths from step 4 and the velocities from step 5.

CASE D. METER CANNOT BE SUBMERGED
If it is impossible to keep the meter and weight in the water be-cause
of high velocities and (or) floating drift, use the following proce-dure:
1: Obtain depths at the measurement verticals by the methc&e%-
plained for case B if a standard cross section is available, or by
the method explained above for case C if no standard cross sec-tion
is available.
2. Measure surface velocities with an optical current meter, as ex-plained
on pages 91-93, 137- 138.
3. Compute the measurement in the normal manner using the sur-face
velocities as though they were the mean velocities in the
vertical, and using the depths from step 1.
4. Apply the appropriate velocity coefficient to the discharge com-puted
in step 3; use a coefficient of 0.86 for a natural channel and
0.90 for an artificial channel.
If an optical current meter is not available, time floating drift over
a measured course. (See p. 261-262.)
It should be noted here that the amount of floating drift or ice is
usually greatly reduced just after the crest of a rise in stage. It may be
possible at that time to obtain velocity observations with a standard
current meter.
COMPUTATION OF MEAN GAGE HEIGHT OF A DISCHARGE MEASUREMENT
The mean gage height of a discharge measurement represents the
mean stage of the stream during the measurement period. Because
the mean gage height for a discharge measurement is one of the
coordinates used in plotting the measurements to establish the
stage-discharge relation, an accurate determination of the mean gage
height is as important as an accurate measurement of the discharge.
The computation of the mean gage height presents no problem when
the change in stage is uniform and no greater than about 0.15 ft (0.05
m), for then the mean fnay be obtained by averaging the stage at the
beginning and end of the measurement. However, measurements
must often be made during periods when the change of stage is
neither uniform nor slight.
As a prerequisite for obtaining an accurate mean gage height, the
clock time at the beginning and end of the measurement should be
recorded on the measurement notes, and additional readings of the
clock time should be recorded on the notes at intervals of 15 to 20 min
during the measurement. After the discharge measurement has been
completed, the recorder chart should be read, and breaks in the slope
of the gage-height graph that occurred during the measurement
should be noted The breaks m slope are useful m themselves and are

also used to determine the gage height corresponding to the clock
times noted during the measurement. If the station is equipped with a
digital recorder, the gage-height readings punched during the meas-urement
are to be read. At nonrecording stations the only way to
obtain intermediate readings is for the stream gager to stop a few
times during the measurement to read the gage, or to have someone
else do this for him.
If the change in stage is greater than 0.15 ft (0.05 m) or if the
change in stage has not been uniform, the mean gage height is ob-tained
by weighting the gage heights corresponding to the clock-time
observations. The weighting is done by using either partial discharge
or time as the weighting factor. In the past the weighting in the
U.S.A. was always done on the basis of partial discharges, but recent
study indicates that discharge-weighting usually tends to overesti-mate
the mean gage height, whereas time-weighting usually tends to
underestimate the mean gage height. On the basis of the present
state of our knowledge, it is suggested that the mean gage height for a
discharge measurement be computed by both methods, after which
the two results are averaged. A description of the two methods fol-lows.
In the discharge-weighting process, the partial discharges meas-ured
between clock observations of gage height are used with the
mean gage heights for the periods when the partial discharges were
measured. The formula used to compute mean gage height is
H=
q,h, + q,h, + q,,h, . . . . . . . . . + q,,h, , (13)
Q
in which
H = mean gage height (ft or m),
Q = total discharge measured (ft”/s or m”/s) = q, + q2 + q:$ . . . . +
Q,! ,
where
91, 427 93, . . . . q,, = discharge (ft”/s or m’/s) measured during time
interval 1, 2, 3, . . . . n and
h,, h2, i2,j, . . . . h,, = average gage height (ft or m) during time
interval 1, 2, 3, . . . . n.
Figure 101 shows the computation of a discharge-weighted mean
gage height. The graph at the bottom of figure 101 is a reproduction of
the gage-height graph during the discharge measurement. The dis-charges
are taken from the current-meter measurement notes shown
in figure 42. The upper computation of the mean gage height in figure
101 shows the computation using equation 13. The lower computation
has been made by a shortcut method to eliminate the multiplication

of large numbers. In that method, after the average gage height for
each time interval has been computed, a base gage height, which is
usually equal to the lowest average gage height, is chosen. Then, the
I
= j167+.40= 1.77 a8
.o JO .a0 do .,o 50 .oo 30 .84 .oo .¶8
2
I
0 1330 -
FIGURE lOl.-Computation of discharge-weighted mean gage height.

differences between the base gage height and the average gage
heights are used to weight the discharges. When the mean difference
has been computed, the base gage height is added to it.
In the time-weighting process, the arithmetic mean gage height for
time intervals between breaks in the slope of the gage-height graph
are used with the duration of those time periods. The formula used to
compute mean gage height is
H=
t,h, + t2h2 + t3h3. . . . . + t,h,
T
(14)
in which
H = mean gage height, in feet or meters,
T = total time for the measurement, in minutes = t, + t2 + t3
‘..f t tt,
t,, tz, t:i . . . . t,, = duration of time intervals between breaks in
slope of the gage-height graph, in minutes, and
h,, hp, h, . . . . h, = average gage height, in feet or meters, during
time interval 1, 2, 3, . . . . n.
Using the data from figure 101, the computation of the time-weighted
mean gage height is as follows:
Awage gage haght Tune rnterual hxt
(h) (t)
1.92---.-----_- _______ -------15 28.80
1.70---.---------------------15 25.50
1.67-w-.----- ___-_-__________ 15 25.05
1.88---------------------15 28.20
Total -----------------------60 107.55
Mean gage height = 107.55/60 = 1.79 ft
In the example used above there is little difference between the
discharge-weighted mean gage height (1.77 ft) and the time-weighted
mean gage height (1.79 ft); the average of the two values, 1.78 ft, is
the preferred mean gage height for the discharge measurement.
When extremely rapid changes in stage occur during a measure-ment,
the weighted mean gage height is not truly applicable to the
discharge measured. To reduce the range in stage during the meas-urement,
measurements under those conditions should be made more
rapidly than those made under constant or slowly changing stage. It
should be realized, however, that shortcuts in the measurement pro-cedure
usually reduce the accuracy of the measured discharge. There-fore
measurement procedures during rapidly changing stage must be
optimized to produce a minimal combined error in measured dis-charge
and computed mean gage height.

MEASUREMENT PROCEDURES DURING RAPIDLY CHANGING STAGE
The preceding discussion on computing the mean gage height of
discharge measurements demonstrated that under conditions of
rapidly changing stage, measurement procedures must be
streamlined, even at the expense of some accuracy. The reduction in
measurement time makes it possible to obtain a gage-height value
that is representative of the measured discharge. Where streams are
uncontrolled, flood rises are more rapid on small streams than on
large streams, because small streams are subject to flash floods that
may rise and fall with sufficient rapidity to produce peak flows of
almost momentary duration. Consequently the discussion that fol-lows
distinguishes between the procedures to be followed for measur-ing
large streams and those for small streams, during periods of
rapidly changing stage. The procedure to be followed for measuring
streams whose flow is controlled by hydroelectric powerplants was
discussed on page 140.
CASE A. LARGE: STREAMS
During periods of rapidly changing stage on large streams, the time
consumed in making a discharge measurement may be reduced by
modifying the standard measurement procedure in the following
manner:
1. Use the 0.6-depth method (p. 134). The 0.2-depth method (p. 135)
or the subsurface method (p. 136) may be used if placing the
meter at the 0.6-depth creates vertical angles requiring time-consuming
corrections, or if the vertical angle increases because
of drift collecting on the sounding line.
2. Reduce the velocity-observation time to about 20-30 s.
3. Reduce the number of sections taken to about 15-18.
By incorporating all three of the above practices a measurement
can be made in 15-20 min. If the subsurface method of observing
velocities is used, some vertical-velocity curves will be needed later to
establish coefficients to convert observed velocity to mean velocity.
Carter and Anderson (1963) have shown that discharge measure-ments
having 30 verticals, for which the two-point method of observa-tion
was used with a 45-s period of observation, will have a standard
error of 2.2 percent (see p. 181-183). That means that two-thirds of
the measurements made using standard procedures would be in error
by 2.2 percent or less. They have also shown that the standard error
for a 25-s period of observation, using the 0.6-depth method with
depth and velocity observed at 16 verticals, is 4.2 percent. The error
caused by using the shortcut method is generally less than the error
to be expected as a result of the shifting flow patterns that commonly

occur during periods of rapidly changing stage, and in addition, un-certainty
concerning the appropriate mean gage height for the mea-surement
is eliminated.
CASE B. SiMALL S-IXEAMS
The discussion that follows deals with the measurement of flash
floods on small streams. Flash floods begin and end with such abrupt-ness
that if the flow is to be measured, the hydrographer must have
advance warning of the occurrence of such an event. The warning will
enable him to reach the measuring site and make all necessary prep-arations
for current-meter measurements before the stream starts to
rise at the site. Once the rise begins it is essential that the many point
observations required be made as rapidly as possible because of the
rapidly changing discharge.
After arriving at the measuring site where the flash flood is ex-pected,
the hydrographer first marks the location of the observation
verticals he intends to use. These marks are placed on the bridge rail
or cableway that is used for discharge measurements. He then deter-mines
the elevation of the streambed, referred to gage datum, at
those verticals. That is done both to save time during the actual
discharge measurement and because he may be unable to sound the
streambed when the flood is in progress. An auxiliary staff gage that
can be read from the measuring bridge or cableway should be part of
the gaging equipment.
In measuring the discharge during a flash flood, the procedure dif-fers
in the following ways from that used in making a conventional
current-meter discharge measurement.
1. Use 6 to 10 observation verticals in the measurement cross
section.-The actual number of verticals used will depend on the
width and uniformity of the cross section. Current-meter observa-tions
are started when the stage starts to rise and are continued until
the flow recedes to normal, or near-normal stage. After completing
one traverse of the cross section, the next traverse is started im-mediately
in the opposite direction, and observations continue to be
made back and forth across the stream.
2. Time is saved by making a single velocity observation at each
observation vertical.-If depths, velocities, and the absence of floating
drift permit, the 0.6-depth method (p. 134) or O.Zdepth method (p.
135) is used. Otherwise, an optical current meter is used in the
surface-velocity method (p. 137).
3. Readings of the auxiliary staff gage are made at every third veloc-ity
observation, and clock time is also recorded.-That is done because
the rapid change in stage will commonly make it impossible to later
obtain accurate stages, corresponding to the time of each velocity

observation, from the automatic gaging-station record. Furthermore,
during periods of rapidly changing stage, a staff-gage record is
usually more reliable than an automatic-gage record because of
“drawdown” at the intake or because of well or intake lag. Moreover if
the gaging station is equipped with a digital recorder, the frequency
of punches will seldom be adequate for a flash flood.
After the stream has receded, determinations of streambed eleva-tion
at the observation verticals are again made to learn if scour or fill
has occurred. If there has been a change in streambed elevation, the
change is prorated with time, or in accordance with the best judgment
of the hydrographer, to provide the values of depth needed to compute
discharge. The most reliable discharge results are obtained, of course,
where the streambed is stable or relatively so, leaving no serious
uncertainty about stream depths during the measurement.
4. Computation procedure-Normally, the discharge of a stream is
computed for each current-meter traverse of the measurement cross
section, using observed velocities, depths, and incremental channel
widths. Because of the rapid change of stage that occurs during the
course of a velocity-observation traverse, that conventional computa-tion
procedure should not be used when measuring the discharge of
flash floods. If the conventional procedure is used there is great uncer-tainty
as to the stage that applies to the computed discharge value.
The recommended computation procedure for a flash flood is as fol-lows.
The first step is to construct an individual relation of mean velocity
to stage for each observation vertical. The mean velocity, it will be
recalled, is obtained by applying an appropriate coefficient to each
observed value of surface or subsurface velocity. For each vertical,
mean velocity is plotted against stage, and each point is identified by
clock time. A single smooth curve is usually fitted to the points, but
the scatter of the points may indicate the need for two curves-one for
the rising limb of the hydrograph and the other for the falling limb.
In either event, all the data needed are now available for construct-ing
the stage-discharge relation for the entire cross section. The dis-tance
between observation verticals (incremental width) is known,
and for any selected stage the corresponding depth and mean velocity
at each observation vertical are likewise known. Those data are then
used, in the conventional manner, to compute the total discharge
corresponding to the selected stage. By repeating that operation for
several stages, one obtains a stage-discharge relation for the entire
range of stage, or, if necessary, two such relations-one for the rising
limb of the hydrograph and one for the falling limb. As a final step,
the stage-discharge relation(s) is applied to the stage hydrograph to
compute the discharge hydrograph. In the absence of a reliable au-

/
tomatic stage record, the numerous visually observed values of stage
provide the stage hydrograph.
CORRECTION OF DISCHARGE FOR STORAGE DURING MEASUREMENT
If a discharge measurement is made at a significant distance from
the gage during a change in stage, the discharge passing the gage
during the measurement will not be the same as the discharge at the
measurement section because of the effect of channel storage between
the measurement section and the gage.
Adjustment is made for channel storage by applying to the meas-ured
discharge a quantity obtained by multiplying the channel sur-face
area by the average rate of change in stage in the reach. The
equation used is
Qc =Qm k WL 2~ (15)
where
QG = discharge passing the gage control (ft”/s or m3/s),
Q,,, = measured discharge (ft”/s or m%),
W = average width of stream between measurement section and
control (ft or m),
L = length of reach between measurement section and control
(ft or m),
Ah = average change in stage in the reach L during the meas-urement
(ft or m), and
At = elapsed time during measurement (s).
A reference point or a temporary gage is set at the measurement
cross section if channel storage is likely to be significant. The water-surface
elevations at the section and at the gage are determined be-fore
and after the measurement to compute Ah. If the measurement is
made upstream from the control, the adjustment will be plus for fall-ing
stages and minus for rising stages; if made downstream from the
control, the adjustment will be minus for falling stages and plus for
rising stages.
Figure 102 shows the front sheet of a measurement that has been
made 0.6 mi upstream from the control during a period of changing
stage. The computation of the adjustment for storage for the meas-urement
shown in figure 102 follows:
Measurement made 0.6 mi upstream, L = 3,170 ft.
Average width (W) between measurement section and control
= 150 ft.
Change in stage at control, 5.84 to 6.74 ft = +0.90 ft.
Change in stage at measurement section, 12.72 to 13.74 = -1-1.02
ft. (Readings taken at measurement section from a reference
point before and after measurement.)

Average change in stage (Ah) = (0.90 + 1.02) + 2 = 0.96 ft.
Elapsed time during measurement = 1% hr = 4,500 s.
Measured discharge Q,,, = 8,494 ft”/s.
Qc; = 8,494 - 150 (3,170)4o5.0g06 = 8,494 - 101 = 8,393 ft “/s. Use
7
8,390 ft3/s.
FIGURE 102.-Discharge-measurement notes with discharge adjusted for channel
storage.

The adjusted discharge figure is the one used for defining the stage-discharge
relation.
The adjustment of measured discharge for storage during a period
of changing discharge is a separate and distinct problem from that of
making adjustments for variable slope caused by changing discharge.
(See p. 418-421.) Regardless of whether or not the discharge is to be
adjusted later for variable slope, the storage adjustment to discharge
is made immediately after completion of the discharge measurement.
SUMMARY OF FACTORS AFFECTING THE ACCURACY OF A
DISCHARGE MEASUREMENT
The factors that affect the accuracy of a discharge measurement
have been discussed in appropriate sections of the preceding text.
This section provides a brief recapitulation of those factors.
1. Equippment.-Accurate measurement requires that measure-ment
equipment be properly assembled and maintained in good con-dition.
To avoid damage in transport, the equipment should be packed
in appropriate containers or compartments of the vehicle used by the
hydrographer. Current meters are especially susceptible to damage
when in use, because measurements must often be made when drift or
floating ice is present in a stream.
2. Characteristics of the measurement section.-The basic charac-teristics
of the measurement section affect measurement accuracy.
The attributes desired in a measurement section are those listed on
page 139. If possible, the section should be deep enough to permit use
of the two-point method of measuring velocity. The presence of bridge
piers in or near the measurement section adversely affects the distri-bution
of velocities. Piers also tend to induce local bed scour which
affects the uniformity of depth. Those adverse effects are increased if
the bridge piers tend to collect drift on their upstream faces.
3. Spacing of observation verticals.-The spacing of observation
verticals in the measurement section can affect the accuracy of the
measurement. Twenty-five to 30 verticals should normally be used,
and the verticals should be spaced so that each subsection will have
approximately equal discharge. However, a measurement vertical
should be located fairly close to each bank and at “breaks” in depth.
The spacing of the verticals should also he reduced in the vicinity of
bridge piers. If many bridge piers are present in the section or if the
streambed is nonuniform, more verticals than the recommended
25-30 should be used.
4. Rapidly changing stage.-When the stage changes rapidly dur-ing
a discharge measurement, the computed discharge figure loses
some of its significance, and there is uncertainty as to the appropriate
gage height to apply to that discharge figure. Consequently, the
standard procedure for making discharge measurements should be

shortened when the stage is changing rapidly, as explained on pages
174-177, even at the expense of some accuracy. The reduction in
measurement time makes it possible to obtain a mean gage height
that is representative of the measured discharge.
5. Measurement of depth and velocity.-Inaccuracies in sounding
and in the placement of the current meter are most likely to occur in
those sections having great depths and velocities. Heavy sounding
weights should be used to reduce t,he vertical angle made by the
sounding line, and where vertical angles exist, tags and (or) correc-tion
tables should be used in determining vertical distances. Where
velocities are not perpendicular to the measurement section, the
cosine of the angle between the perpendicular and the direction of the
current must be determined. If a velocity-azimuth-depth assembly (p.
129-130) is not used, it is necessary to assume that the angle of the
surface current prevails throughout the vertical; that assumption
may be erroneous.
6. Ice in the measuring section.-Reliable measurements may
usually be made when measuring from ice cover if the measurement
verticals are free of slush ice. Slush ice interferes with the operation
of the current-meter rotor .and also causes difficulty in determining
the effective depth of water. If the effective depth is considered to be
that portion of the depth in which the current meter indicates veloc-ity,
the assumed effective depth may be too small if slush ice is inter-fering
with free operation of the rotor. Collections of slush ice are
generally thickest near the upstream end of ice-covered pools, and
those areas should therefore be given little consideration as meas-urement
sections. If the ice cover is layered so that there is water
flowing between ice layers, it is almost impossible to obtain a reliable
discharge measurement, particularly if the water layers are too thin
to permit insertion of the meter between ice layers. The exposure of a
wet current meter to subfreezing air temperatures may cause serious
underregistration of the current meter as a result of ice forming in
the meter bearings and contact chamber. Therefore, once the meas-urement
is started, the current meter should be kept in the water as
much as possible to avoid exposure to the cold air.
7. Wind.-Wind may affect the accuracy of a discharge measure-ment
by obscuring the angle of the current, by creating waves that
make it difficult to sense the water surface prior to sounding the
depth, and by affecting the velocity at 0.2-depth in shallow streams,
thereby distorting the vertical-velocity distribution. When making
boat measurements, the wind-caused waves may induce vertical mo-tion
in a cable-suspended meter, or the wind may cause an oscillatory
horizontal movement of the boat against the tag line; either move-ment
may affect the operation of the current meter. Table 11 sum-

marizes the results of an investigation (Kallio, 1966) on the effect of
vertical motion on the operation of Price, vane-type, and Ott (cosine
rotor 8646-A) current meters. The plus signs in table 11 indicate
overregistration by the meter; the minus signs indicate underregis-tration.
ACCURACY OF A DISCHARGE MEASUREMENT MADE UNDER
AVERAGE CONDITIONS
Carter and Anderson (1963) made a statistical analysis of the error
in discharge measurements made in natural streams under average
measuring conditions. They tested the following four assumptions on
which the computation of discharge measurements is based:
1. The rating of the current meter is applicable to the conditions of
the measurement.
2. The velocity observed at a point is a true time-averaged velocity.
3. The ratio is known between the velocity of selected points in the
vertical and the mean velocity in the vertical.
TABLE Il.-Registration errors, in percentage of stream velocity, caused by vertical
motion of current meter
Vertd motion Ut/s)
stream velocity (fcis)
02 0.4 0.6 0.8 10 1.2 15
Price current meter
(suspended by a cable)
05........................- ..................... -2.0 +10 +36 +72 Cl20 +150 +210
l.O....................- ......................... -30 -1.0 +10 +24 +40 +50 f56
15 ................. _-_-------------------------- -6.7 -67 -40 +1.3 +8.0 +25 f27
2O....~...............................~..~ ...... -2.5 -25 -2.5 -2.0 f4.0 +14.0
25...........~~~..............................~ 0
0"
c4.0
3.~~~~~~~~~~~~~~~~~~~~~~~.~..~..~...~.. .......... 0 i i i
-2.3
-A!.:
4o.............................~ ................ 0 0 0 0 -13 -1.3 i
5o............~~~..~.~....................~.~~ .. t.4 t10 +.6 0 -.2 +.a
7o................~..~~~......................~. -.7 -4 0 fl -.4 07 -4
1oo..........~.~.-..~ ............................ - 5 - 3 0 0 -3 -‘7 -1.3
Vane-type current meter
(suspended by a rod)
2.5-.--------------.....-------------------......
+4.0 f60 t20
t50 +10 +12
t33 +a.7 t10
+2.0 +6.5 t90
t2.0 +4.4 t6.4
-17 t3.7 c5.3
+12 tt3 +.3
-1.0 -26 -28
-.7 - 7 -.3
t44
t10
+6.7
+9.5
+76
t6.7
Cl 0 4.0
0
t72 +100 +160
fll +15 t26
t3.3
+8.5 ~~"0 +tl"7 .5
+a.0 f7.2 f64
f73 +77 t6.7
+25 +3.&3 +33
-.4 -2 -2.0
0 t.3 -4
Ott current meter
(cosine rotor 8646-A, standard tailpiece without vertical stabilizer,
attachment to cable hanger)
o5----------.-.------~.-.~-~----------------~~.. 0 t6.0 t10 c20 t30
10.-----------.-----------......---------------- 0 0 0 +4.0 t9.0
1.5------------.---------~-~--------------------- ; t13 t4.0
2.o------------.--------.......~.~--------------- z : t.5 t20
2.5------------.-----------......~--------------- 0 0 t1.6
3o------------.-~-~.......--------------~~...... ; : t +3 -+10
4o~.-~-.~~----.-----------------------.......... 0 +5 t1.0 f16
5.O------------.----.......~~-----------.....~--- ; 4 '0 6 "4 '06 t10
7.o------------.--------...---------------~...... +.3
and two-pin
+44 +70
+15 +30
+73 t17
+4.5 t95
+2a +64
t2.3 +6.0
+25 +3.a
t14 -20
+.7 t1.4

4. The depth measurements are correct, and the velocity and depth
vary linearly with distance between verticals.
Assumption 1 was tested by comparing the ratings obtained for
Price current meters when rated in flumes of different sizes. It was
found that the ratings can be repeated within a fraction of 1 percent.
When a Price meter was tested in a wind tunnel under differing
degrees of turbulence, its performance was not affected by increased
turbulence. The similarity of results using the Price, Ott, and Neyrpic
current meters has already been discussed on page 89. It was
therefore assumed that the standard deviation (SRi) of the error ratio
between measurement results obtained with different current meters
equals 1 percent.
Assumption 2 was tested in 23 different rivers where velocities for
consecutive time periods of 15,30,45,90,120, and 240 s were observed for
a 1-hr period at points corresponding to 0.2, 0.4, 0.6, and 0.8 depth.
The measurement verticals ranged in depth from 2.4 to 26.7 ft (0.7 to
8.1 m), and velocities ranged from 0.43 to 7.9 ft/s (0.13 to 2.4 m/s).
Statistical analysis showed that velocity fluctuations were randomly
distributed in time and space and that if 45-s observations were taken
at the 0.2- and 0.8-depth positions in 30 verticals, the standard devia-tion
(SRI) of the error ratio between observed and true point velocity
was 0.8 percent.
Assumption 3 was tested using more than 100 stream sites. The
standard deviation (SRs) of the error ratio between the mean velocity
obtained from 0.2- and 0.8-depth observations and the true vertical
velocity, using 30 verticals for the discharge measurement, was 1.15
percent.
Assumption 4 was tested using discharge measurements made at
127 stream sites, in which more than 100 verticals were measured in
each cross section. The discharge for each site was again computed
using the data for I/2, I/4, l/5, l/7, and l/10 of the total number of
verticals in each cross section. Error ratios between those computed
discharges and the discharges computed using all observation verti-cals
were determined. When 30 observation verticals were used, the
standard deviation (S,) of the error ratios was 1.6 percent.
The standard error of a discharge measurement (ST) was computed
from the equation
ST = -/ 62, Y + (s14)2 (SI$ 1’ + (S&r)“. (16)
For a measurement using velocity observations of 45 s at the 0.2- and
0.8-depth positions in each of 30 verticals, S, equaled 2.2 percent.
That means that if single discharge measurements were made at a
number of gaging sites using the standard method recommended in

6. DISCHARGE-MOVING-BOAT METHOD 183
this manual, the errors of two-thirds of the measured discharges
would be less than 2.2 percent.
SELECTED REFERENCES
Buchanan, T. J., and Somers, W. P., 1969, Discharge measurements at gaging stations:
U.S. Geol. Survey Techniques Water-Resources Inv., book 3, chap. A8, 65 p.
Carter, R. W., and Anderson, I. E., 1963, Accuracy of current-meter measurements:
Am. Sot. Civil Engineers Jour., v. 89, no. HY4, p. 105-115.
Chandler, T. S., and Smith, Winchell, 1971, Optical current meter use in southern
California: Am. Sot. Civil Engineers Jour., v. 97, HY9, p. 1461-1469.
Corbett, D. M., and others, 1943, Stream-gaging procedure: U.S. Geol. Survey Water-
Hulsing, Harry, Smith, Winchell, and Cobb, E. D., 1966, Velocity-head coefficients in
open channels: U.S. Geol. Survey Water-Supply Paper 1869-C, p.7.
International Standards Organization, 1968, Liquid flow measurement in open chan-nels
by velocity area methods: IS0 Recommendation R748, Geneva, 34 p.
Kallio, N. A.: 1966, Effect of vertical motion on current meters: U.S. Geol. Survey
Water-Supply Paper 1869-B, 20 p.
Pierce, C. H., 1941, Investigations of methods and equipment used in stream gaging;
Part 1, Performance of current meters in water of shallow depth: U.S. Geol. Survey
Water-Supply Paper 868-A, 35 p.
Rouse, Hunter, 1950, Engineering Hydraulics: New York, John Wiley and Sons, p. 222,
223.
Schubauer, G. B., and Mason, M. A., 1937, Performance characteristics of a water
current meter in water and air: Natl. Bur. Standards Research Paper RP 981.
Smoot, G. F., and Novak, C. E., 1968, Calibration and maintenance of vertical-axis
type current meters: U.S. Geol. Survey Techniques Water-Resources Inv., book 8,
chap. B2, 23 p.
Townsend, F. W., and Blust, F. A., 1960, A comparison of stream velocity meters: Am.
Sot. Civil Engineers Jour., v. 86, no. HY4, p. 11-19.
and hydrometeorology: Flood Control Series no. 22, p. 38-47, 51-55.
Young, K. B., 1950, A comparative study of mean-section and mid-section methods for
computation of discharge measurements: U.S. Geol. Survey open-file report, 52 p.
CHAPTER 6.-MEASUREMENT OF DISCHARGE BY
THE MOVING-BOAT METHOD
INTRODUCTION
On large streams and estuaries the conventional methods of
measuring discharge by current meter are frequently impractical and
involve costly and tedious procedures. There may be no suitable
facilities at remote sites. Where suitable facilities do exist, they may
be inundated or inaccessible during floods. At some sites, unsteady
flow conditions require that measurements be made as rapidly as
possible. Measurements on tide-affected rivers must not only be made
rapidly, but often continually, throughout a tidal cycle. The moving-

boat technique is a method of rapidly measuring the discharge of
large streams. It requires no fixed facilities, and it lends itself to the
use of alternate sites if conditions make this desirable.
The moving-boat technique is similar to the conventional
current-meter measurement in that both use the velocity-area ap-proach
in determining discharge. (See chapter 5.) In each method, a
measurement is the summation of the products of the subsections of
the stream cross section and their respective average velocities. Both
techniques require that the following information be obtained:
1. Location of sampling verticals 1, 2, 3,. . JZ across the stream in
reference to the distance from an initial point.
2. Stream depth, d, at each observation vertical.
3. Stream velocity, V, perpendicular to the cross section at each
observation vertical.
During a traverse of the boat across the stream, a sonic sounder
records the profile of the cross section, and a continuously operating
current meter senses the combined stream and boat velocities. A ver-tical
vane alines itself in a direction parallel to the movement of
water past it, and an angle indicator attached to the vane assembly
indicates the angle between the direction of the vane and the true
course of the boat. The data from these instruments provide the in-formation
necessary for computing the discharge for the cross section.
Normally, data are collected at 30 to 40 observation points in the
cross section for each run. Experience has shown that discharges
determined by the moving-boat technique match, within 5 percent,
discharges determined by conventional means.
The principal difference between the conventional measurement
and the moving-boat measurement lies in the method of data collec-tion.
The standard current-meter method of measurement uses what
might be called a static approach in its manner of sampling; that is,
the data are collected at each observation point in the cross section
while the observer is in a stationary position. This is in contrast to the
dynamic approach to data collection utilized in the moving-boat
method. Here, data are collected at each observation point while the
observer is aboard a boat that is rapidly traversing the cross section.
THEORY OF THE MOVING-BOAT METHOD
The moving-boat measurement is made by traversing the stream
along a preselected path that is normal to the streamflow. The
traverse is made without stopping, and data are collected at intervals
along the path. During a traverse of the cross section, the boat
operator maintains course by “crabbing” into the direction of the flow
sufficiently to remain on line (fig. 103). The velocity, V,, of the boat

with respect to the stream-bed along the selected cross-section path is
the velocity at which the current meter is being pushed through the
water by the boat. The force exerted on the current meter, then, is a
combination of two forces acting simultaneously: one force resulting
from the movement of the boat through the water along the cross-section
path and the other a consequence of the natural streamflow
normal to t.hat path.
The velocity measurement taken at each of the sampling points in
the cross section is a vector quantity that represents the relative
velocity of water past the vane and meter. This velocity, Vv, is the
vector sum of V, the component of stream velocity normal to the cross
section at the sampling point, and V,, the velocity of the boat with
respect to the streambed along the selected path. The vector diagram
in figure 104 depicts this relation.
The sampling data recorded at each observation point provide the
necessary information to define V,. The pulses-per-second reading
from the rate-indicator unit is used in conjunction with a rating table
to obtain the vector magnitude, Vv, while the angle reading, (Y, repre-senting
the angle the vane makes with the cross-section path, defines
the direction of the vector.
l Floats
D 13
Markers
@--- --- ---x3
at
7
D Qj
‘Markers
FIGURE 103.~-Sketch of stream with markers.

Stream velocity, V, perpendicular to the boat path (true course) at
each sampling point, 2, 3, 4, . . . (n. - l), can be determined from the
relation
V = Vv sin ff. (17)
The solution of the above equation yields an answer which represents
that component of the stream velocity that is perpendicular to the
true course even though the direction of flow may not be perpendicu-lar.
This is the desired component.
From the same vector diagram, it can be seen that
Lb = s V, cos a dt, (18)
where Lb is the distance that the boat has traveled along the true
course between two consecutive observation points, provided the
stream velocity is perpendicular to the path. Where the velocity is not
perpendicular, an adjustment is required as explained on pages
207-208, where the adjustment of total width and area is discussed.
If one assumes that CYis approximately uniform over the relatively
short distance that makes up any one increment, then (Y may be
treated as a constant. Therefore, equation 18 becomes
However,
(19)
(20)
where L,, is the relative distance through the water between two
consecutive observation points as represented by the output from the
rate indicator and counter. Therefore,
FIGURE 104.-Diagram of velocity vectors.

Lb = L, cos a. (21)
Finally, tl, stream depth at each observation point, is obtained by
adding the transducer depth to the depth obtained from the sonic-sounder
chart. Upon determining V, Lb, and d for each vertical, the
midsection method of computing a discharge measurement is used.
(See p. 80-82.)
Much of the accuracy of a moving-boat discharge measurement
depends upon the skill of the boat operator in maintaining a true
course. Although even the most experienced pilot cannot be expected
to keep the boat absolutely on course for an entire run, it is still
extremely important that the measurement begin and end on line
and that any deviations from the true course be kept as few in
number and as small in magnitude as possible.
If velocity readings are taken while the boat is moving off course in
an upstream direction, those readings will be greater than the true
velocities; if the readings happen to be taken when the movement is
toward the downstream direction, then the sampled velocity readings
will be less than the true velocities. Thus, if one assumes the equal
likelihood of overregistering or underregistering the stream veloci-ties
because of deviations from the true course, the errors can be
considered compensating in nature. However, to further insure the
reliability of the measurement, it is recommended that the results of
at least six individual runs, each with from 30 to 40 observation
points, be averaged to obtain the discharge when steady-flow condi-tions
exist, This is practicable because of the ease and speed with
which the extra runs can be made.
For unsteady-flow conditions on tidal streams, it will usually be
desirable not to average the results from a series of runs but rather to
keep them separate so as to better define the discharge cycle.
EQUIPMENT
Specialized instrumentation consisting of a sonic sounder, a vane
with indicator, a special current meter with its associated electronic
equipment, and an easily maneuverable small boat with some
modifications, provide the capability needed for a moving-boat meas-urement.
VANE AND ANGLE INDICATOR
A vane with an indicating mechanism is mounted on the bow of the
boat, with the vane centered approximately 3 to 4 ft (0.9 to 1.2 m)
below the water surface (fig. 105). This assembly consists of a vertical,
stainless-steel shaft with a pointer connected to its upper end and a
thin vertical-aluminum fin, I-ft (0.3 m) high and l?&ft (0.46m) long,

attached to its lower end. The shaft is housed in an aluminum bearing
tube and is mounted with ball bearings at the upper end and a teflon
bearing (no lubrication needed) in the lower end of the tube so that
the assembly (vane, shaft, pointer) is free to rotate as a unit. The
vertical vane alines itself in a direction parallel to the movement of
the water past it. The pointer is attached to the shaft so that it will be
in line with the vane, pointing directly into the flow past the vane.
The angle between the direction of the vane and the true course of the
boat (the line of the cross section) is indicated on a dial by the pointer.
The circular dial, calibrated in degrees on either side of an index
point, swivels freely about the upper end of the vertical shaft, just
below the pointer. A sighting device attached to the dial provides a
means of alining the index point on the dial with the true course. In
positive (downstream) streamflow the pointer above the dial will al-ways
point to the upstream side of the true course. Because the
upstream side may be to the left or right side, depending on the
direction in which the boat is traveling, and also because of possible
negative velocities, the dial is calibrated in degrees (from 0 to 90) on
both sides of its index point.
CURRENT METER
The current meter used by the U.S. Geological Survey is a compo-nent
propeller type with a custom body made for mounting on the
leading edge of the vane (fig. 105). The component propeller is less
susceptible than are other types of meters to vertical components of
velocity and was chosen to minimize errors created by the bobbing of
the boat.
A 24-toothed gear passing in the proximity of a magnetic field is
FIGURE 105.-Sketch of- boat showing equipment.

used to generate 24 pulses per revolution of the propeller. The large
number of pulses for each revolution facilitates the conversion of the
pulse rate to an analog readout. An electronic pickup assembly regis-ters
these pulses and feeds them into a frequency-to-voltage conver-ter,
and they are then displayed as a reading on an electrical meter.
At one end of the meter cable is a metallic probe that is screwed
into the meter body at the opening just behind the propeller nut (fig.
106). The probe is a permanent magnet that provides the magnetic
field necessary for pulse generation. To function properly, the probe
tip must be positioned within a few thousandths of an inch of the
24-toothed gear located within the meter. Adjustment of the probe
position, which is seldom required, should be done with care to pre-vent
damage to the probe tip.
Before the meter is used, the cup within the hub of the current-meter
propeller should be filled with thin oil (Ott propeller oil) as
shown in figure 106. The bearing assembly is then inserted into the
hub, and the propeller nut is tightened. After the conclusion of a
series of measurements, the cup should be emptied completely and
cleaned before storage.
FIGURE 106.-Component propeller-type meter.

RATE INDICATOR AND COUNTER
One of the principal functions of the rate indicator and counter is to
register the pulses received from the current meter, feed them into a
frequency-to-voltage converter, and then display them as a reading
on its electrical meter (fig. 107). These pulses are received through
the current-meter cable which is plugged into the marked receptacle
provided in the front panel of the unit. The current meter generating
the pulses is calibrated so that the reading on the electrical meter in
pulses per second can be converted to a particular velocity in feet per
second through the use of a rating table (fig. 108). The value read
from the electrical meter at any particular instant represents an in-stantaneous
readout of velocity.
Two scale selections are available for the rate-indicator unit. If the
switch is set at the “500” selection, the readout is taken from the
lower scale of the panel meter; at the 1,000 setting, the upper scale is
used. The 500 scale is the more sensitive of the two, and therefore its
use is recommended during those measurements in which the veloc-ity
of the water past the meter is not great enough to give readings
that exceed 500 pulses per second.
In addition to serving as a pulse-rate indicator from which velocity
determinations can be made, this unit has also been designed to pro-vide
a method of automatically selecting measurement points in a
section at regular intervals of travel distance. This design makes use
of the fact that each revolution of the meter propeller generates 24
OFF
FIGURE 107.-Control panel of rate indicator and counter.

evenly spaced pulses, and that from the calibration of the meter it can
be determined that one’ pulse is equal to some fraction of a foot of
meter travel through the water, or of water travel past the meter. By
using a set of frequency-dividing modules, provision is made for these
pulses to be electronically counted to a preset number, at which time
an audible signal is generated and the sounder chart is automatically
marked. The counter then automatically resets itself, and the process
is repeated. The purpose of the audible signal is to let the boat crew
know when a sampling location is reached. At this point they will
take an angle reading from the pointer and a readout from the elec-trical
meter. The markings on the sounder chart are automatically
triggered by an electrical impulse transmitted to the depth-sounder
unit by a relay in the meter electronics. The relay cable from the
counter to the sounder should be plugged into the appropriately
marked receptacle on the front panel of both units. The markings on
the sounder chart locate observation points in the cross section and
thus show where depth readings should be taken.
Preset intervals that are available on each unit are as follows:
Range selectron Pulse CO”RtS Dwtance, rn feet
1 1,024 18.75
2 2,048 37.5
3 4,096 75
4 8,192 150
5 16,384 300
The distances listed above are typical; exact ones depend upon the
calibration of the particular current meter used. If possible, the
pulse-selector switch should be set for a distance that will divide the
measured width between the two floats into from 30 to 40 increments.
For example, if the distance between floats is 500 ft (150 m), range 1
should be selected; for a distance of 1,000 ft (300 m), range 2 should be
used, and so on. Each distance listed in the table above represents&,
the relative distance through the water, and it will be somewhat
larger than the corresponding Lb value, the distance along the true
course that the boat has traveled. Lb is the distance one should use to
determine the number of observation points that will be taken in a
given cross section. However, the listed L, values can be used to
estimate roughly the number of observation points-the estimated
number will always be less than the actual number of observation
points.
The rate indicator and counter has two internal power supply
packs, each consisting of a set of nickel-cadmium rechargeable
batteries. A battery test switch located on the front panel of the unit
can be used to test the condition of either the 3.6-volt or the 12-volt
power supply (fig. 107). Testing should be done with both the main

power and the marker switches off. A reading of the panel meter
above the test switch will indicate the degree of charge. A needle
deflection greater than the battery testline mark indicates a satisfac-tory
charge level for most measurement requirements. A fully
charged battery pack will operate satisfactorily from 12 to 16 hr. A
marginal reading, with needle deflection just to the test mark, indic-ates
approximately 4 to 8 hr of useful battery operation remaining. A
reading below the mark serves as a warning that a battery charge is
needed.
BATTERY CHARGER
The battery charger serves as a dual unit for charging either one of
the two battery supply packs located within the rate indicator and
counter unit. Its charge plug is inserted into the charge receptacle
located on the panel of the rate indicator and counter. The other plug
should be connected to a ll&volt, 60-cycle line power supply. With
proper care the batteries should provide many years of service.
SONIC SOUNDER
A portable sonic sounder (fig. 109) is used to provide a continuous
strip-chart record of the depth of the stream, that is, a profile of the
cross section between the two floats. Its transducer releases bursts of
ultrasonic energy at fixed intervals. The instrument measures the
time required for these pulses of energy to travel to the streambed, to
be reflected, and to return to the transducer. With a known propaga-tion
velocity of sound in water, the sounder computes and records the
depth. Accuracy of the recording depth sounder is approximately
+0.5 ft (0.15 m). The sounder used in this application is a commer-cially
available model with a minor modification for automatically
marking the chart at each observation point in response to an electri-cal
pulse from the meter electronics. The sounder is powered by a
standard lead-acid battery of 6 or 12 volts, depending on the model of
the sounder.
One minor modification to the sonic sounder is the installation of a
receptacle on its front panel into which is plugged the relay cable
from the rate indicator and counter. The purpose of this relay connec-tion
is to transmit the electrical pulses from the counter unit that will
automatically trigger the vertical-line markings on the sounder
chart. This provision for automatically marking the sounder chart at
regular intervals of distance traveled eliminates the need for the
manually operated “mark” switch, except in the event that the relay
cable is damaged or missing. Then, as an expedient measure, the
chart is marked at each observation point by manually pulling the
switch at each tone signal sounded by the counter unit.
Three paper-feed speeds are provided with the unit. The small lever

in the lower left-hand corner of the recorder chassis is the control. The
set of speeds available will vary according to the model. Some models
NORMAL 2, ’ ’ ,5
OFF/
ClANnPv al?.-nsq ‘8
FIGURE 109.-Sonic sounder and control panel

provide choices of 12, 30, and 60 inlhr (0.30, 0.76, and 1.52 m/hr), and
others 36, 90, and 180 in/hr (0.91, 2.29, and 4.57 m/hr). A suitable
chart speed is one that results in a spacing of approximately 0.25 in
between the vertical-line markings that are set on the chart during
the measurement. Spacing wider than that needlessly wastes chart
paper, whereas much narrower spacing results in poor resolution of
the streambed trace. Narrow spacing also causes difficulty in deter-mining
the fractional part of a full spacing that should be assigned to
the final width increment. Width of spacing is dependent upon the
range setting on the counter unit, the current-meter velocity, and the
chart speed. Table 12, computed for a current-meter velocity of 5 ftls
(1.52m/s), provides an example of typical spacing distances expected
for various combinations of chart speed and range distance.
BOAT
Any easily maneuverable small boat that is sufficiently stable for
the stream on which it is to be used is adequate for a moving-boat
measurement. A photograph of a boat with the vane assembly
mounted is shown in figure 110.
Preparation of the boat.-A 12x 12x?&in steel plate should be so
attached that it is centered on the bow of the boat, perpendicular to
the centerline of the boat, and as nearly vertical as possible. This
plate must be securely anchored because at high velocities great force
will be exerted on it. It may be necessary, depending on the style of
boat being used, to erect handrails on the forward part of the boat,
similar to those shown in figure 105. This is done for the safety of the
angle reader who must stand in the bow.
Mounting of the equipme&.-The 12x12-in aluminum plate on the
vane assembly is attached to the 12x 12-in steel plate on the bow of
the boat. It is necessary to clamp these two plates together and drill
four holes for accepting bolts to permanently fasten the plates to-gether.
The general location of the bolt holes should be near the four
corners, but exact placement is not critical.
The two cap screws in the depth adjustment clamp that hold the
aluminum bearing tube of the assembly (fig. 111) can be loosened so
TABLE 12.-Spacing of vertccal-line markings, in Lnches, on the sonic-sounder chart for
various combinations of chart speed and range distance
[Computed for a current-meter velocity of 5 ftki ]
Range dmtance
Chart speed
18 75 ft 37.5 ft 75 ft 150 ft 300 ft
36 inlhr ----_ ______ -----_- ______
0:::
0.08 0.16 0.32 0.64
90in/hr -______-----__-___--____ .20 .40 .80 1.6
180inhr ---____----------__-____ .20 .40 .80 1.6 3.2

Ppwll ot
c r:
FIGURE llO.-Boat with mounted vane assembly
!
FIGURE Ill.-Detailed view of vane-mounting assembly.

that the tube may be either raised or lowered in order to position the
meter at the desired depth. This depth should preferably be at least 3
ft (0.91 m) to avoid the effect of surface disturbances and not greater
than 4 ft (1.22 m) to avoid the danger of too great a torque being
exerted at high velocities. Caution should be exercised to avoid high
boat speeds, for the drag on the vane assembly is proportional to the
square of the velocity of the water past the vane and therefore in-creases
very rapidly with speed.
The sonic-sounder transducer is mounted on a support arm at a
depth of either 2 or 3 ft (0.61 or 0.91m). It can be positioned by first
loosening the two cap screws that secure the support arm to the alu-minum
bearing tube of the vane assembly and then moving the arm
either up or down to the desired depth.
Because the vane assembly is mounted perpendicular to the cen-terline
of the boat, it will change slightly from its original vertical
position as a result of the raising of the bow of the boat during the
moving-boat measurement. To offset this change and thus allow for
vertical positioning of the assembly during normal boat operation,
the mounting assembly provides for a compensating angle adjust-ment
to be accomplished through the use of two adjusting bolts and a
pivot plate (fig. 111). By screwing these bolts either inward or out-ward,
the lower portion of the assembly can be pivoted toward or
away from the boat. If the adjusting bolts are touching the aluminum
plate when the assembly is in a vertical position, they must be
screwed away from the plate so that the lower portion of the assembly
can then be pivoted toward the boat and secured in position by use of
two clamping bolts. The degree of adjustment would depend upon the
operating velocity of the boat during the measurement.
Removal of the equipment.-After the measurements are com-pleted,
the vane assembly can be removed while leaving the alumi-num
plate bolted to the steel plate on the bow of the boat. This is
accomplished by first loosening the wing nuts on the two clamping
bolts of the plate and then removing the clip and sliding out the pivot
pin that secures the assembly to the aluminum plate (fig. 111). Prior
to doing this, the meter and the transducer cables should be discon-nected
from the rate indicator and the sonic sounder, respectively.
MEASUREMENT PROCEDURES
Procedures for a moving-boat measurement include selection and
preparation of a suitable measuring site, preparation and assembly of
the equipment used for the measurement, and a selection of settings
for the instruments used to collect the data.
SELECTION AND PREPARATION OF THE MEASUREMENT SITE
Some preparation is required at the site prior to starting a series of

moving-boat measurements. First, a path for the boat to travel is
selected, it being as nearly perpendicular to the flow direction as
possible. Then, two clearly visible range markers are placed on each
bank in line with this path. The color of these markers should con-trast
sharply with the background. Spacing between the markers is
dependent upon the length of the path, the longer paths requiring
greater spacing. Approximately 100 ft (30 m) of spacing is needed for
each 1,000 ft (300 m) of path length. Next, anchored floats are placed
in the stream 40 to 50 ft (12 to 15 m) from each shore along the
selected path (fig. 103). In making a traverse, this distance is needed
for maneuvering the boat when entering or leaving the path. The
floats should be placed so that the depth of water in their vicinity is
always greater than 3 to 4 ft (0.9 to 1.2 m), which is vane depth. Large
plastic bleach containers are suitable for use as floats; Styrofoam
cubes can also be used. It is preferable not to place the floats directly
in the boat path but rather 10 to 20 ft (3 to 6 m) upstream. Their
purpose is to mark the beginning and ending points of the boat meas-urement,
and by offsetting them upstream they can serve that pur-pose
without being in the way as the boat approaches along the
selected path. Finally, the width of the stream is measured by trian-gulation,
stadia, or other methods, and the exact locations of the
floats are determined. Because the floats are close to the bank, a tape
measure can be used to determine the distance from edge of water to
each float. These distances should be recorded in the spaces provided
on the front page of the discharge-measurement notes, for they will be
used in the computation of the measurement.
If a station is to serve as a site for moving-boat discharge meas-urements
on a continuing basis, it will probably be desirable to con-struct
permanent range markers. Such markers would serve two
useful purposes. First, determination of stream width would become a
relatively simple procedure because of the availability of the constant
distance between the markers once this distance has been estab-lished.
A tape measure could be used to obtain the horizontal distance
from the nearest marker to the water’s edge on each bank. Subtract-ing
these two distances from the established distance between the two
streamward markers would provide the width of the stream. A second
advantage would be that if the need arose, the markers could serve as
permanent initial points from which cross-section profiles of the
measurement section could be constructed.
PREPARATION OF THE EQUIPMENT
The special equipment and instruments necessary for a moving-boat
measurement have been described in some detail on pages 187-
197 under the general heading “Equipment.” The purpose of this

section of the manual is to summarize, for the convenience of the boat
crew, the steps involved in the assembly of the equipment and in the
selection of the instrument settings.
ASSEblBLY OF -l-HE EQUIPh4F.N-I‘
The steps listed below should be followed in assembling the equip-ment:
1. Permanently mount a steel plate to the bow of the boat (p. 195)
and then attach the aluminum plate of the vane assembly to it
(p. 197). Both of these steps are “one time” operations that
should be completed in advance of the trip.
2. Several days prior to the trip, check the batteries in the rate-indicator
and counter unit and the storage battery for the sonic
sounder to see that they are adequately charged. This will pro-vide
time to charge the batteries, if necessary, before the start
of the trip.
3. Attach the sonic-sounder transducer to its support arm on the
vane assembly (fig. 105).
4. Attach the current meter to the leading edge of the vane (fig.
105).
5. Use the pivot pin and clip and the two clamping bolts of the
aluminum plate to secure the vane assembly to the plate (fig.
111).
6. Position the current meter at the desired depth (3 to 4 ft). This is
done by loosening the two cap screws in the depth adjustment
clamp and then raising or lowering the aluminum bearing tube
to the proper position before retightening the screws. Measure
the meter depth and record it in the measurement notes once
positioning is completed.
7. Route the current-meter cable up the vane assembly and plug it
into the marked receptacle on the rate indicator and counter
unit. To prevent entanglement, the cable should be taped to the
aluminum bearing tube in several places. It is necessary to
provide some slack in the cable at its lower end to allow for the
movement of the meter as the vane rotates during the meas-urement.
8. Position the sonic-sounder transducer at a depth of 2 or 3 ft. This
is accomplished by first loosening the two cap screws that se-cure
the support arm to the aluminum tube and then sliding
the arm either up or down the tube to the proper position before
tightening the screws. Measure the transducer depth and re-cord
it in the measurement notes at this time.
9. Route the transducer cable up the vane assembly, securing it by
tape to the aluminum bearing tube; feed it through the hole

provided near the hinge of the sonic-sounder case; and then
plug it into the marked receptacle at the back of the dividing
plate.
10. Insert the battery cable of the sonic sounder into the marked
receptacle at the back of the dividing plate of the unit. It can be
fed through one of the holes provided near the hinge. A stand-ard
6- or 12-volt storage battery, depending on the sonic-sounder
model used, should be used as a power supply (p. 193).
11. Plug the relay cable from the counter unit to the sonic sounder
into the marked receptacle on the front of each unit.
12. Use the two adjusting screws (fig. 111) to provide for the compen-sating
angle adjustment of the vane assembly as described on
page 197.
SELECTION OF THE INSTKUbfENT SETTINGS
The notekeeper is responsible for the functioning of the rate indi-cator
and counter and the recording depth sounder. To assure proper
operation of the equipment, it is necessary that he make several
preliminary instrument settings for each unit prior to the measure-ment.
The following is a list of the steps involved in obtaining these
settings:
Sonic sounder:
1. Check to see that the pulleys turn smoothly and that the stylus
enters the track easily.
2. Set the operation switch to “stand by” position.
3. Turn on the unit by rotating the “record” switch clockwise to
some low-numbered position and wait a few minutes for the tubes to
warm up.
4. Set the depth-range selection at phase 1 (O-60 ft) and advance
the gain control to obtain the “zero mark” near the top of the sounder
chart.
5. Set the “zero mark” on the zero line of the recorder paper
through use of the zero adjustment screw located behind the top pul-ley.
6. Continue to advance the gain until the “echo mark” appears
somewhere below the “zero mark.” If no echo appears when the gain
is opened, switch the range control to the next phase (60-120 ft) and
so on until the bottom is found.
7. Determine the optimum chart speed through use of table 12;
then use the small lever in the lower left-hand corner of the recorder
chassis to make this selection.
8. Change the operating switch from “stand by” to “normal” posi-tion
several minutes before the measurement begins. This will start

the chart recording and provide an opportunity for a final check of
instrument operation before the measurement begins.
Rate indicator and counter:
1. Select the desired scale for the rate-indicator meter located on
the panel.
2. Check both battery packs with the battery test switch. This final
check will have been preceded by a test several days before the meas-urement
date in order to provide time to charge the batteries if
needed (p. 199).
3. Set the rate-indicator switch to “on” position.
4. Set the marker switch to “on” position. (The actual marking will
not begin until the “start” button is depressed.)
5. Select a range setting that will provide between 30 to 40 obser-vation
points. Because of the scale settings available, this may not
always be possible, in which case choose that comprise setting that
will come closest to meeting this provision.
After all the control settings are completed, the instruments are
ready for use. The “start” and “stop” buttons on the panel of the
counter unit are used to begin and end instrument operation at the
precise moments the bow of the boat reaches the first and second
floats, respectively. The operation of these button controls in regard
to the starting and stopping procedure is described in the section of
the manual that immediately follows.
FUNCTION OF THE CREW MEMBERS
Three crew members are necessary for making a moving-boat dis-charge
measurement. They include a boat operator, an angle ob-server,
and a notekeeper. Before crew members begin making dis-charge
measurements by the moving-boat method, it is important
that they develop a high degree of proficiency in all phases of the
technique. This can be done by making practice measurements at a
site where the discharge is known and then comparing the moving-boat
discharge with the rated discharge. If there is no suitable site
available for that purpose, the boat crew should make a series of
moving-boat measurements at a single location and compare results
for repeatability.
BOAT OPERATOR
Before the measurement begins, the boat operator should become
thoroughly familiar with the sampling site. In tidal streams the
operator should be familiar with conditions during all phases of the
tidal cycle. This will help him avoid running the boat aground in
shallow depths and damaging the submerged equipment. While man-

euvering the boat, it is necessary to avoid sudden sharp turns that
might result in damage to the meter cable by causing it to be wrapped
around the vane assembly.
The operator should select an approach path for the boat that will
allow it to be properly maneuvered into position prior to passing the
first float. The path should begin from a downstream position as close
to the riverbank A s depth considerations permit. From such a starting
point the boat can be accelerated to near its normal operating speed
and the turn into the measuring section can be completed before the
measurement begins. By attaining both the proper speed and aline-ment
prior to reaching the float, the instrument readings will have
time to stabilize before the initial sample is taken.
During a traverse the only function of the boat operator is to pilot
the boat. He maintains course by “crabbing” into the direction of flow
sufficiently to remain on line throughout the run. As varying stream
velocities are encountered in the cross section, he should rely more
upon steering adjustments to keep the proper alinement than upon
acceleration or deceleration of the boat. Alinement is determined by
sighting on the shore which is being approached. Much of the accu-racy
of the measurement depends on the skill of the boat operator in
maintaining a true course with the boat.
Because the stream velocity is calculated as a sine function of angle
alpha (fig. 104, eq. 17), small angles should be avoided whenever
possible. It is desirable to maintain angle alpha at approximately 45”.
The reason for this is that an error of several degrees in reading angle
alpha would be more significant at. small angle readings than the
same error at larger angle readings. In order to maintain an angle of
45”, the velocity of the boat must be equal to that of the stream. This
can be done if the stream velocity is greater than 2.5 ftls (0.75 m/s);
however, control of the boat is difficult to maintain below that veloc-ity.
For example, in tidal streams the stream velocity will often vary
from 0 to several feet per second; therefore, it is not always possible to
maintain an angle as large as 45”, and the measurement must be
made using smaller angles.
ANGLE OBSEKVEK
A second man alines the dial of the vane indicator through its
sighting device and, upon receiving the audible signal from the pulse
counter, he reads the angle formed by the vane with respect to the
true course. He reports the angle to the notekeeper who then records
it. If the boat has strayed from the true path, the angle reader should
sight parallel to the cross-section markers rather than at the markers
themselves.

NOTEKEEPER
The notekeeper has several functions to perform. Prior to the
measurement it is his responsibility to see that the preparation of all
equipment pertaining to the rate indicator and counter and to the
sonic sounder is completed satisfactorily. That includes not only
equipment assembly but also selection of appropriate instrument set-tings.
The accuracy of the sonic sounder varies with changes in the veloc-ity
of sound in water, which in turn varies slightly with temperature,
dissolved solids, and other variables. Thus sounder output should be
compared to a known depth. Any significant error detected in the
comparison can be expressed as a percentage of the known depth, and
this percentage would be applicable to all depths determined by the
sonic sounder. Consequently, this percentage correction should be
applied to the total area and total discharge.
A check to determine that the current meter and rate indicator are
functioning properly is also desirable. Such a check can be made by
comparing the indicated velocity to a velocity determined by the Price
current meter. This test is intended to determine proper operation
only and is not intended for calibration purposes.
It is the notekeeper’s responsibility to operate the controls provided
on the equipment for starting and stopping the counter. It is impor-tant
to the accuracy of the measurement that this unit promptly
begin and end its operation at the first and second floats, respectively.
This is accomplished by operating the “start” and “stop” buttons on
the panel of the counter in the following manner:
1. Approximately 1 s before the boat reaches the first float, the
“start” button is depressed; then it is released at the moment of pass-ing.
This marks the sounder chart, resets the counter, and starts it.
Marking of the sounder chart and sounding of the beeper (tone
signal) will be automatic during the measurement. This will occur at
regular intervals as determined by the setting of the range switch on
the panel of the counter unit.
2. At the moment the bow of the boat reaches the second float, the
(‘stop” button is depressed for 1 s and then released. This marks the
sounder chart, signifying the end of the measurement, and stops the
counter.
During the measurement the notekeeper records the angle reading
at each signal as it is called out by the angle reader. He also reads and
records the instantaneous “velocity” from the rate indicator meter at
the same time. Readings are taken at all observation points as de-fined
by the tone signals, including the two float positions.
If the time between consecutive measurements is short, it is desira-

ble to leave the operating switch of the sonic sounder in the “normal”
position until the measurement series is concluded. In this way the
chart continues to advance between measurements, but there are no
vertical line markings. This absence of vertical lines provides a gap
on the chart that clearly sets off one measurement from another.
COMPUTATION OF THE DISCHARGE
MEASUREMENT
COMPUTATION OF UNADJUSTED DISCHARGE
The method of computing discharge measured by the moving-boat
technique is basically similar to the computation method used for
conventional current-meter discharge measurements. (See P. 80-
82). The discharge in a subsection, y, is the product of the subsection
area of the stream cross section and the average velocity in the sub-section.
The midsection method of computation is used in which it is
assumed that the average velocity at the observation vertical is the
average velocity for a rectangular subsection. The rectangular sub-section
extends laterally from half the distance from the preceding
observation vertical to half the distance to the following observation
vertical and extends vertically from the water surface to the sounded
depth (fig. 112). The summation of the discharges of the subsections,
41, 42, 43, * . . q,,, is the total unadjusted discharge of the stream. A
step-by-step outline of the computation procedure, which refers to the
sample measurement notes shown in figure 113, is given here as a
guide to the hydrographer who computes the discharge from the field
observations.
1. The data in the first column of figure 113 are the angle readings
recorded by the notekeeper during the measurement. Because these
readings begin and end at the float positions (there are no edge-of-water
readings), they represent the values observed at locations 2, 3,
4 ) . . . (n -1).
2. Each value in column 2 represents an incremental distance the
boat has traveled along the cross-section path between two consecu-tive
observation points. For example, CX,(~c ol. 1) represents the angle
reading at location x, and L,,,r (col. 2) is the incremental distance the
boat has traveled along the true course, extending from the previous
observation point, x -1, to the location x where the reading was
taken.
The values in column 2 can be read directly from a table (fig. 108)
by using the angle values recorded in column 1 and the range number
as determined by the range selection on the counter unit. Two excep-tions
are the first and last values in the column, representing the
distance to each float from its nearest edge of water. They are deter-

mined by direct measurement prior to the actual run. This is neces-sary
because the actual boat run does not begin and end at the edge-of-
water positions and thus is not set up to measure those distances.
Therefore, the beginning angle reading, (Ye, at the first float is not
used for obtaining distance from the edge of water to that float. It
should also be noted that L!,:, is always recorded as one-half of the
value found in the table. This is necessary because the counter unit
has been programed to signal at a “half-count” on its first count
routine. All remaining values can be recorded directly from the table
of LI, values, without any changes, with the possible exception of the
one determined from the last angle reading which was made at the
second float. This angle reading may or may not have been made at
-
FIGURE llZ.--Definition sketch of midsection method of computation superimposed
on a facsimile of a sonic-sounder chart.

the end of a full count by the counter unit. In the sample measure-ment
the value recorded was three-fourths of that in the table be-cause
the sounder chart distance between the last two vertical mark-ings
was approximately three-fourths of the normal spacing.
3. Each value recorded in column 3 represents the distance from
the initial point (marker) to the observation point where the data
were collected. The data in column 2, together with the “distance to
float” and the “distance to marker” values recorded on the front sheet
of the discharge measurement notes (fig. 113) are used to obtain these
cumulative distances. For a moving-boat measurement, these dis-tances
are defined as follows:
b, = distance from initial point (marker) to edge of water
b, = b, + measured distance to float from edge of water
b, = b, + L,,,
bq = b:, + L,,
FIGURE 113.-Sample computation notes of a moving-boat measurement.

i;,,:;; = i;,,,; i Lb( ,,-,)
b,, = b(,,-,, + measured distance from float to edge of water
b trl+,) = b,, + distance to final point (marker).
4. Each of the incremental widths in column 4 represents the
distance that extends laterally from half the distance from the pre-ceding
meter location (x-l), to half the distance to the next, (x+1).
These values are obtained by using the distances in column 3.
5. Each of the values in column 5 represents the stream depth at a
sampling point in the cross section. These values are obtained by
adding the transducer depth to each of the depth readings recorded on
the sounder chart at the sampling locations.
6. The data in column 6 are the pulses-per-second readings re-corded
by the notekeeper during the measurement.
7. The values recorded in column 7 represent the instantaneous
velocity of the water past the vane at each observation point. They
are read directly from the meter-rating table (fig. 108), using the
pulses-per-second values of column 6.
8. The data in column 8 are the sine function values of the angle
readings in column 1. These values may be obtained from the sine
table in figure 108, using the angle readings of the first column.
9. Each of the values in column 9 represents the stream velocity
normal to the cross section at that particular sampling point.. To
obtain these values, it is necessary to multiply each I’,* value in
column 7 by the corresponding sin CY value in column 8.
10. The values in column 10 represent the individual subsection
areas for the measurement. They are obtained by multiplying the
widths of column 4 by their corresponding depths in column 5. The
incremental areas are then summed to provide the total unadjusted
area for the measurement.
11. Each quantity in column 11 represents the unadjusted dis-charge
through one of the subsections of the discharge measurement.
These values are summed to provide the total unadjusted discharge of
the measurement.
12. This column is used for recording any descriptive remarks per-taining
to the measurement.
ADJUSTMENT OF TOTAL WIDTH AND AREA
As explained on page 186, the relation expressed by the equation L,,
= L,, cos (Y is used to obtain the incremental widths across the stream.
This equation is based on the assumption that a right-triangle rela-tionship
exists among the velocity vectors involved. If the flow is not
normal to the cross section, that assumed situation does not exist and
the use of the equation can result in a computed width that is too

large or too small (fig. 1141, depending on whether the vector quantity
representing the oblique flow has a horizontal component that is op-posed
to, or in the direction of, that of the boat path. Thus in figure
114 the computed width would be AB’ of the right triangle AB ‘C
rather than the true width AB of oblique triangle ABC. In this case
the computed width is too large, whereas the computed width DE’ of
right triangle DE% is less than the actual width DE of oblique
triangle DEF.
Ideally the correction for error in the computed width would be
applied to that particular increment in the cross section where the
error occurred. However, in practice only the overall width is directly
measured, and thus only the total width is available for comparison
with the computed quantities. Therefore, if the sum of the computed
incremental widths does not equal the total measured width of the
cross section, it is assumed that each increment requires a pro-portionate
adjustment.
The moving-boat method uses the relation between the measured
and computed widths of the cross section to determine a width/area
adjustment factor. To obtain that coefficient, the measured width of
the cross section is divided by its computed width, that is
where
k, = width/area adjustment factor,
B,,, = measured width of cross section, and
B, = computed width of cross section.
The coefficient (k,) is then used to adjust both total area and total
discharge of the measurement, on the basis of the previously men-tioned
assumption that the error in width is evenly distributed, on a
percentage basis, across each width increment of the cross section.
The computation notes in figure 113 provide an example of the
application of a width/area adjustment coefficient.
ADJUSTMENT OF MEAN VELOCITY AND TOTAL DISCHARGE
During a moving-boat discharge measurement, the current meter
is set at a predetermined fixed depth of from 3 to 4 ft (0.9 to 1.2 m)
below the water surface. In other words, this technique uses the sub-surface
method of measuring velocity. (See page 136.) The measure-ment
is computed by using constant-depth subsurface velocity obser-vations
without adjustment coefficients, as though each observed
velocity were a mean in the vertical. In adjusting the computed dis-charge,
each measured velocity should ideally be multiplied by a
coefficient to adjust it to the mean velocity in its vertical. However, it

(Computed width]
FIGURE 114.-Comparison of actual and computed values
of incremental widths.

is assumed that in the larger streams where the moving-boat teeh-nique
would be applicable, these coefficients would be fairly uniform
across a section, thus permitting the application of an average veloc-ity
coefficient to the total discharge. Information obtained from sev-eral
vertical-veolocity curves, well distributed across the measure-ment
section, would be needed to determine a representative velocity
coefficient for the total cross section.
DETERMINATION OF VERTIC4L-VELOCITY ADJUSTMENT
FACTOR
Vertical-velocity curves (p. 132- 133) are constructed by plotting
observed velocities against depth. The vertical-velocity curve method
calls for a series of velocity observations (by conventional methods) at
points well distributed between the water surface and the streambed.
Normally these points are chosen at O.l-depth increments between
0.1 and 0.9 of the depth. Observation should also be made at least 0.5
ft (O.l.5 m) from the water surface and 0.5 ft (0.15 m) from the
streambed; for this particular application, a velocity reading should
be made at the moving-boat sampling depth of from 3 to 4 ft (0.9 to 1.2
m) below the water surface. Once the velocity curve has been con-structed;
the mean velocity for the vertical can be- obtained by
measuring the area between the curve and the ordinate axis with a
planimeter, or by other means, and then dividing this area by the
length of the ordinate axis.
To obtain a velocity-correction coefficient at location x in the cross
section, the mean velocity in the vertical is divided by the observed
velocity at the measured depth, that is,
where
kv = vertical-velocity adjustment factor,
7 = mean velocity in the vertical, and
V = observed velocity (3- or 4-ft depth).
To arrive at a representative average coefficient, coefficients should
be determined at several strategically located verticals that are rep-resentative
of the main portion of the streamflow. Once an average
coefficient has been determined, it should not be necessary to rede-termine
it each time when making future discharge measurements at
the same site. However, it would be necessary to test its validity at
several widely varying stages and, in estuaries, at widely different
parts of the tidal cycle.
Investigations on the Mississippi River at both Vicksburg and St.
Louis, on the Hudson River at Poughkeepsie, and on the Delaware

7. DISCHARGE-TRACER-DILUTION METHOD 211
River at Delaware Memorial Bridge all indicated coefficients that lie
in the narrow range of 0.90 to 0.92 for adjusting the subsurface veloc-ity
to the mean velocity. Carter and Anderson (1963) present a table
of velocity ratios and standard deviations for various relative depths.
That table indicates that for depths of 10 ft (3 m) or more, an average
coefficient of 0.90 is satisfactory for adjusting velocities obtained 4 ft
(1.2 m) below the surface to mean velocity. The sample from which
the data in that table were obtained consisted of 100 stream sites at
each of which 25 to 30 verticals had been used. Similar conclusions
concerning subsurface velocity coefficients can be drawn from table 2
(p. 132).
API’LICATION OF VELOCITY ADJUSTMENT TO COMPUTED DISCHARGE
Application of the vertical-velocity adjustment factor is made im-mediately
after the width-area adjustment has been applied to the
computed discharge. In other words, after the computed discharge has
been multiplied by the width-area adjustment factor, the resulting
product is multiplied by the vertical-velocity adjustment factor. The
final product is the adjusted, or “true,” discharge for the measure-ment.
(See fig. 113.)
SELECTED REFERENCES
Buchanan, T. J., and Somers, W. P., 1969, Discharge measurements at gaging st,ations:
U.S. Geol. Survey Techniques Water Resources Inv., book 3, chap. A8, 65 p.
Carter, R. W.. and Anderson, I. E., 1963, Accuracy of current-meter measurements:
Am. Sot. Civil Engineers Jour., v. 39, no. HY4, p. 105-115.
Smoot, G. F., and Novak, C. E., 1969, Measurement of discharge by the moving-boat
method: U.S. Geol. Survey Techniques Water Resources Inv., book 3, chap. All,
22 p.
CHAPTER 7.-MEASUREMENT OF DISCHARGE
BY TRACER DILUTION
GENERAL
The measurement of stream discharge by dilution methods depends
on the determination of the degree to which an added tracer is diluted
by the flowing water. Any substance can be used as a tracer if it meets
the following criteria:
1. It dissolves readily in water at ordinary temperatures.
2. It is either absent in the water of the stream or present only in
very low concentrations.
3. It is not decomposed in the water of the stream and is not retained
or absorbed in significant quantity by sediments, plants, or
other organisms.
4. It can be detected in extremely low concentrations by simple
methods.

5. It is harmless to man and animals in the concentration it assumes
in the stream.
Until recent years chemical salts, primarily common salt (NaCl),
were usually used as the tracers injected into the streams. The use of
salt tracers, on all but the smallest streams, was limited, however, to
the sudden-injection method, because of the difficulty of handling the
large quantities of salt solution required by the usually more accu-rate
constant-rate-injection method. In recent years, and particularly
in the U.S.A., the use of dye tracers in the constant-rate-injection
method has become the most popular method of discharge measure-ment
by tracer dilution. That has resulted from the development of
fluorescent dyes and fluorometers that can detect those dyes at very
low concentrations. The use of fluorescent dyes is not as popular in
Europe as in the U.S.A. There, kolorimetric analysis, using sodium
dichromate as the tracer dye, is the most widely used means of
measuring discharge by the constant-rate-injection method. How-ever,
where the sudden-injection method is to be used, the use of
common salt as a tracer is still preferred, particularly on the smaller
streams, because of the greater ease in handling salt and in determin-ing
concentrations. Radioactive elements, such as gold 198 and
sodium 24, have also been used in recent years as the tracers in the
sudden-injection method, but the use of such elements is still (1980)
considered experimental.
The tracer-dilution methods of measuring discharge are more dif-ficult
to use than the conventional current-meter method, and under
most conditions the results are less reliable. Dilution methods should
therefore not be used when conditions are favorable for a current-meter
measurement of discharge. Tracer-dilution methods of measur-ing
discharge in open channels can be used advantageously in rough
channels that carry highly turbulent flow.
THEORY OF TRACER-DILUTION METHODS
In the tracer-dilution methods of measuring discharge, a tracer
solution is injected into the stream to be diluted by the discharge of
the stream. From measurements of the rate of injection, the concen-tration
of the tracer in the injected solution, and the concentrations of
the tracer at a sampling cross section downstream from the injection
site, the stream discharge can be computed.
Either of two methods may be used for determining the discharge of
a stream by tracer dilution. The first method, the constant-rate-injection
method, requires that the tracer solution be injected into the
stream at a constant flow rate for a period sufficiently long to achieve
a constant concentration of the tracer in the streamflow at the
downstream sampling cross section. The second method, the sudden-

injection method, requires the instantaneous injection of a slug of
tracer solution and an accounting of the total mass of tracer at the
sampling cross section. Another use is often made of the sudden-injection
method that is not concerned with degree of dilution. Where
the cross-sectional area of the flow is constant, as in pressure conduit,
the sudden-injection method may be used to determine the velocity of
flow; discharge can then be computed by using that velocity and the
known cross-sectional area. (See p. 533.1
THEORY OF THE CONSTANT-RATE-INJECTION METHOD
A constant-rate-injection system is shown schematically in figure
115. If the tracer is injected for a sufficiently long period, sampling of
the stream at the downstream sampling cross section will produce a
concentration-time curve similar to that shown in figure 116. The
stream discharge is computed from the equation for the conservation
of mass, which follows:
or
where
q is the rate of flow of the injected tracer solution,
Q is the discharge of the stream,
C,, is the background concentration of the stream,
C, is the concentration of the tracer solution injected into the
stream, and
C, is the measured concentration of the plateau of the
concentration-time curve (fig. 116).
L Q+q -Tracer concentration=Cp
FIGURE 115.-Constant-rate-injection system.

THEORY OF THE SUDDEN-INJECTION METHOD
If a slug of tracer solution is instantaneously injected into a stream,
sampling of the stream at the downstream sampling cross section will
produce a concentration-time curve similar to that shown in figure
117. The equation for computing stream discharge, which is again
based on the principle of the conservation of mass, is
1 1
Q = I,(cv-cc,,dt ’
(25)
where
Q is the discharge of the stream,
V, is the volume of the tracer solution introduced into the
stream,
C, is the concentration of the tracer solution injected into the
stream,
C is the measured tracer concentration at a given time at the
downstream sampling site,
C, is the background concentration of the stream, and
t is time.
The terml=(C - CJ dt is the total area under the concentration-time
curve. In &actice the term J:(C - C,)dt can be approximated by the
Plateau
Time A
FIGURE 116.-Concentration-time curve at downstream sampling site for constant-rate
injection.

where
i is the sequence number of a sample,
N is the total number of samples, and
t, is time when a sample, C,, is obtained.
FACTORS AFFECTING THE ACCURACY OF TRACER-DILUTION METHODS
Even if it is assumed that measurements of concentrations and of
the injection rate are error free, there still remain three factors that
affect the accuracy of tracer-dilution methods of measuring dis-charge.
Those factors are stream turbidity, loss of tracer between the
injection site and the downstream sampling site, and incomplete mix-ing
throughout the stream cross section before the downstream sam-pling
section is reached.
TURBIDITY
Turbidity may either increase or decrease the recorded tracer
fluorescence depending upon the relative concentrations of tracer and
turbidity (Feuerstein and Selleck, 1963). To minimize the effect of
turbidity, samples should be permitted to stand long enough to allow
Time -
FIGURE 117.-Concentration-time curve at downstream sampling site for sudden injec-tion.

suspended solids to settle prior to fluorometric analysis (p. 231, 240).
Use of a centrifuge for the purpose of separating the suspended solids
is even more effective, but a centrifuge is seldom used for that pur-pose
in stream-gaging work.
LOSS OF TRACER
The computation of stream discharge, as mentioned earlier, is
based on equations for the conservation of mass. Consequently, the
accuracy of the computed discharge will be adversely affected if some
of the tracer is lost in the reach of channel between the injection site
and the downstream sampling site. Tracer losses are primarily due to
sorption and chemical reaction between the tracer and one or more of
the following: streambed material, suspended sediments, dissolved
material in the river water, plants, and other organisms. For most of
the tracers used, chemical reaction is a minor factor in comparison
with sorption. The degree of tracer loss by sorption for a particular
tracer varies primarily with the type and concentration of suspended
and dissolved solids in the water. In routine stream gaging by the
tracer-dilution method no attempt is made to quantify tracer loss by
sorption; instead, the “best” tracer available from the standpoint of
being least affected by sorption is used.
Photochemical decay is also a source of tracer loss which varies
with the tracer material used and its residence time in direct sun-light.
Loss from that source is usually negligible, even with fluores-cent
dyes, if the proper dye is used and if residence time in direct
sunlight is limited to only a few hours, as it usually is in stream-gaging
work.
Equations 24 and 25 show that loss of tracer will result in a com-puted
discharge that exceeds the true stream discharge.
CRITERIA FOR SATISFACTORY MIXING
Tracer-dilution measurements require complete vertical and lat-eral
mixing at the sampling site. Vertical mixing is usually accom-plished
very rapidly compared to lateral mixing; therefore, the
distance required for lateral mixing is the primary consideration.
Frequently, long reaches are needed for complete lateral mixing of
the tracer. The mixing distance will vary with the hydraulic charac-teristics
of the reach. Engmann and Kellerhals (1974) have demon-strated
that ice cover significantly reduces the mixing capacity of a
reach of river.
When the constant-rate-injection method is used, complete mixing
is known to have occured when the concentration CB, shown in figure
116, has the same value at all points in the downstream sampling
cross section. When the sudden-injection method is used, complete

mixing is considered to have occurred when the area under the
concentration-time curve, shown in figure 117, has the same value at
all points in the downstream sampling section.
For a reach of channel of given geometry and stream discharge, the
length of reach required for adequate mixing of the tracer is the same
for either of the two methods of tracer injection. Several formulas are
available for estimating the required mixing length for a particular
set of conditions, but these formulas, while useful as guides, are too
simplistic to give adequate consideration to the degree of mixing de-sired.
Perfect mixing is seldom the optimum goal (see below) because
perfect mixing usually requires an extremely long reach of channel,
along with a correspondingly long period of injection in the constant-rate-
injection (CRI) method and a correspondingly long period of
sampling in the sudden-injection ($3) method.
Figures 116 and 117 are only rudimentary illustrations of the two
methods. For either method to be successful an understanding is
needed of the interrelations among mixing length and injection and
sampling times. Figure 118 attempts to illustrate those interrelations
for both types of injection. It is important to realize that unless
adequate mixing is known to exist at a given sampling site, the tracer
cloud in the $31 method must be sampled for its entire time of passage
at several locations laterally in the channel, such as at A, B, and C in
figurs 118. Similarly, in the CR1 method the plateau concentration
must be sampled at several locations laterally in the channel. Experi-ence
indicates that regardless of method or stream size, at least three
lateral sampling points should be used at each sampling site.
Figure 118 indicates that there is an optimum mixing length for a
given stream reach and discharge. Use of too short a distance will
result in an inaccurate accounting of the tracer mass passing the
sampling site. Use of too great a distance will yield excellent results,
but only if it is feasible to inject the tracer for a long enough period
(CR1 method) or to sample for a long enough period (SI method). An
optimum mixing length is one that produces mixing adequate for an
accurate discharge measurement but does not require an excessively
long duration of injection or sampling.
As mentioned earlier, figure 118 shows that the tracer cloud result-ing
from a sudden injection must be sampled at the sampling site
from the time of its first appearance there until the time (T,) of its
disappearance at all points in the sampling cross section. For the
same mixing reach and discharge, if the CR1 method is used, a
plateau will first be reached at all points in the sampling cross section
at time T, after injection starts at the injection site. Thus, it is seen
that for the CR1 method the duration of injection must at least be
equal to T, and injection should continue long enough thereafter to

-.
8

insure adequate sampling of the plateau. It should be noted that a
stable condition of mixing is usually first attained in midchannel.
Tracer lag along the streambanks will generally prolong the time
required for complete lateral mixing.
The CR1 method has become increasingly popular because reliable
injection apparatus is available and the sampling process is relatively
simple. If an injection period well in excess of T, is used, the sampling
can be done leisurely at several points in the sampling cross section.
In the SI method the injection is simple, but the sampling process is
much more demanding. More reliable results are usually obtained by
the CR1 method.
Figure 118 indicates that a satisfactory discharge measurement
requires “nearly equal” areas under the concentration-time curves for
the sampling points in the SI method and “nearly equal” concentra-tion
plateaus for the sampling points in the CR1 method. A numerical
criterion--P,, , the percentage of mixing-is often used as a quantita-tive
index of the consistency of sampling results for the sampling
cross section. A satisfactory discharge measurement can usually be
obtained if the value of P,,, is 95 percent or greater. The computation
of P,,, is discussed in the paragraphs that follow.
Percentage of mixing, P,,,, is defined in this manual by the equation
IX,, - X,,,IQc~ + . . .@JJ~ (26)
where
XI,L&, . . . are the areas under the concentration-time curves
or, for constant-rate injection, the C, concen-trations
at the points A, B, C, . . . across the
sampling section;
x,,, is the mean area under the concentration-time
curves or, for constant-rate injection, the mean
C, concentration for points A, B, C, . . . across
the sampling section;
Q-l,Q,s,Qc, . . . are the subsection discharges applicable to the
points, A, B, C, . . .;
Q is the total stream discharge.
If the distribution of discharge is unkncwn at the sampling section,
the cross-sectional subareas applicable to each point should be used in
place of Q,., , Q,,, Q(.; total cross-sectional area should be used in place
of Q. If both discharge and area distribution are unknown, as will
often be the case, the appropriate widths may be used. Terms I X4 -
X,,, ( , IX,, - X,,, 1, IX,. - X,,, 1, . . . are absolute values.
The percentage of mixing can also be determined graphically, as
shown in figure 119. Values of C, or $,:(C - C,,)dt, depending on the

injection method used, are plotted for each sampling point against the
distance from an initial point at water’s edge. The mean value C, or
j-,,?C - CJdt i’s d etermined by dividing the area under the distribu-tion
curve for C, or $,:(C - Cb)dt by the total width of the section. The
percentage of mixing, P,,,, is then given as
P,,, = --L-
( >
100 (27)
A+B
where
A is the area under the C, distribution and mean C, curves, or
the area under the so”(C - C,)dt distribution and mean
j-,;(C - CJdt curves;
B is the area above the C, distribution and under the mean C,
curves or the area above the j,r(C! - C,)dt distribution and
under the mean J,,“(C - C,)dt curves.
The graphical technique illustrated in figure 119 can also be used if
the distribution of discharge or area is known. The only change in the
procedure that is required is a change in the abscissa of figure 119. In
place of “distance from edge of water” either cumulative discharge or
cumulative area from edge of water is substituted.
CALIBRATION OF MEASUREMENT REACH
Several theoretical studies have been made by the U.S. Geological
Survey (for example, Yotsukura and Cobb, 1972) in which equations
have been derived for determining the length of measurement reach
required for satisfactory or complete mixing. However, the derived
equations cannot be applied in the field without detailed information
Percent mixing=
Mean fi
mean C2
Distance from edge of water
Cdt or
FIGURE 119.-Concentration-distribution curve illustrating the graphical method of
determining the percentage of mixing.

on channel geometry and velocity distribution for the reach of chan-nel.
Consequently several gross formulas have been developed from
the theoretical equations strictly for use as guides in determining a
satisfactory length of measurement reach. Some of the simplified
formulas follow:
a. Point injection at midchannel (English units)-
1.
where
L is distance downstream from the injection point,
V is mean velocity,
g is acceleration of gravity,
D is mean depth,
S is gradient of water surface or streambed, and
W is stream width.
2.
L=06 R’/’ W2
. ngJz-$
(28)
(29)
where R is the hydraulic radius and n is the Manning roughness
coefficient.
3. L=2V $2. (30)
b. Point injection at bankside (English units)-
L=8V5. (311
Studies indicate that if more than one injection point is used, the
mixing distance will vary inversely with the square of the number of
injection points, provided that the injection points are located so that
the dye will disperse equal distances both to the left and right of the
injection points. This statement may seldom hold true for natural
stream conditions, but it does indicate that the mixing length may be
shortened considerably by using additional injection points.
In Europe the formula commonly used as a guide for determining
the required length, L, between the injection site and sampling sec-tion
is
L=O.l3C (“.7cg+ 6) bh’ (metric units),
where
b is the average width of the wetted cross section,
h is the average depth of flow,
C is the Chezy coefficient for the reach (15 <C <SO), and
g is acceleration of gravity.

Equation 32 is intended for use where injection is made at a single
point in midstream.
Before making a discharge measurement by the tracer-dilution
method, the proposed measurement reach should be calibrated to de-termine
the length required for adequate mixing and the possibility
of significant tracer loss. If repeated tracer-dilution measurements of
the stream are to be made, it will be especially advantageous to make
the calibration study comprehensive. One of the equations, 28 to 32,
may be used as a guide in selecting a length of reach for the @ibra-tion
tests; the quantity of tracer to be used for any given discharge is
discussed later on pages 23% 237. Instructions for calibration testing
follow.
Select an injection site on the stream, and on the basis of one of the
equations, 28 to 32, select several downstream sampling sites. Inject
the tracer and then sample the water at three or more points in the
cross section at each of the selected sampling sites. Take adequate
samples at each point to define the plateau of the concentration-time
curve if the constant-rate-injection method is used, or to define the
entire concentration-time curve if the sudden-injection method is
used. Analyze the samples and determine the percentage of mixing by
use of equation 26. As mentioned earlier, for a satisfactory measure-ment
of discharge the percentage of mixing should be at least 95.
Mixing distances and losses may vary with discharge, and the reach
may therefore have to be calibrated at more than one discharge. The
quantity of tracer lost, if any, between successive sampling sites can
be determined by a comparison of the values of C, (constant-rate-injection
method) or of so”(C’ - C,,)dt (sudden-injection method) ob-tained
at each site. That determination provides a basis for the final
selection of a sampling site from the several sites tested.
EFFECT OF INFLOW OR OUTFLOW BETWEEN INJECTION
AND SAMPLING SITES
A satisfactory tracer-dilution measurement of discharge made in a
reach that has no inflow or outflow between the injection and sam-pling
sites will give the discharge occurring at all cross sections in the
reach.
If tributary inflow enters the reach and if the tributary inflow is
well mixed with the water in the main stream, the discharge meas-ured
will be that at the sampling site. If the tributary inflow is not
well mixed, that fact may be evident from the difference in concen-trations
at the various sampling points in the sampling cross -section;
a low percentage of mixing would indicate that the particular sam-pling
site could not be used for a satisfactory measurement of dis-charge.

If outflow occurs between the injection and sampling sites and if the
tracer becomes completely mixed anywhere upstream from the out-flow
channel, the discharge measured at the sampling site will be
that for the reach upstream from the outflow channel. If the tracer
does not become completely mixed upstream from the outflow chan-nel,
the discharge measured at the sampling site will be indetermi-nate;
the magnitude of the “measured” discharge will be dependent
on the quantities of both tracer and water that are carried off in the
outflow.
MEASUREMENT OF DISCHARGE BY FLUORESCENT DYE
DILUTION
As mentioned earlier, the most popular type of tracer for the meas-urement
of streamflow in the U.S.A. is fluorescent dye. The cost of the
dye is relatively small because the quantity of dye needed for a dis-charge
measurement is small; modern fluorometers are capable of
accurately measuring dye concentrations of less than 1 pg/L (micro-gram
per liter) and can detect concentrations as low as 0.02 pg/L.
FLUORESCENT DYES
Fluorescence occurs when a substance absorbs light at one
wavelength and emits it at another, and usually longer, wavelength.
The dyes commonly used as tracers are strongly fluorescent. They are
organic dyes of the rhodamine family and are commercially available.
Dyes selected for use as tracers should (1) have a high detectability
range, (2) have little effect on flora or fauna, (3) have a low sorption
tendency, (4) have a low photochemical decay rate, (5) be soluble and
disperse readily in water, (6) be chemically stable, (7) be inexpensive,
(8) be easily separated from common background fluorescence, and (9)
be easy to handle.
On the basis of recent studies in the U.S.A. on the adsorption poten-tial
and detectability of dyes, Rhodamine WT dye is recommended as
the best dye available for use in dye-dilution measurements of dis-charge.
Formerly used at times, but no longer recommended are
Rhodamine B, BA, and Fluorescein.
FLUOROMETER
The fluorometer is an instrument that gives a measure of the
strength of the light emitted by a fluorescent substance. Figure 120 is
a schematic diagram of a fluorometer. The flurometer briefly de-scribed
in this manual is the Turner model 111 fluorometer, and it is
discussed because it is the instrument that is in general use by the
U.S. Geological Survey. However, there are many satisfactory
fluorometers that are commercially available, and for detailed in-

structions concerning any particular fluorometer it is necessary that
the hydrographer consult the service manual prepared by the manu-facturer
of that instrument. The fluorometry techniques described in
this manual are oriented toward use of the Turner fluorometer, but
those techniques are applicable to most types of fluorometer.
(Note.-The use of brand names in this manual is for identification
purposes only and does not imply endorsement by the U.S. Geological
Survey.)
DESCKIPTION OF FLUOKOMETEK
The principle of the operation of the Turner model 111 fluorometer
is described in the operating manual (1963, p. 12) as follows:
This fluorometer is basically an optical bridge which is analogous to the accurate
Wheatstone Bridge used in measuring electrical resistance. The optical bridge meas-ures
the difference between light emitted by the sample and that from a calibrated rear
light path. A single photomultiplier surrounded by a mechanical light interrupter sees
light alternately from the sample and the rear light path. Photomultiplier output is
alternating current, permitting a drift-free A-C amplifier to be used for the first
electronic stages. The second stage is a phase-sensitive detector whose output is either
positive or negative, depending on whether there is an excess of light in the forward
(sample) or rear light path, respectively. Output of the phase detector drives a servo
amplifier which is in turn connected to a servo motor. The servo motor drives the light
cam (and the “fluorescence” dial) until equal amounts of light reach the photomulti-plier
from the sample and from the rear light path. The quantity of light required in
the rear path. to balance that from the sample is indicated by the “fluorescence” dial.
Each of this dial’s 100 divisions add equal increments of light to the rear path by means
of a light cam.
PEOTOMULTIPLJER PLUORESCEN(
LIGHT INTERRUmER
LTRAVIOLET
LAMP
E SELECTOR
aPerturen
Y cooLmG FAN 3x, 10x, 30X)
FIGURE 120.-Schematic diagram of the fluorometer (from G. K. Turner Associates,
1963, p.13).

7 DISCHARGE TRACER DILUTION METHOD 225
Lamps.-At least three different lamps can be used as a light
source for the fluorometer when the fluorescence ofrhodamine dyes is
tested. They are the general purpose ultraviolet lamp, the far ul-traviolet
lamp, and the green T-5 lamp. Although all three lamps
work well, the far ultraviolet and green T-5 lamps are recommended
as a light source because their outputs are compatible with the
fluorescent properties of the dyes. Sensitivity of the fluorometer is
increased approximately twofold to tenfold when the far ultraviolet
and green T-5 lamps, respectively, are substituted for the general
purpose ultraviolet lamp.
Filters.-The sensitivity of the fluorometer is directly related to the
filter system employed. Light having undesirable wavelengths may
be screened out by placing filters at two points in the fluorometer: (1)
between the source light and the water sample and (2) between the
water sample and the photomultiplier.
The filter (primary) recommended for use with rhodamine dyes for
the absorbed light has a peak color specification of 546 rnp (millimi-crons);
that is, the greatest amount of light passed through the filter
is at a wavelength of 546 rnp. Light at other wavelengths is subdued
or eliminated. The recommended filter (secondary) for the emitted
light has a peak color specification of 590 rnp. The peak color
specifications for these filters are near the peak excitation and emit-tance
wavelengths of the rhodamine dyes and will eliminate most
natural background fluorescence. The filters may be used regardless
of the type of lamp that is installed.
Doors.-Three main types of doors available for use with the
fluorometer are the standard-cuvette (test tube) door, the
temperature-stabilizing door, and flow-through door. All three doors
are easily interchanged.
The standard-cuvette door is the easiest to use in the field for in-termittent
sampling and should be used with the green T-5 lamp. If
the far ultraviolet lamp is used, a high-sensitivity kit should be in-stalled-
on this door because it will increase the overall sensitivity of
the fluorometer about tenfold. It is important to note that excessive
sensitivity will be obtained if the high-sensitivity kit and green T-5
lamp are used together.
The temperature-stabilizing door is recommended for the final test-ing
of samples. This door is similar to the standard-cuvette door with
t,he high sensitivity k_it. hut. has, in &lition, a w~ter-~~)~led, copper
block that surrounds the cuvette. Cooling water may be pumped or
tap water of constant, or near-constant, temperature may be run
through the door to stablize the sample temperature. Only round
12x75mm cuvettes can be used with this door.
The flow through door permits contmuous sampling which can be

recorded. A pump is used to circulate water from the stream through
the cuvette in the door. The results may be recorded on any recorder
with a 0 to 1 milliamp or 0 to 10 millivolt readout. The intake hose
used with the flow-through door should be made of plastic or other
nonabsorptive material. Different fittings and cuvette sizes are avail-able
for this door, The sensitivity of the flow-through door is about the
same as that of the standard-cuvette door with the high sensitivity
kit. That is so because of the larger cuvette used in the flow-through
door.
Normally dye concentrations are not determined in the field be-cause
it is difficult to attain sufficient accuracy under such conditions.
The flow-through door arrangement may be used for preliminary
calibration of a reach, however. As a rule, bottle samples are collected
and transferred to the laboratory for accurate fluorometric analysis.
EFFECT OF ‘I‘EMPERATURE ON FLUOROMETRY
Accurate dilution discharge measurements require accurate
fluorometry, and accurate fluorometry can only be attained in the
laboratory where operating conditions are favorable. Temperature
has a significant effect upon the fluorescence intensity of dyes.
Fluorescence decreases with increasing temperature. This charac-teristic
of the dyes has been investigated by several researchers,
among them Feuerstein and Selleck (1963). For best results, all sam-ples,
including background and standard solutions, should be placed
in a laboratory temperature bath and kept at constant temperature
prior to fluorometric analysis. If the same temperature is used for all
samples, no temperature corrections will be needed. If temperatures
cannot be held constant, temperature corrections, as given in table 13
for Rhodamine WT dye, should be applied to dial readings or to con-centrations.
Dunn and Vaupel (1965) point out the need for corrections to
fluorometer dial readings as a result of changing compartment tem-peratures.
However, tests by the U.S. Geological Survey showed that
these corrections were needed only during the warmup period. A IS-to
2-hr warmup will usually eliminate the need for this type of correc-tion,
although minor changes may still be observed thereafter. The
warmup characteristics of each fluorometer should be determined. If
possible, the fluorometer should not be operated where large temper-ature
changes can occur rapidly.
CALIBRATION CHARAC?‘ERISTICS OF THE FLLJOROMETER
Most fluorometers have a linear calibration ratio, meaning that dye
concentration is directly proportional to the dial reading on the
fluorometer and is related by the equation

TABLE 13.-Temperature-correction coefficients for Rhodamwxe WT dye
Temperature-correction
coemclent
F” C
-20 -11.1
-15 -8.3
-10 -5.6
1.36
1.25
1.16
1.13
1.09
-1 -.6 1.02
0 0 1.00
+.6
:::
2.2
2.8
3.3
2:
8.3
11.1
.99
.97
.96
.94
.93
.91
29
.86
.80
.74
‘T, is the standardc uvette-samplete mperaturea nd T is the cuvette-sampltee mpera-ture
at the tune the sample wm tested in the fluorometer.
C =aD, (33)
Where
C is the dye concentration of the sample tested,
a is a coefficient, and
D is the fluorometer dial reading for the sample tested.
Solutions of known concentration are tested with the fluorometer,
and the relation between concentration and dial reading is deter-mined
from equation 33.
Some fluorometers, however, do not have linear calibration ratios,
and it is therefore necessary to determine the nature of the relation
between concentration and dial reading by testing with standard so-lutions
over a wide range of concentrations. A plot of concentration
versus fluorometer-dial reading will give the shape of the calibration
relation for the particular fluorometer. Experience to date indicates
that nonlinear response occurs more frequently and to a greater de-gree
at the low end of the curve; special effort should be made, there-fore,
to define that part of the curve.
If a fluorometer is found to have a nonlinear calibration relation,
the instrument should be returned to the manufacturer for replace-

ment of parts or adjustment. Before an instrument is returned, one
should be certain that the relation is truly nonlinear and not the
result of an error in calibration. Inadequate instrument warmup is
frequently the cause of a nonlinear calibration. If the instrument has
to be used and the calibration is nonlinear, the derived nonlinear
calibration curve should be used.
It is recommended that, if possible, dial readings of less than 10 be
avoided, because the normal instrument error inherent in fluorome-ter
operation can result in relatively large percentage errors for low
dial readings. Low dial readings can be avoided by use of the proper
fluorometer aperture. For example, the Turner fluorometer has four
apertures, each designed to allow the passage of a different amount of
light (fig. 120). The amount of light passed at each scale is approxi-mately
proportional to scale number; that is, the 30x scale will pass
about 30 times as much light as the lx scale. The relation between
scales, for any fluorometer used, should be determined by testing each
of several samples of different dye concentrations on more than one
scale. A plot of dial readings for one scale against corresponding dial
readings on another scale will give the desired relation. It should be
mentioned here that low dial readings are unavoidable when testing
the background (natural) fluorescence of river water. (See p. 231.)
PREPARA’I-ION OF STANDARD DYE SOI.UTI0N.S FOR FLUOROSfETER
CALIBRA.fION
In calibrating the fluorometer it is necessary to first prepare sam-ples
of dye solution of known relative concentration, then test the
samples in the fluorometer, and finally relate the readings on the
fluorometer dial to the known relative concentrations. This matter of
relative concentrations should be explained at this point. The accu-rate
determination of stream discharge depends on the measurement
of concentrations relative to each other; the absolute values of the
concentrations are of no importance as long as the values of the con-centrations
are all determined in the same manner and all bear the
same ratio to the absolute or true concentrations. Where the term
“concentration” is used in this manual, it refers to “relative concen-tration”;
the two terms are used here interchangeably. The calibra-tion
characteristics of the fluorometer were discussed in the preceding
section of this manual. This section explains the preparation of stan-dard
dye solutions of various concentrations for use in the calibration
process.
Standard dye solutions are prepared by diluting, with known
amounts of water, the dye solution furnished by the manufacturer of
the dye. The relative concentration of the furnished solution is the
value given by the manufacturer. For example, if the manufacturer’s

20-percent dye solution is used, its relative concentration is
200,000,000 pg/Z. If the relative concentration of that solution differs
from the true or absolute concentration by some small percentage, all
diluted samples that are prepared from that batch of dye solution will
have relative concentrations that differ from their absolute values by
that same small percentage. Chlorinated tapwater should not be used
in the dilution, because the chlorine present in the water quenches
the fluorescence of rhodamine dyes.
The equipment and materials needed to make the dilutions are
listed below. Where glass is specified for the equipment, other nonab-sorptive
materials may also be used.
1. Volumetric flasks (glass) of 100, 250, 500, 1,000, and 2,000 mL
capacity.
2. Volumetric pipettes (glass) in an assortment of sizes.
3. Beakers (glass), or l-gal (3.75 mL) glass jars.
4. Wash bottles (polyethylene).
5. Sample bottles (glass).
6. Masking tape and pen.
7. Distilled water. River or chlorinated tap water should not be used;
however, tap water exposed to the air for 24 hr will lose its
chlorine.
The dilution process is performed in steps, as illustrated in the
example shown below. The relative concentration at each step is com-puted
from the equation
c, = C#V,
Va + Vi ’ (34)
where
C,, is the new concentration,
C, is the initial concentration,
Vi is the volume of initial concentration, and
V,, is the added volume of water.
A flow chart similar to that shown in the example below is recom-mended
when making the dilute solutions.
Example.-The original dye solution, as obtained from the manu-facturer,
is a 20-percent solution of Rhodamine WT. In making the
solutions of known relative concentration, the process will be checked
by duplicating the procedure for each of two samples. In other words,
two samples of equal size of the original solution, are diluted in pre-cisely
the same manner. The resulting two dilute solutions are each
diluted further in the same manner, and so on. As a result we will
have two independent sets of standard solutions for use in calibrating
the fluorometer.
To get back to the dilution process, 20 mL of the original 20-percent

solution is diluted to 2,000 mL with pure water. The concentration of
the resulting solution is computed by use of equation 34. The process
is repeated twice, each time using the solution last obtained, as indi-cated
in the following flow chart:
20 mL of (200x 10”)
G, =
,uglL dye solution
2,000 mL total solution
= & (200x106) = 2x106/.,&g/L
1
20 mL of (2X 10”)
PglL solution
1
= -& (2 x 10”) = 20,000 /.Lg/L
20 mL of 20,000
E.cg/L solution
= &20,000) = 200 jAg/L
The solution obtained, with concentration equal to 200 pg/L, is
referred to in this manual as a working standard solution because
any lesser concentration that may be desired can be prepared from it
by one additional serial dilution. For example, a dilution ratio of
l/200 will provide a solution with a concentration as low as 1 pg/L. No
dilution ratios of less than l/200 should ever be used. The working
standard solution should be stored for future use. Experience has
indicated that standard solutions of 200 or more ,uglL when properly
stored in hard glass dark bottles out of direct light will keep for
periods of at least 6 months. There is evidence, though not conclusive,
to indicate that very weak standard solutions tend to deteriorate or to
adhere slightly to the bottles in which they are stored.
The stored working standard solution may be used for periodically
checking the fluorometer calibration to determine if changes in the
calibration have occurred, and enough of the standard solution should
be retained for future use if the same dye lot from the manufacturer is
to be used for discharge measurements. New sets of standard so-lutions
should be prepared after 6 months to avoid the risk of decay of
fluorescence in the stored standard solutions. In addition, new sets
should also be prepared when new batches of dye are to be used for
discharge measurements because the dyes received from the manu-facturer
may vary from batch to batch.
If the fluorometer calibration is known to be linear, from previous
tests using standard solutions made with distilled or unchlorinated
tap water, only a limited few concentrations need be prepared and
tested for the discharge-measurement calibration of the fluorometer.
The concentrations prepared should approximate the plateau concen-tration
expected in stream samples that will be taken during the
discharge measurement.

OPERATION OF THE FLUOROMETER
The U.S. Geological Survey uses the Turner model 111 fluorometer.
The fluorometer is operated in accordance with the following instruc-tions.
Allow a warmup period of 1% to 2 hr before any tests are made.
This warmup period will permit the instrument temperature to stabi-lize.
If possible, have all samples, including standard and background
solutions, at the same temperature. Establish the zero point on the
fluorometer by inserting the dummy cuvette in the cuvette holder,
after which the dial is adjusted to zero with the blank knob. To test a
standard solution, fill the cuvette with that solution, but before put-ting
the cuvette into the fluorometer, wipe the outside of the cuvette
dry with laboratory-grade paper tissue. That prevents distortion from
droplets on the glass or contamination of the fluorometer, and possi-ble
erroneous readings when testing other samples. After wiping,
insert the cuvette in the holder and close the fluorometer door. After
the fluorometer dial reaches a stable reading, record the reading. As
mentioned earlier, test each pair of several standard solutions of dif-ferent
concentrations on more than one fluorometer scale for calibra-tion
of the instrument. An alternate, and perhaps more desirable,
course of action is to first test all field samples on one fluorometer
scale. If that scale accommodates all field samples, calibrate only that
one scale in the range found pertinent.
If a water sample from a discharge measurement is being tested,
first rinse the cuvette with tap water and then, after shaking out
excess droplets, rinse the cuvette with the sample being tested. The
cuvette may then be filled. It is important that any sediment in the
sample be allowed to settle and that any oxygen bubbles be removed.
(Cold samples taken from streams with a high dissolved-oxygen con-tent
will often have bubbles form on the sides of the cuvette.) If the
samples have been allowed to sit in a temperature bath overnight, the
sediment will have settled and the oxygen bubbles will usually have
been released. If the oxygen bubbles have not been eliminated by
allowing the samples to warm up before testing, they can usually be
removed by tapping the cuvette before testing.
The blank and background samples should be tested at intervals
during the fluorometer operation as a check against possible instru-ment
malfunction or change in instrument calibration. Background
samples are water samples used to define the natural fluorescence of
the stream. Natural fluorescence should be determined for any dye-dilution
measurement. Always correct water-sample concentrations
for this background effect.
The frequency of testing known relative concentrations will depend
primarily on the number of stream samples. Known relative concen-trations
are ordinarily tested before and after the stream samples,
but more frequent testing is desirable where numerous samples are
involved

Sample bottles made of polyethylene, glass, or similar nonabsorp-tive
material can be used repeatedly for sampling. After each meas-urement
all sample bottles should be thoroughly rinsed and drained.
The bottles, if stored, should be well separated from any dye-contaminated
equipment.
Whatever the equipment used, care should be taken at every step
in the discharge determination to prevent contamination of stream
samples, standard solutions, and the equipment used for measure-ment
and analysis. A sample can be contaminated, from the
standpoint of concentration, by the addition of pure water as well as
by the addition of minute quantities of dye from the analyst’s hands
or other source.
DYE-INJECTION APPARATUS
Apparatus for the injection of dye solution at a constant rate is of
three types: mariotte vessel, floating siphon, and pressure tank.
MARIOTTE VESSEL
The features of the mariotte vessel, shown in figure 121 are (1) an
(2) Air-vent tube

(5) Airtight filler
ca
Partial
vacuum
-IL
---D--y e solution
I) Reservoir for
dye solution
(3) Airtlght cork with hole in
,-center for air-vent tube
Heaa on
orifice
=I-
(6) Orifice and
-t
- valve
-s-u- rface --
Tapered
- end
(4) Graduated readout
, tube
(7) Drain plug
FIGURE 121.-Mariotte vessel (constant-head device).

airtight tank that holds the dye solution, (2) an air-vent pipe inserted
into the tank through (3) a rubber stopper that will form an airtight
seal both on the tank and the vent pipe, (4) a plastic or glass readout
tube for determining the level of the liquid in the tank, (5) a filling
plug that must be airtight, (6) a discharge orifice and valve, and (7) a
flushing orifice and valve.
The lower tip of the air-vent pipe should be tapered to prevent the
tip from being placed directly on the bottom of the tank and thereby
obstructing the air flow. Discharge at more than one point may be
obtained by installing the desired number of orifices in the tank.
The operation of the vessel is as follows. When the discharge valve
(6) is opened, the level of the dye solution in the tank (1) will drop,
creating a partial vacuum above the liquid (the top of the tank must
be airtight). As the level of the liquid continues to drop, the vacuum
increases causing the level of liquid in the air vent (2), which is open
to the atmosphere, to drop until it reaches the bottom of the vent. As
the solution continues to be discharged, air will enter the tank
through the vent causing an equilibrium between the partial vacuum
formed above the liquid surface and the weight of the liquid above the
bottom of the air vent. When this equilibrium has been reached, a
constant discharge will have been attained and will continue until
the liquid in the tank drops to the bottom of the air vent. The acting
head is the different in elevation between the bottom of the air vent
and the orifice.
FLOATING SIPHON
Constant injection of a dye solution is possible through the use of
the floating siphon device shown in figure 122. The device is designed
to discharge at a constant rate by maintaining a fixed head on the
orifice. The features of the floating siphon are (1) a tank that holds the
solution, (2) a float with siphon tube and guide assembly, and (3)
priming valves that can be used in activating the siphon. The dis-charge
tube with orifice is permanently attached to the float in the
position shown. Note that regardless of the position of the float within
the reservoir, the operating head on the orifice remains the same.
Stable, uniform movement of the float and siphon assembly is possi-ble
through the use of guides and a balance counterweight. When the
siphon is effective, the float and assembly will drop with the water
surface but at the same time maintain a constant discharge because
of the steady head operating on the orifice.
The mariotte vessel and the floating siphon can both be equipped
with readout gages that are used to calibrate the reservoirs volumet-rically.
These gages can be read at selected time intervals during the
injection period to determine the constant-flow rate. The flow rate can

also be determined by volumetrically measuring the discharge from
the orifice for a given period of time.
I’RESSURE TANK
A constant-rate injection of dye solution may be obtained by use of
a pressure tank in combination with a flow regulator (fig. 123). The
flow regulator maintains a constant pressure differential across a
valve in the regulator, thus giving a constant flow rate at any setting
of the regulator. A pressure differential of a few pounds per square
inch must be maintained for the flow regulator to function properly.
The solution to be injected is poured into the pressure tank, and the
tank is sealed. Air is then pumped into the tank, providing the neces-sary
pressure for the regulator. The solution is forced from the tank,
by the pressure, through the regulator and to the injection lines.
Most commercially available flow regulators have a purge meter
Siphon
Guide I
Graduated
scale
3;
-- (2) Float --
(1) Reservoir for
dye solution
Guide I l Balance
FIGURE .22.-Floating siphon (constant-head device).
counterweight

attached to them. These meters may be used to obtain the approxi-mate
desired flow rate. The flow rate used in the computations should
be determined from a volumetric measurement of the tank discharge.
Pressure tank and flow regulator systems are commercially availa-ble.
These systems are as light as 8 lb (3.6 kg), when empty, for an
operating-pressure tank capacity of about 2 gal (7.5 L). Flow re-gulators
may be obtained for flow rates between 0.012 and 4 gallhr or
more. Flow rates once established will be maintained within ?2 per-cent.
DETERMINATION OF QUANTITIES OF FLUORESCENT DYE FOR
MEASURING DISCHARGE
QUANI‘I-I-I’ OF DYE NEEDED FOR 14EASUKE14EN1 BY THE
(:ONS I’AN~I--KA’fE-IN~E(:-I‘ION METHOD
The volume of dye required to make a discharge measurement
FIGURE 123.-Pressurized constant-rate injection tanks for injection of dye into
streams.

using the constant-rate-injection method will depend on the dis-charge
of the stream and on the total injection time. That volume can
be estimated using the equation
v, = 1.02 x 108 (35)
where
Vd
Cd
c2
Q
tt
is the volume, in milliliters, of dye solution to be added to
the water in the injection tank,
is the concentration, in micrograms per liter, of the dye
solution added to the water in the injection tank. If a 20
percent dye solution is added, the concentration of C,, is
considered to be 200,000,000 pg/L. (See p. 228-229 for a
discussion of relative and absolute concentration values.)
is the plateau concentration, in micrograms per liter, de-sired
at the sampling site,
is the estimated stream discharge, in cubic feet per second,
and
is the total injection time, in hours.
The value of 1.02 x 10’ is a combination of conversion factors. A con-centration
value for C, of 5 pg/L is recommended for Rhodamine WT.
The volume of tracer solution injected, which consists of the volume
dye solution (V,,) plus added water, and the rate of injection are
mutually dependent. Their limiting values are based on the size and
characteristics of the dye-injection apparatus that is used. The ca-pacity
or volume of the apparatus divided by t, gives the upper limit-ing
value of the rate of injection, q. Any paired values of q and volume
(qt,) that are within the capability of the apparatus are satisfactory.
However, it is recommended that no value of q less than 2x lo-” fV/s
(0.57mL/s) be used, because low injection rates are difficult to meas-ure
accurately. It is further recommended that V,, be diluted suffi-ciently
to give the injection solution a concentration of no more than
25 x 10” pg/L, because more highly concentrated solutions tend to clog
the injection apparatus.
QUAN-fIl3’ OF DYE: NE:E:DE:D FOK SIEASUKEX,IENT U’ .fHE SUDDEN-IN,
JKI-ION .IkYI‘HOD
If discharge is to be measured by the sudden-injection method, it is
recommended that common salt be used as the tracer, rather than
dye. (See p. 250-256.) However, as a matter of general interest, an
equation is given here for computing the quantity of dye required for
a discharge measurement of that type.
The volume of dye required to make a discharge measurement by
the sudden-injection method can be estimated using the following

empirical equation:
vi = 3x107
where
v ‘,I is the volume, in milliliters, of dye solution of concentra-tion
C’,, to be introduced into the stream,
CD is the peak dye concentration, in micrograms per liter de-sired
at the sampling site,
Q is the estimated stream discharge, in cubic feet per second,
and
t I) is the estimated time, in hours, for the dye peak to travel
from the injection site to the sampling site.
The value of 3 x lo7 is a combination of empirical equation constants
and conversion factors. A concentration value for C,, of 10 pg/L is
recommended for Rhodamine WT.
PROCEDURES FOR MEASURING DISCHARGE BY THE DYE-DILUTION
METHOD
The only dye-dilution method that will be discussed here is the
constant-rate-injection method. The sudden-injection method is not
considered here because not only is it usually a less accurate method,
but it is extremely laborious when dye is used and it can be applied
with less effort by using common salt as a tracer. As mentioned ear-lier,
the sudden-injection method requires that the entire
concentration-time curve be defined, and for that purpose it is desira-ble
to sample the stream concentration at intervals of less than a
minute during periods of rapidly changing concentration. If the dye-dilution
technique is used, it means that within a minute or so, grab
samples must be obtained at all three sampling points in the sam-pling
cross section. Furthermore, because it is recommended that at
least 20 samples be taken at each sampling point to define the
concentration-time curve, it means that a minimum of 60 stream
samples must be analyzed by fluorometer, along with calibration and
background samples. In short, it is not practical to use dye as a tracer
in the sudden-injection method. Although recording fluorometers
with flow-through doors are available, they seldom provide the preci-sion
required for a discharge measurement. When salt is used as the
tracer, conductivity readings can be obtained at a point in a matter of
a few seconds, by using a temperature-compensated probe and porta-ble
meter. (See p. 252-255.)
The following field procedures are recommended for determining

stream discharge by the dye-dilution method:
1. Select and calibrate the measurement reach (p. 220-222).
2. Select exact locations for the injection and sampling sites. Data
obtained from the calibration tests are used in making the site selec-tions,
and consideration should be given to accessibility and con-venience
for conducting field operations. Bridges are often excellent
for the purpose. The injection site for either single- or multiple-point
injection should be one where the injection system can be readily
observed and, if necessary, serviced. Select sampling sites where
sampling is possible anywhere in the cross section. Locate a
minimum of three sampling points in the cross section so that the
section can be checked for lateral mixing.
The best location for a single-point injection is normally at the
center of the cross section. A center injection generally produces the
minimum possible mixing length if the dye is to be introduced at only
one point. Space the injection points for a multiple-point injection so
that each dye injection diffuses equal lateral distances.
3. Prepare the sample bottles. Show the following information on
each bottle:
a. The sampling site (may be abbreviated).
b. Location of the sampling point in the cross section.
c. Sample number (if desired).
d. Sample time (use military time, that is, 24-hr clock system).
e. Date.
Make these notes with a ballpoint pen using masking tape for labels
on the bottles. Note the time (sample time) when the sample is ob-tained.
4. Determine the amount of dye needed for injection from equa-tion
35. The total injection time used in equation 35 includes the time
required for the concentration plateau to have been reached at the
sampling section and sufficient time to permit at least 15 min of
sampling of the plateau.
5. Prepare the dye solution and injection equipment. Make cer-tain
that the solution is thoroughly mixed. Exercise caution in
transporting the dye and do not carry excessive quantities of it on
field trips. Dye in solution can be easily removed from containers by
the use of pipettes. Adverse weather conditions, particularly high
wind or rain, create serious problems in handling the dyes. Pre-packaging
of specific quantities of dye will facilitate operations in the
field. River water taken at the site may be used in preparing the
injection solution, but do not obtain river water immediately below a
sewage outfall or at sites where chlorine is injected into the river
system.
6. Obtain several background samples upstream from the injec-

tion site. Do this before handling the dye.
7. Obtain three samples of injection solution. These samples, each
of about 2 oz (60 mL), may be taken immediately before or after the
solution is injected into the stream.
8. Inject the diluted dye solution. Determine the actual rate of dye
injection by timed observations of volume depletion in the injection
tank. If a mariotte vessel is used for injection, check the fittings for
air leakage before and during injection. Discharge will become con-stant
within a few seconds after the orifice is opened if the tank is
airtight. The sound of air bubbling from the air vent through the
solution can be heard when the vessel is operating properly.
9. Do not inject the highly concentrated dye solution near the
streambed; otherwise, the bed may be stained by the dye and exces-sive
dye loss will result.
10. The time of arrival of the concentration plateau can be esti-mated
from data obtained when the reach was calibrated. It is usually
desirable to start sampling a little before the estimated time of
arrival of the concentration plateau. Define the plateau with at least
five samples at each of the three sampling points in the sampling
cross section. If a fluorometer is available, the arrival and passage of
the dye can be determined by using the flow-through door and rec-order
accessory, or by periodically testing individual samples using
the standard door. Do not mistake a possible temporary leveling of
the concentration-time curve as being the actual plateau. A short
time should elapse between the taking of samples to minimize the
effect of nonrepresentative surges of high or low concentration.
11. In obtaining stream samples at the sampling site, take samples
just below the water surface and far enough from the banks to avoid
areas of slack water. If possible, the sampling site should be at a
contracted section of the stream or at one where velocities are fairly
uniform across the entire section. The following equipment is needed
for grab sampling:
a. Sampling device and line (for sampling from a structure).
b. Boots or waders (for sampling by wading).
c. Boat, motor, paddle, gasoline can, life jacket (for sampling by
boat).
d. Bottles (glass or plastic, 4-oz, wide-mouth bottles are recom-mended).
e. Masking tape (for labeling samples).
f. Ballpoint pens (for making identifying notations on sample
labels).
g. Watch.
12. Contamination of stream samples is always a possibility. When
handling any dye, keep hands and clothes clean as a safeguard

against accidental contamination. Rinse bottles at least three times
in stream water immediately before sampling. This precaution is
necessary because bottles are used repeatedly and some may have
had high concentrations of dye in them previously. Dye from stained
hands can contaminate samples, resulting in erroneous concentration
determinations; therefore, keep hands away from the uncapped
mouths of bottles and out of the sample water.
13. Clean the injection and mixing equipment.
14. Store and carry sample bottles in an upright position to pre-vent
leakage and to allow sediment to settle.
ANALYSIS AND C:O~lPU~I‘Al-IONS
Fluorometer analysis should not begin until the standard concen-tration
solutions have been prepared. Place all samples, including
background samples and standard concentration solutions, in a con-stant-
temperature bath. By keeping the samples in the bath over-night,
any sediment present will have an opportunity to settle, and
any oxygen bubbles present will usually be released. After fluorome-ter
warmup, all samples may be analyzed. Use of a constant-temperature
bath will eliminate the need for temperature correc-tions.
However, if for any reason a temperature bath was not used,
the first step in the analysis procedure that follows is to make tem-perature
corrections.
1. Correct each fluorometer reading for the effect of temperature
by the following method. A standard cuvette-sample temperature is
selected. This may be the mean, median, mode, or any other conve-nient
cuvette-sample temperature recorded while testing the sam-ples.
The difference between each recorded cuvette-sample tempera-ture
and the standard temperature is used to select the appropriate
coefficient from table 13. Temperature-correction coefficients are
usually prorated with respect to time between temperature observa-tions.
Multiply the fluorometer dial-readings by the coefficients to
obtain adjusted dial readings.
2. Next correct the dial readings, or temperature-adjusted dial
readings if such adjustment had been necessary, for the effect of
background fluorescence, as determined from the background sam-ples.
This background correction is applied to each water sample and
to each sample of standard concentration.
Usually all fluorometer testing will be done using a single
fluorometer aperture. If more than one aperature is used, obtain a
background reading for each aperature and use a mean background
value for correcting the dial readings. Do not use a mean background
value if a definite change in background has been noted. A change in
background fluorescence may result from a variety of causes such as

unstable fluorometer operation, increased suspended-sediment load,
and the presence of sewage or industrial wastes. Enter the back-ground
readings in the notes. Subtract the background readings from
the adjusted dial readings from step 1 above to obtain the final cor-rected
dial readings.
3. Use the final corrected dial readings for the standard solution of
known relative concentration to compute the fluorometer coefficient,
a, in equation 33 (p. 227). When this standard solution is tested sev-eral
times during a period of sample testing, the value of the coeffi-cient
is normally prorated, with respect to time, between testings.
4. Determine the relative concentrations of samples by multiply-ing
the corrected dial readings, from step 2 above, by the coefficient,
a.
5. Compute the stream discharge by use of equation 24. Because
the background concentrations have already been subtracted from
the stream sample concentrations, equation 24 becomes
Q = [ g-12 1 q,
which can be simplified, without significant loss of precision, to
Q =($i) q. (37)
An average value of C, is used in the computations. If the individual
C, values show little variation among them, use the arithmetic mean.
If the variation is significant, obtain the mean value of C, by weight-ing
the mean plateau concentrations for each sampling point by the
percentage of discharge associated with the sampling point. If the
discharge distribution is unknown, but the area distribution is
known, obtain the mean value of C, by weighting the plateau concen-trations
for each sampling point by the percentage of area associated
with each sampling point. If both the discharge and area distributions
are unknown, as will usually be the case, compute the mean value of
C, by using percentage of width as the weighting factor.
6. Determine the percentage of mixing by using equation 26, or by
use of the graphical procedure described on page 219-220. Reliable
results are generally obtained when the percentage of mixing is 95 or
more. Reliable results are also possible for flow conditions where the
percentage of mixing is less than 95 if the discharge distribution at
the sampling section is uniform or known.
A sample computation of the constant-rate-injection method is

presented here based on data obtained on March 25, 1965, at Little
Seneca Creek near Boyds, Md., in the course of a detailed investiga-tion
of dye-dilution methods of measuring discharge. The average
width of Little Seneca Creek at the time of the measurement was
30-35 ft (9-10 m). Depths averaged between 1 and 2 ft (0.3 and 0.6
m). The streambed was composed mostly of gravel, with some rock
outcrops. Flow in the measuring reach passed through several bends.
Calibration of the measurement reach at about the stage to be
measured had indicated that a measuring reach of 1,800 ft (550 m)
was satisfactory for adequate mixing when the dye was injected at
three points across the stream. The calibration further indicated that
the time required for the concentration plateau to arrive at the sam-pling
site was about 45 min. Three sampling points, designated A, B,
and C, respectively, were to be used at the sampling site. Grab-samples
were taken immediately before and during the passage of the
concentration plateau.
1. The required volume of dye (V,,), to be supplied from a mariotte
vessel, was computed from equation 35,
v, = (1.02~109 -$ Qtt .
rf
The approximate value of the plateau concentration (Cr) desired at
the sampling site was 5 ,uglL. The estimated value of stream dis-charge
(Q) was 50 ft3/s. The total injection time (tt) was estimated to
be 80 min (1.33 hr)-45 min for traveltime and 35 min to insure a
concentration plateau of adequate duration. The dye to be used was
Rhodamine WT, 20-percent solution, and C,, was therefore equal to
2 X 10’ pg/L. Consequently,
v, = (1.02x10x)
& (50) (1.33) = 170 mL.
( >
2. The discharge rate of diluted dye solution (q) from the injection
vessel that was selected was 1.50 x lo- ft”/s. The volume of solution
needed in the injection tank was equal to qt,, where t, was 1.33 hr, or
4,800 s. That volume was therefore
(1.50~ lo-“) (4800) = 0.72 ft?, or approximately 20,000 mL.
The 170 mL of dye solution was mixed with sufficient stream water to
give an injection solution of 20,000 mL.
3. The concentration of the solution in the injection tank (C,,) was
computed from equation 34,

C,K
c7i = v, + vi
= (200,000,000) (170)
20,000
= 1,700,000 pg/L.
4. Timed observations of the change in the level of the dye solution
in the injection tank showed the actual rate ofoutflow to be 1.51 x lo-”
ft:‘/s.
The steps that follovv were taken in the office to complete the mea-surement.
1. A working standard solution of concentration 200 pg/L had pre-viously
been prepared (p. 229-230). A dilution ratio of l/40 was
applied to that solution to obtain two standard sample solutions
whose concentration was 5.00 pg/L.
Standard solutions of 5.00 pg/L were used for calibration of the
fluorometer because that was the expected value of the plateau con-centration
of the stream. (The concentration of the standard solutions
should approximate the concentrations of the stream samples that
will be used to compute stream discharge.)
2. A form for keeping notes was prepared as shown in figure 124.
Column 1 of figure 124 shows the time when the sample was obtained
in the field, and column 2 shows the time when the sample was tested
in the fluorometer.
3. The samples had not been placed in a constant-temperature
bath, and consequently temperature corrections were necessary. The
samples, including those for background testing (stream water un-touched
by dye) and for fluorometer calibration (5.00 Fg/L), were
tested in the fluorometer. Columns 3 and 4 of figure 124 show dial
readings on the fluorometer aperture that was used. Column 5 shows
two temperature readings. The upper reading is the temperature of
the water being circulated through the fluorometer door. The lower
reading is the temperature of the fluorometer compartment. Obtain
that temperature from a thermometer that can be taped to the com-partment
side at the left of the secondary filter. Column 6 shows the
temperature of the cuvette sample. That temperature is taken im-mediately
after the fluorometer dial is read by removing part of the
water from the cuvette, inserting the thermometer in the cuvette, and
replacing the cuvette in the door. Allow the thermometer to stabilize
before reading. Compute temperature-correction coefficients from the
observed cuvette-sample temperatures.
4. A standard cuvette sample temperature of 82°F (27.8”C) was
selected for use. Temperature coefficients from table 13, correspond-

ing to the differences between 82°F and the observed cuvette-sample
temperatures in column 6 of figure 124, were then obtained and re-corded
in column 7.
53 ) 72.0 1 /.cxJ 72.0 1 I.2 70.0 1.074y 15.25 1.
I I I I , I I I I I
I I I I pkm J
7i.i.wwr /II Fluorometer Filteq (546 my,5YOmc/),& uJtrav/okt hp. Temper&~ -
rted 3-29-65
FIGURE 124.-Sample analysis sheet used for computing discharge by the
constant-rate-injection method of dye dilution.

5. The adjusted dial readings in column 8 were obtained by mul-tiplying
the values in either column 3 or column 4 by the temperature
coefficients in column 7.
6. The average temperature-adjusted fluorometer reading for
background fluorescence, obtained by testing the unaffected stream
water, was recorded in column 9. Its value, 1.2 in this test, was then
subtracted from all temperature-adjusted readings in column 8, and
the corrected dial readings were recorded in column 10.
7. The fluorometer coefficient, a, in column 11, was obtained as
the average of the ratios of the known concentration of the two back-ground
samples (5.00 pg/L) to their corrected dial readings. The
background samples were tested at the beginning and end of the
fluorometer analysis, and the fluorometer coefficients obtained were
prorated with time for use in the analysis.
8. The concentrations of the samples listed in column 12 were
obtained by multiplying the fluorometer coefficients in column 11 by
the corrected dial readings in column 10.
9. The concentrations obtained for each sampling point are nor-mally
plotted against sampling time to determine the average con-centration
of the plateau C, at each of the three sampling points, A,
B, and C. In this example, no plots were made; instead, C, for each
sampling point was computed, in column 12 of figure 124, as the mean
of the last five values obtained, it being evident that those values
were plateau values.
10. Because the three sampling points, A, B, and C, were evenly
spaced across the stream, each of the three values of C, from step 9
were given equal weight in computing the mean value of C, for the
entire sampling section:
mean C, = 5.62+5.50+5.33
3
= 5.48 /.LgIL.
11. The discharge was computed from the simplified form of equa-tion
24 that is shown as equation 37 on page 241.
= (1.51x10-“) = 46.8 ft 3/s.
12. Mixing percentage (P,n) was computed, using appropriate
widths in equation 26:

Because the sampling points were evenly spaced, W,, W,, and WC
may each be replaced by 1, and Wtotal may be replaced by 3. Then
P, = 100 -
[ 15.62~5.481 + ]5.50-5.48]+]5.33-5.48]]x50
3t5.48)
= 100 - (0.31)x50
16.44
= 99 percent (satisfactory)
In the original study of Little Seneca Creek, the discharge had been
measured by current meter for a comparison with the discharge ob-tained
by the dye-dilution method. The current-meter discharge was
47.3 ft3/s, whereas the dye-dilution discharge was 46.8 ft3/s. The two
values differ by 1 percent.
SIMPLIFIED PROCEDURES FOR MAKING NUMEROUS DYE-DILUTION
MEASUREMENTS OF DISCHARGE
The preceding description of the method of measuring discharge by
the constant-rate-injection method was highly detailed to give com-plete
understanding of the procedure. It should be apparent that
there are many details to be considered in collecting and analyzing
the samples. If only an occasional dye-dilution measurement is to be
made, the procedures described above should be followed. If numerous
dye-dilution measurements are to be made on a routine basis, “mass
production” methods may be instituted to simplify and speed the pro-cedure.
The first simplifying step is the laboratory production of two
batches of solution, each of which represents a working standard
concentration. Bulk production of the two concentrations will consid-erably
reduce the amount of time that would otherwise be required
later for serial dilutions and for calibrating the fluorometer. The
standard concentration that is needed for tluorometer calibration is
one that closely approximates the C, (plateau) concentrations that
will be obtained in the discharge measurements. The value of C, will
usually approximate 5 PglL. Consequently one working standard so-lution
of 2OOpg/L should be produced in adequate quantity from the
stock of 20-percent Rhodamine WT dye. The concentration of 200
PglL is high enough to permit storage of the solution for at least 6
months with little danger of deterioration and is still low enough to
produce, with a single dilution, concentrations that approximate any
C, values that may be obtained in a discharge measurement.

7 DISCHARGE TRACER DILUTION METHOD 247
The other solution of working standard concentration that should
be produced in bulk is one that can be used as the injection solution in
a discharge measurement without further dilution. By way of back-ground
explanation we examine figure 125, the basis of which is
equation 37. Figure 125 shows the relation among Q, q, and C, for a
constant value of C,. The constant value of C, that is used is 5 PgfL,
which is the optimum value of the plateau concentration in the
constant-rate-injection method. Concentration values of C, ranging
from 0.05 percent (0.5 x lo6 pg/L) to 2.5 percent (25 x lo6 pug/L) are
shown in the diagonal lines of figure 125. To produce a C, solution of,
say 0.4 percent, 8 L of water is added to the parenthetical quantity of
137.2 mL of 20-percent Rhodamine WT dye. Examination of figure
125 shows that with a given injection concentration (C,) a wide range
of discharges may be measured by merely changing the injection rate
(9). For example, a C, concentration of 0.4 percent (4~ 10” pg/L) per-mits
the measurement of stream discharges from 15 ft”/s to almost
300 ft”/s, while still creating a plateau concentration (C,) of 5 pg/L.
Even those discharge limits may be exceeded by allowing C, to vary
from its value of 5 pg/L. By using figure 125 with a knowledge of the
range of discharges to be measured, a suitable value of C, can be
selected for use as a working standard concentration.
To recapitulate what has been said up to this point, two working
standard concentrations should be used for laboratory production of
bulk solutions.
1. A concentration (C,) of 4x lo6 wg/L, or one more suitable for the
range of discharges to be measured, should be used for one solution.
That solution will be used, without further dilution, as the injection
solution for discharge measurements.
2. A concentration of 200 pg/L should be used for the second solu-tion.
A single dilution of that solution will provide standard solutions
for calibrating the fluorometer at concentration C, (usually about 5
Fg/L). Both solutions must be made from the same batch of 20-percent
Rhodamine WT dye that is received from the manufacturer.
The discharge measurements will be made in the manner described
in the earlier sections of this chapter, but before analysis by fluorome-ter,
all samples and standard solutions should be allowed to sit over-night
in a laboratory temperature bath. That will eliminate the need
for temperature corrections to fluorometer dial readings.
As the hydrographer gains experience with the dye-dilution
method, he will find that he can dispense with the computation of
percentage of mixing (I’,,,) at the conclusion of his fluorometer
analysis. By visual inspection of the computed individual plateau
concentrations, he will be able to judge whether or not satisfactory
mlxmg had been attained at the site of his sampling

I ‘h I I

MEASUREMENT OF DISCHARGE BY SODIUM DICHROMATE
DILUTION
GENERAL
In Europe calorimetric analysis, using sodium dichromate
(Na, Cr,O,. 2H,O) as the tracer, is the most widely used means of
measuring discharge by the constant-rate-injection method. Because
calorimetric analysis is rarely used in the U.S.A., the method will be
described here only in brief; detailed descriptions are available in a
report by the International Standards Organization (1973) and in a
paper by Hosegood, Sanderson, and Bridle (1969).
The solubility of sodium dichromate is relatively high-the stock
solution commonly used has a concentration of 600 g/L-and the salt
satisfies most of the requirements for a tracer that are listed on page
211. Complications resulting from the presence of chromium ions in
the water being gaged seldom occur, because natural waters gen-erally
contain few such ions. However, the nature and quantity of
suspended sediment in the natural water can seriously affect the
accuracy of analysis because of the possibility of sorption of sodium
dichromate by the sediment. Another consideration in the use of
sodium dichromate as a tracer is its potential toxicity to aquatic life,
particularly in localized areas of high concentration; drinking-water
standards in the U.S.A., for example, recommend a limiting concen-tration
of 0.05 mg/L for chromium ions (Environmental Protection
Agency, Environmental Studies Board, 1972, p. 62).
The factors that enter into the selection of a reach of channel for a
measurement of discharge by sodium dichromate dilution are identi-cal
with those discussed earlier on pages 215-223. The types of ap-paratus
for constant-rate-injection-mariotte vessel, floating siphon,
and pressure tank-were described on pages 232-235.
The method of sampling for a discharge measurement by the
constant-rate-injection method is similar to that described for fluores-cent
dyes (p. 237-240).
PRINCIPLE OF COLORIMETRIC ANALYSIS
Calorimetric analysis permits the measurement of extremely low
concentrations of sodium dichromate. In that type of analysis a col-orimeter
is used to compare (1) the natural dilution of stream samples
after tracer injection with (2) the known dilution of a stock solution of
the salt. The comparison is based on differences in the absorption of
light by the solutions after a reagent has been added to each of them.
The calorimeter is calibrated by the use of standard solutions, and
it is recommended that the calorimeter used be one that gives a linear

relation between color intensity (concentration) and meter reading.
The calorimeter coefficient is then equal to the known concentration
of the standard solutions divided by the average of the calorimeter
readings.
METHOD OF ANALYSIS BY COLORIMETER
As mentioned earlier, the stock solution commonly used for dis-charge
measurements contains 600 g of sodium dichromate in each
liter of solution. The injection rate of this stock solution depends on
the estimated river discharge and the desired increase or rise in con-centration
of chromium ions (Cr”) corresponding to the plateau con-centration.
That rise in concentration, (C, - Cb) in the equation that
follows, is generally in the range of 0.04 to 0.08 mg/L.
Discharge is computed by use of the equation
Q= icc , -,C 1qb y (38)
where
Q is stream discharge (m”/s),
q is rate of flow of injected solution (m”/s or mL/s x lo-“),
C, is concentration of the injected solution (mg/L),
C, is concentration of the plateau of the concentration-time
curve shown in fig. 116 (mg/L), and
C,, is background concentration of the stream (mg/L).
MEASUREMENT OF DISCHARGE BY SALT DILUTION
GENERAL
As mentioned earlier, when salt is the tracer used in measuring
discharge by the tracer-dilution technique, the sudden-injection
method is generally used. Although the sudden-injection method is
usually less accurate than the constant-rate-injection method, the
difficulty of handling the large quantities of salt solution required by
the constant-rate-injection method make the method impractical.
Common salt (NaCl) is the salt tracer generally used because it is
relatively cheap and it meets all the criteria for a tracer that are
listed on page 211.
The basic principles behind the salt-dilution method are as follows.
The ion concentration of a dilute salt solution, such as natural river
water, increases as the salt content increases. Consequently, the eas-ily
measured electrical conductivity (conductance) of the solution is
an index of the salt concentration. Furthermore, over a wide range of
concentrations the conductance is directly proportional to salt con-centration.
Therefore, after injection of a concentrated salt solution

into a stream, the discharge can be computed by use of the ratios of
the conductances of the injected and sampled salt solutions, instead of
the ratios of the salt concentrations themselves. The procedure fol-lowed
in the salt-dilution method is analogous to that used in the
dye-dilution method in that relative conductance values are used
rather than absolute values.
The factors that enter into the selection of the reach of channel for a
salt-dilution measurement of discharge are identical with those dis-cussed
earlier on pages 215-223. Although loss of salt in the meas-urement
reach by sorption is a negligible concern, reaches that have
areas of slack water should be avoided, if possible, because the stor-age
and slow release of tracer from those areas greatly prolongs the
time required for the entire salt cloud to pass the sampling site. The
sampling site should be free of excessive turbulence because the oper-ation
of the electrode cell that is placed in the stream to measure
relative conductance is adversely affected by the presence of air bub-bles.
The salt-dilution method of measuring discharge in open channels
is littled used in the U.S.A. but is popular elsewhere, as in the
U.S.S.R. The description of the salt-dilution technique that follows,
and the sample computation that concludes the discussion, have been
taken from a description of salt-dilution technique that follows, and
the sample computation that concludes the discussion, have been
taken from a description of salt-dilution stream gaging in the
U.S.S.R. (World Meteorological Organization, 1962, p. 47-49). The
subject is discussed under the following three headings:
1. Preparation and injection of the concentrated salt solution.
2. Measurement of relative conductance at the sampling site.
3. Computation of discharge.
PREPARATION AND INJECTION OF THE CONCENTRATED SALT SOLUTION
The following equipment is needed for the preparation and injec-tion
of the concentrated salt solution at the injection site:
1. Two tanks, each having a capacity of 60- 70 L; one tank is used for
preparation of the solution and the other for injection of the
solution.
2. A measuring vessel of 10-L capacity, having a mark showing the
exact level for 10 L of liquid.
3. A wooden or aluminum paddle for mixing the solution.
4. A vessel having a capacity of 0.3-0.5 L for adding small volumes of
solution to the 10-L measuring tank.
5. A glass flask with a ground glass stopper, having a capacity of
20-30 mL, in which a sample of the solution is retained.
The quantity of salt (NaCl) required for injection depends on the

discharge to be measured; l-2 kg of salt is needed for each cubic
meter per second of stream discharge. The smaller unit quantity of
salt is used for streams having a low natural concentration of dis-solved
material. In estimating the quantity of salt to be brought to
the injection site, consideration should also be given to the possibility
that the discharge measurement will have to be repeated.
The preparation and measurement of the injection solution takes
place at the injection site, but at a distance from the river to avoid any
accidental spill of salt or salt solution into the river. An accident of
that kind could affect the results of the discharge measurement. To
prepare the injection solution, the quantity of salt needed is first
determined from an estimate of the discharge and the natural concen-tration
of dissolved materials in the stream. The computed quantity
of salt is then placed in one of the large tanks, and river water is
added to the tank at the rate of 10 L to each 3 kg of salt. The mixture
is then stirred to obtain a saturated salt solution. After the larger
undissolved crystals have settled to the bottom of the tank, the solu-tion
is transferred to the second large tank, and its volume is care-fully
measured in the process, the transfer being made by means of
the 10-L measuring vessel. An additional amount of river water suffi-cient
to fill the small glass flask (20-30 mL) to its brim is then added
to the measured solution in the second large tank. The flask and
stopper are carefully rinsed in that tank, after which the contents of
the tank are thoroughly stirred once more. The small glass flask is
then filled with the solution, tightly stoppered, and is delivered to the
sampling site downstream for later use there. The large tank now
holds the volume of salt solution that was originally measured into it.
The large tank is then moved to the river, and at a signal from the
sampling site that all is in readiness there, the tank is overturned to
spill its contents almost instantaneously into midstream. That act
completes the work to be done at the injection site.
MEASUREMENT OF RELATIVE CONDUCTANCE AT THE SAMPLING SITE
A conductance meter (fig. 126) that is a modification of a
Wheatstone bridge is set up at the sampling site. The principal ele-ments
of the meter are a rheochord, a lO,OOO-ohm resistance
chamber, and an electrode cell immersed in the stream, well away
from the bank. The resistance chamber is used to compensate for the
natural conductance of the water in the stream so that the needle of
the galvanometer reads zero. The indicator on the rheochord is also
set at zero. When this has been done, the signal to inject the salt
solution is sent to the injection site.
After the solution has been poured into the stream at the injection

I
1

site, the current is switched on in the conductance meter, and the
stability of the compensation for natural conductance is checked. If
the galvanometer needle has deviated from zero, it is returned to zero
by changing the resistance. Constant observation of the needle then
begins. When the needle begins a perceptible movement to the right,
it is a sign that the solution, or ionic wave, is approaching, and the
stopwatch is started. From that time on, the galvanometer needle is
maintained in a position approximating the zero reading by turning
the rheochord handle. Every 15 s the needle is returned exactly to
zero and the indicator position on the rheochord scale is read. That
reading represents relative conductance (P) expressed in tenths of a
percent (O/00):
P, = 1,000
[
w%v - u-x), uwo 1’ (39)
where EC is conductance (electrical conductivity), subscript W refers
to the ionic wave, and subscript o refers to the natural water in the
stream. (Note.-Conductance is the reciprocal of resistance.)
As the ionic wave passes the sampling site, relative conductance
increases rapidly at first, reaches a peak, and then recedes slowly to
zero or to a constant value slightly above or below zero. When the
rheochord readings remain constant for 5 or 6 readings (1% min) near
the zero value, the measurement is terminated. Immediately thereaf-ter
the determination of the relative conductance of the injection
solution begins, using the sample in the small flask obtained at the
injection site just before the measurement began. For this determina-tion
the following equipment is needed:
1. A 10-L measuring vessel.
2. A jug for adding water to the measuring vessel.
3. A wooden or aluminum paddle for mixing the solution.
4. A 1-mL glass pipette.
The measuring vessel is rinsed three or four times with river water.
It is then filled with river water to the 10-L mark, and the electrode
cell of the conductance meter is immersed in it. The rheochord needle
is set to zero, the current is switched on, and the resistance is adjusted
to set the galvanometer needle to zero. The pipette is next rinsed in
the injection solution that had been delivered in the small flask, and
the pipette is used to add 1 mL of that solution to the 10 L of river
water in the measuring vessel. The pipette is then rinsed three times
in the vessel to insure that all of the extremely small volume of salt in
the 1 mL of solution is introduced into the vessel. The contents of the
vessel are then thoroughly mixed, and the relative conductance of the
greatly diluted injection solution is measured with the meter, using
the technique described for measuring relative conductance in the

ionic wave. The ratio of dilution for the sample of injection solution is
l:lO,OOO, because 1 mL of injection solution was mixed with 10 L of
river water.
COMPUTATION OF DISCHARGE
The simplest way to describe the computation of discharge from
salt-dilution data is by means of an example. Assume that in the
preceding discussion of methodology, the stream discharge had been
estimated to be about 4.5 m3/s. The unit quantity of salt to be used
was 2 kg/m3/s of discharge; consequently about 9 kg of salt was pre-pared.
Water was added to the salt at the rate of 10 L per 3 kg of salt.
As a result, 30 L (0.03 m3) of injection solution was prepared. This
value is shown on line 1 on the left-hand side of the computation sheet
in figure 127. At the sampling site, 10 L of river water (line 2) was
mixed with 1 mL of injection solution (line 3), giving a dilution ratio
of 10,000 (line 4). The resistance of the river water was found to be
969 ohms (lines 5 and 6), and the resistance of the sample of diluted
(l:lO,OOO) injection solution was found to be 691 ohms (line 7). The
relative conductance of that sample, as read on the rheochord in
tenths of a percent, was 402 (line 8). On line 9, the rheochord reading
for the dilute sample of injection solution is checked mathematically
by use of the measured resistances. The equation used on line.9 is
identical with equation 39. On line 10 the relative conductance of the
injected solution is computed by multiplying the relative conductance
of the diluted injection sample by the dilution ratio.
On the right-hand side of figure 127 are shown the relative conduc-tance
values read on the rheochord scale at 15-s intervals during the
15min passage of the ionic wave. Subtotals are shown for the three
columns of relative conductance values; the grand total is 1,933. The
data are presented graphically in figure 128, where relative conduc-tance
is plotted against time.
Discharge is computed from equation 40, the denominator of which
is the area under the curve of relative conductance versus time:
(40)
where
Q is discharge, in cubic meters per second,
VI -is volume of the injected solution, in cubic meters,
PP is relative conductance of the injected solution, in tenths of
a percent,
F is the product of the sampling interval, in seconds, multi-plied
by the sum of the observed values of relative
conductance, and
AF is a correction factor for any change in reading of the rela-

tive conductance of the natural river water between the
start and end of the measurement:
P
Lw =
- pen,
start2
(& - tJ, where t, - t, is the time, in sec-onds,
that elapsed during the measurement.
The discharge is computed in lines 11-16 on the left-hand side of
figure 127. Line 11 shows the sampling interval-15 s; line 12 shows
the sum of the observed relative conductances of the ionic wave-
1,933; line 13 shows the computation of F-28,995; line 14 shows the
computation of M-there was no change in natural relative con-ductance
during the 900 s that elapsed during the measurement.
The value of the denominator of equation 40 is shown on line 15.
The discharge, computed in accordance with equation 40, is shown on
line 16.
MEASUREMENT OF DISCHARGE BY DILUTION OF
RADIOACTIVE TRACERS
GENERAL
The use of radioactive material for measuring discharge by tracer
FIGURE 127.-Sample computation of discharge using salt dilution in the sudden injec-tion
method. (From World Meteorological Organization, 1962, p. 49.1

dilution will not be described in detail, because the method is still
(1980) considered to be in the experimental stage. Radioactive tracers
should be ideal for the dilution method because concentrations as low
as 10ey ci/L may be accurately determined with a counter or count-rate
meter whose sensing probe is immersed in the stream.
The radioactive element that has been most commonly used is gold
198, which has a half-life of 2.7 d. Tests have also been made using
sodium 24, which has a half-life of 14.9 hr. It is necessary that the
radioactive tracer have a short half-life so that the radioactivity in-troduced
into the stream will decay to an insignificant level in a short
-
I
I I I
2 4 6 8 10 12 14
TIME, IN MINUTES
FIGURE 128.-Curve of relative conductance versus time for the ionic wave in the
sample problem. (From World Meteorological Organization, 1962, p. 48.)

time. That requirement introduces a problem in logistics, in that the
radioactive element must arrive from the nuclear plant and be used
at the measurement site at the scheduled time, so that excessive
decay of the radiation does not occur before the discharge measure-ment
is made. Another factor that tends to discourage the use of
radioactive tracers is the requirement of a government license merely
to handle the material; radiation shielding must be provided while
shipping and handling the material because of the potential threat to
public health. In addition, approval must usually be obtained at all
government levels, including the local level, before the radioisotope
can be used in a stream, and local fear of radioactive pollution is often
difficult to overcome.
METHODOLOGY
A measurement reach of channel is selected, using one of the equa-tions,
28 to 32 (p. 221-222), as a guide in determining the length of
reach needed for satisfactory mixing. Before the measurement is
started, the instrument for counting gamma-ray emissions-Geiger
or scintillation counter-is calibrated, taking into account the exact
conditions under which the counter will be used.
A measured quantity-of the radioisotope is introduced into the
stream at the injection site by being quickly poured out of a bottle; or
more frequently, a glass bottle containing the radioisotope is placed
in a wire-screen container that is then lowered into the stream, after
which the glass bottle is shattered to release the isotope for mixing in
the streamflow. At the sampling site downstream, where the probe of
the Geiger or scintillation counter is immersed in the stream,
gamma-ray emissions are continuously counted. The counters are
started well before the arrival of the isotope-stream mixture so that
the counts received from natural (background) radiation sources may
be measured. The counters continue to count throughout the passage
of the isotope-stream mixture until the count returns to the back-ground
level. The total net count (N) is equal to the gross count
obtained minus the background count accumulated during the period
of the gross count.
The discharge is computed from the equation
Q=FA
N’
(41)
where
Q = stream discharge (volume per unit time),
F = a calibration factor for the probe and counting system,
A = total quantity of radioactivity introduced into the stream,
and
N = total net count recorded by the counter.

SELECTED REFERENCES
Barnes, H. H., and Kilpatrick, F. A., 1973, Techniques for measurement of discharge
by dye dilution, in Koblenz, 1970, Symposium on hydrometry: Internat. Assoc. Sci.
Hydrology, Pub. 99, p. 251-259.
Cobb, E. D., and Bailey, J. F., 1965, Measurement of discharge by dye-dilution
methods: U.S. Geol. Survey Surface-Water Techniques, book 1, chap. 14, 27 p.
Dunn, Bernard, and Vaupel, D. E., 1965, Effects of sample and fluorometer-compartment
temperatures on fluorometer readings: U.S. Geol. Survey Prof. Paper
525-D, p. D225D227.
Engmann, J. E. O., and Kellerhals, Rolf, 1974, Transverse mixing in an ice-covered
river: Water Resources Research, v. 10, no. 4, p. 775-784.
Environmental Protection Agency, Environmental Studies Board, 1972, Water quality
criteria 1972-a report of the Committee on Water Quality Criteria: Washington,
U.S. Govt. Printing Office, 594 p.
Feuerstein, D. L., and Selleck, R. E., 1963, Tracers for dispersion measurements in
surface waters: California Univ., Berkeley Sanitary Eng. Research Lab., Report
no. 63-1, 69 p.
Frederick, B. J., Reck, C. W., and Carter, R. W., 1962, Use of a radioisotope to measure
water discharge: U.S. Geol. Survey Prof. Paper 450-D, p. 185-186.
Glover, R. E., 1964, Dispersion of dissolved or suspended materials in flowing streams:
U.S. Geol. Survey Prof. Paper 433-B, 32 p.
Godfrey, R. G., and Frederick, B. J., 1963, Dispersion in natural streams: U.S. Geol.
Survey open-file report, 75 p.
Hosegood, P. H., Sanderson, P. R., and Bridle, M. K., 1969, Manual of dilution gaging
with sodium dichromate: Water Research Assoc. ILR no. 34, Medmenham, Mar-low,
Buckinghamshire, England, 36 p.
International Standards Organization, 1973, Liquid flow measurement in* open
channels-Dilution methods for measurement of steady flow-constant-rate-injection
method: International Standard 555, Geneva, 18 p.
Kilpatrick, F. A., 1968, Flow calibration by dye-dilution measurement: Civil Eng., V.
38, no. 2, p. 74-76.
Pritchard, D. W., and Carpenter, J. H., 1960, Measurements of turbulent diffusion in
estuarine and inshore waters: Internat. Assoc. Sci. Hydrology, Bull. no. 20, p.
37-50.
Schuster, J. C., 1965, Canal discharge measurements with radioisotopes: Am. SOC.
Civil Engineers Trans., v. 91, no. HY2, part 1, p. 101-124.
Spencer, E. A., and Tudhope, J. S., 1958, A literature survey ofthe salt-dilution method
of flow measurement: Inst. Water Engineers Jour., v. 12, no. 2, p. 127-138.
Turner, G. K. Associates, 1963, Operating and service manual, model 111 fluorometer:
Palo Alto, Calif., 28 p.
U.S. Bureau of Reclamation, 1971, Water measurement manual [2d ed.]: Water Re-sources
Tech. Pub., p. 166-168.
and hydrometerorology: Flood Control Series no. 22, p. 47-49.
Wright, R. R., and Collings, M. R., 1964, Application of fluorescent tracing techniques
to hydrologic studies: Am. Water Works Assoc. Jour., v. 56, no. 6, p. 748-754.
Yotsukura, Nobuhiro, and Cobb, E. D., 1972, Transverse diffusion of solutes in natural
streams: U.S. Geol. Survey Prof. Paper 582-C, 19 p.

CHAPTER 8. MEASUREMENT OF DISCHARGE BY
MISCELLANEOUS METHODS
GENERAL
This chapter deals with the measurement of discharge when condi-tions
are such that it is not feasible to use either a velocity meter or
tracer-dilution equipment. The situations and methodologies dis-cussed
include the following:
A. High flow
1. Timed observation of floats
B. Low flow
1. Volumetric measurement
2. Use of a calibrated portable weir plate
3. Use of a calibrated portable Parshall flume
C. Unstable flow-roll waves or slug flow
1. Use of photographic techniques
Not discussed here is the practice followed in many countries, other
than the U.S.A., in which discharge is measured by observing the
head on gaging-station controls that are built in conformity with
laboratory-rated weirs or flumes. The transfer of a laboratory dis-charge
rating to a structure in the field requires the existence, and
maintenance, of similitude between laboratory model and prototype,
not only with regard to the structure, but also with regard to the
approach channel. For example, scour and (or) fill in the approach
channel will change the head-discharge relation, as will algal growth
on the control structure. Both the structure and the approach channel
must be kept free from accumulations of debris, sediment, and veg-eta1
growth. Flow conditions downstream from the structure are
significant only to the extent that they control the tailwater eleva-tion,
which may influence the operation of structures designed for
free-flow conditions.
The existence or development of conditions that differ from labora-tory
conditions will necessitate in place calibration of the control to
establish the extent of departure from the laboratory discharge rat-ings.
In place calibration requires the measurement of discharge by
current meter or by other means, as described in chapters 5 through
9. Because experience in the U.S.A. has indicated that departure from
laboratory conditions is the norm, rather than the exception, gaging-station
controls are always calibrated in place by the U.S. Geological
Survey.
The reader who is interested in the measurement of discharge by
the use of precalibrated controls is referred to publications by the
World Meteorological Organization (1971) and the International
Standards Organization (1969).

8. DISCHARGE-MISCELLANEOUS METHODS 261
FLOATS
Floats are seldom used in stream gaging but are useful in an
emergency for measuring high discharges under the following cir-cumstances:
1. No conventional or optical current meter is available.
2. A current meter is available but the measurement structure-bridge
or cableway-has been destroyed, and equipment for
measuring from a boat is unavailable.
3. A conventional current meter is available, but floating ice or drift
make it impossible to use the meter.
Surface floats are used in those situations, and they may be almost
any distinguishable article that floats, such as wooden disks; bottles
partly filled with either water, soil, or stones; or oranges. Floating ice
cakes or distinguishable pieces of drift may be used if they are present
in the stream.
Two cross sections are selected along a reach of straight channel for
a float measurement. The cross sections should be far enough apart so
that the time the float takes to pass from one cross section to the other
can be measured accurately. A traveltime of at least 20 s is recom-mended,
but a shorter time may be used for streams with such high
velocities that it is not possible to find a straight reach of channel
having adequate length. The water-surface elevation should be refer-enced
to stakes along the bank at each cross section and at one or
more intermediate sites. Those elevations will be used at a later date,
when conditions permit, to survey cross sections of the measurement
reach, and the end stakes will be used to obtain the length of the
reach. The surveyed cross sections will then be used to derive an
average cross section for the reach.
In making a float measurement a number of floats are distributed
uniformly across the stream width, and the position of each with
respect to distance from the bank is noted. The floats should be intro-duced
a short distance upstream from the upstream cross section so
that they will be traveling at the speed of the current when they reach
the upstream section. A stopwatch is used to time their travel be-tween
the end cross sections of the reach. The estimated position of
each float with respect to the bank is also noted at the downstream
cross section.
If there is no bridge or cableway from which to introduce the floats
in the stream, the floats will have to be tossed in from the
streambank. If that is the situation that exists at a wide stream, it
may be impossible to position any floats in the central core of the
stream where most of the flow occurs. A float measurement of dis-charge
made under those conditions would be meaningless. However,
the difficulty of introducing floats at intervals across the entire width

of a wide stream can be overcome if a boat can be obtained for the
purpose.
The velocity of a float is equal to the distance between the end cross
sections divided by the time of travel. The mean velocity in the verti-cal
is equal to the float velocity multiplied by a coefficient whose
value is dependent on the shape of the vertical-velocity profile of the
stream and on the depth of immersion of the float with respect to
stream depth. A coefficient of 0.85 is commonly used to convert the
velocity of a surface float to mean velocity in the vertical.
The procedure for computing the discharge is similar to that used
in computing the discharge for a conventional current-meter meas-urement.
(See chapter 5.) The discharge in each subsection of the
average cross section is computed by multiplying the area of the
subsection by the mean vertical velocity for that subsection. The total
discharge is equal to the sum of the discharges for all subsections.
Float measurements of discharge that are carefully made under
favorable conditions may be accurate to within ~10 percent. Wind
may adversely affect the accuracy of the computed discharge by its
effect on the velocity of the floats. If a nonuniform reach is selected
and few floats are used in the cross section, measurement results may
be in error by as much as 25 percent.
VOLUMETRIC MEASUREMENT
The volumetric measurement of discharge is only applicable to
small discharges, but it is the most accurate method of measuring
such flows. In that method the hydrographer observes the time re-quired
to fill a container of known capacity, or the time required to
partly fill a calibrated container to a known volume. The only equip-ment
required, other than the calibrated container, is a stopwatch.
The container is calibrated in either of two ways. In the first meth-od,
water is added to the container by known increments of volume,
and the depth of water in the container is noted after the addition of
each increment. In the second method, the empty container is placed
on a weighing scales, and its weight is noted. Water is added to the
container in increments, and after each addition the total weight of
container and water is noted, along with the depth of water in the
container. The equation used to determine the volume corresponding
to a depth that was read is
where
V = volume of water in container, in cubic feet or cubic meters,
W:! = weight of water and container, in pounds or kilograms,

W, = weight of empty container, in pounds or kilograms, and
w = unit weight of water, 62.4 lb/ft3 or 1,000 kg/m3.
Volumetric measurements are usually made where the flow is con-centrated
in a narrow stream, or can be so concentrated, so that all
the flow may be diverted into a container. Examples of sites present-ing
the opportunity for volumetric measurement of discharge are a
V-notch weir; an artificial control where all the flow is confined to a
notch or to a narrow width of catenary-shaped weir crest; and a cross
section of natural channel where a temporary earth dam can be built
over a pipe of small diameter, through which the entire flow is di-rected.
Sometimes it is necessary to place a trough against the artifi-cial
control to carry the water from the control to the calibrated con-tainer.
If a small temporary dam is built, the stage behind the dam
should be allowed to stabilize before the measurement is begun. The
measurement is made three or four times to be certain no errors have
been made and to be sure the results are consistent.
Volumetric measurements have also been made under particular
circumstances when no other type of measurement was feasible. One
such circumstance involved a small stream that was in actuality a
series of, deep pools behind broad-crested weirs that acted as drop
structures to dissipate the energy of the stream. At low flows the
depth of water on the weir crest was too shallow to be measured by
current meter, and the velocity in the pools was too slow for such
measurement. To measure the discharge a large container of known
volume was placed on a raft held close to the downstream weir face by
ropes operated from the banks. A sharp-edged rectangular spout of
known width was held so that one end butted tightly against the
downstream face of the weir, the base of the spout being held just
below the weir crest. The other end of the spout led to the container of
known volume. Timed samples of the flow, sufficient to fill the con-tainer,
were taken at a number of locations along the downstream
face of the weir, the raft being moved laterally across the stream,
from location to location, by the ropes. The procedure was analogous
to making a conventional current-meter discharge measurement. In-stead
of measuring depth and velocity at a series of observation sites
in the cross section, as is done in a current-meter measurement, the
discharge per width of spout opening was measured at a series of
observation sites. The discharge measured at each site was multiplied
by the ratio of subsection width to spout width to obtain the discharge
for the subsection. The total discharge of the stream was the summa-tion
of the discharges computed for each subsection.
PORTABLE WEIR PLATE
A portable weir plate is a useful device for determining discharge

when depths are too shallow and velocities too low for a reliable
current-meter measurement of discharge. A 90” V-notch weir is par-ticularly
suitable because of its sensitivity at low flows. Three differ-ent
sizes of weir plate are commonly used by the U.S. Geological
Survey; their recommended dimensions are given in figure 129.
The weir plate is made of galvanized sheet iron, using lo- to 16-
gauge metal. The 90” V-notch that is cut in the plate is not beveled
but is left with flat, even edges. The larger weir plates are made of
thinner material than the smaller weir plates, but the medium and
large plates are given additional rigidity by being framed with small
angle irons fastened to the downstream face. A staff gage, attached to
the upstream side of the weir plate with its zero at the elevation of the
bottom of the notch, is used to read the head on the weir. The staff
gage should be installed far enough from the notch to be outside the
region of drawdown of water going through the notch. Drawdown
becomes negligible at a distance from the vertex of the notch that is
equal to twice the head on the notch. Consequently, if the weir plate
has the dimensions recommended in figure 129, the staff gage should
be installed near one end of the plate.
Comers may be
trimmed if desired
Large 1.75 1.00 0.75 4.0 1.0 16 ga. 24
_~~
All dimensions, other than r, are in feet
FIGURE 129.-Portable weir-plate sizes.

To install the weir, the weir plate is pushed into the streambed. A
pick or shovel may be necessary to remove stones or rocks that pre-vent
even penetration of the plate. A carpenter’s level is usually used
to insure that the top of the plate is horizontal and that the face of the
plate is vertical. Another means of leveling the weir plate is by the
use of a staff gage or level bubble attached at each end of the plate.
The weir plate is then leveled by adjusting it until both staff gages
give identical readings of the water surface or until the level bubbles
are centered. Through eyebolts that are attached to the plate, rods are
driven into the streambed to maintain the weir in a vertical position.
Soil or streambed material is packed around the weir plate to prevent
leakage under and around it. Canvas is placed immediately down-stream
from the weir to prevent undercutting of the bed by the falling
jet. It ordinarily requires only one man to make the installation.
A large weir plate of the dimensions shown in figure 129 can meas-ure
discharges in the range from 0.02 to 2.0 ft”/s (0.00057 to 0.057
m”/s) with an accuracy of +-3 percent, if the weir is not submerged. A
weir is not submerged when there is free circulation of air on all sides
of the nappe. The general equation for flow over a sharp-edged 90
V-notch weir is
where
Q = ChW, (43)
Q = discharge, in cubic feet per second or cubic meters per second,
h = static head above the bottom of the notch, in feet or meters,
and
C = coefficient of discharge.
Each weir should be rated by volumetrically measuring the discharge
corresponding to various values of head. In the absence of such a
rating, a value of 2.47 may be used for C in equation 43 when English
units are used, or 1.36 when metric units are used.
When the weir is installed it will cause a pool to form on the
upstream side of the plate. No readings of head on the notch should be
recorded until the pool has risen to a stable elevation. The head
should then be read at half-minute intervals for about 3 min, and the
mean value of those readings should be the head used in equation 43
to compute discharge. After the completion of the measurement the
weir plate is removed.
PORTABLE PARSHALL FLUME
A portable Parshall flume is another device for determining dis-charge
when depths are too shallow and velocities too low for a
current-meter measurement of discharge. The portable flume used by
the U.S. Geological Survey is a modified form of the standard Par-

shall flume (p.314-319) having a 3-in (0.076 m) throat. The modifica-tion
consists, primarily, of the removal of the downstream diverging
section of the standard flume. The purpose of the modification is to
reduce the weight of the flume and to make it easier to install. Be-cause
the portable Parshall flume has no downstream diverging sec-tion,
it cannot be used for measuring flows when the submergence
ratio exceeds 0.6. The submergence ratio is the ratio of the
downstream head on the throat to the upstream head on the throat.
Although a submergence ratio of 0.6 can be tolerated without affect-ing
the rating of the portable flume, in practice the flume is usually
installed so that the flow passing the throat has virtually free fall.
That is usually accomplished by building up the streambed a couple
of inches under the level converging floor of the flume. (See fig. 130.)
Figure 130 shows the plan and elevation of the portable Parshall
flume. The gage height or upstream head on the throat is read in the
small stilling well that is hydraulically connected to the flow by a
%-in hole. The rating for the flume is given in table 14.
When the flume is installed in the channel, the floor of the converg-ing
section is set in a level position by using the level bubble that is
attached to one of the braces (fig. 130‘). A carpenter’s level can be used
for that purpose if the flume is not equipped with a level bubble. Soil
or streambed material is then packed around the flume to prevent
leakage under and around it. Figure 131 shows a typical field instal-lation.
After the flume is installed, water will pool upstream from
structure. No gage-height readings should be recorded until the pool
has risen to a stable level. As with the portable weir, after stabiliza-tion
of the pool level, gage-height readings should be taken at half-
TABLE 14.-Ratuzg table for S-in modified Parshall flume
Gage height (ft) Dmharge (ft%) Gage height (ft) Dwharge (ft’k) Gage haght (ft) Dmharge (ft’is)
0.01 0.0008 0.21
.02 .0024 .22
.03 .0045 .23
.04 .0070 .24
.05 .OlO .25 .oa -013 .26
.07 ,017 .27
.08 ,021 .28
.09 ,025 .29
.lO ,030 .30
.ll ,035 .31
.12 ,040 .32
,045
,051
,057
,063
,069
.076
,083
.090
.33
.34
.35
.36
.37
.38
.39
.40
0.097
,104
,111
,119
,127
,135
,144
,153
,162
,170
,179
.188
,198
,208
,218
,228
,238
,248
,259
,269
0.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
.55
.56
.57
.58
.59
0.280
,301
,312
.323
.334
.345
.357
,368
,380
,392
,404
,417
,430
,443
,456
,470
,483
.497

minute intervals for about 3 min. The mean value of those readings is
the stage used in table 14 to obtain the discharge. A carefully made
measurement should have an accuracy of -+2 or 3 percent. After com-pletion
of the measurement, the portable flume is removed.
12"T 6"1
r
I-
%” X 3/” 3< $6” angles
Al
c
Material: ?&-In aluminum
Welded construction
Note: - This . stilling well can accommodate
a S-In tloat and be used with a recorder
if continuous measurement is desired for a
period.
FIGURE 130.-Working drawing of modified 3-in Parshall flume.

MEASUREMENT OF STAGE AND DISCHARGE
MEASUREMENT OF UNSTABLE FLOW-ROLL WAVES OR
SLUG FLOW
CHARACTERISTICS OF UNSTABLE FLOW
Unstable or pulsating flow often occurs during flash floods in arid
areas. In pulsating flow the longitudinal profile is marked by a series
of abrupt translatory waves (fig. 132) that rapidly move downstream.
Translatory waves, commonly called roll waves or slug flow, can only
develop in steep channels of supercritical slope and, therefore, are a
matter of concern to the designer of steep-gradient channels. Chan-nels
are usually designed for stable flow. Should pulsating flow occur
at high stages in a channel so designed, the channel capacity may be
inadequate at a discharge much smaller than the design flow. Fur-thermore,
if the overriding translatory wave carries an appreciable
part of the total flow, conventional stream-gaging methods cannot be
used to determine the discharge. Conventional water-stage recorders
FIGURE 131.-Modified 3-in Parshall flume installed for measuring discharge.

of either the float or pressure-sensing type do not react quickly
enough to record the rapidly fluctuating stage; depths and velocities
change too rapidly to permit discharge measurement by current me-ter;
no stage-discharge relation exists for pulsating flow; and the
commonly used formulas for computing stable open-channel dis-charge
are not applicable.
DETERMINATION OF DISCHARGE
In brief, the method of determining the discharge of pulsating flow
requires (1) computation of the discharge (&,,.I in the overriding
waves and (2) computation of the discharge (Q ,) in the shallow-depth,
or overrun, part of the flow. The sum of the two discharges is the total
discharge at the time of observation.
To compute the discharge (Q,,.) in an overriding wave, which is
usually wedge shaped (fig. 1321, the dimensions of the wave are ob-served,
and the volume of the wave is divided by the elapsed time
between the arrival of waves. For example, if the wedge-shaped wave
in a train of waves has a volume of 200 fti’ (5.67 m”) and a wave
arrives every 10 s, the discharge in the overriding wave is 200/10, or
20 ft”/s (0.57 m:‘/s). Average values are usually used in the
computation-for example, the average volumes of five consecutive
waves and the average time interval between the arrival of those
consecutive waves. It should be mentioned at this point that the lon-gitudinal
profile of the wave is actually slightly concave upward and
the wave front, while extremely steep, is not vertical. However, to
simplify the computation of discharge, the waves are assumed to have
a simple wedge shape.
To compute the discharge (Q,) in the shallow-depth, or overrun,
part of the flow, the cross-sectional area of the shallow-depth flow is
FIGURE 132.-Schematic sketch of longitudinal water-surface profile during pulsating
flow.

observed (D, x channel width), and that area is multiplied by its
velocity, V,. Seldom will there be time enough between waves to
obtain velocity observations of V, with a conventional current meter.
V, may be computed by-some stable-flow equation, such as the Man-ning
equation, but preferably the surface velocity of shallow-depth
flow should be measured by optical current meter. (See p. 91-93.) The
surface velocity can then be multiplied by an appropriate
coefficient-O.9 or 0.85, for example-to give the mean velocity, V,.
The final step is to compute the total discharge at the time of observa-tion
by adding Q,, and Q,.
EXAMPLES OF DISCHARGE DETERMINATION
This section briefly describes two examples of discharge determina-tions
made under conditions of pulsating flow in southern California.
Holmes (1936) obtained photographic documentation of a train of
translatory waves in a steep stormflow channel. The rectangular
channel was 43 ft (13.10 m) wide, 8 ft (2.44 m) high, and had a slope of
0.02. The waves themselves lapped at the top of the manmade chan-nel
giving them a height (D2) of 8 ft, and their length (L,) was about
600 ft (180 m). The average distance between wave crests was about
1,200 ft (360 m), and the average time interval between arrival of the
waves (T,,) was 51 s. The channel between waves was dry or nearly so
(D,=O), meaning that the entire discharge was transported in the
waves. The average discharge over the time T,, computed from the
equation
Q = (volume)/T,,=% (IV) (h,) (L,)I(T,,), (44)
was therefore about 2,000 ft3/s (56 m3/s). The channel had been de-signed
for stable-flow conditions and, according to the Manning equa-tion,
had a capacity of about 16,000 ft3/s (405 m3/s). We see then, that
under the observed conditions of unstable flow the channel could ac-commodate
only one-eighth of the design discharge.
Thompson (1968) described the experimental measurement of pul-sating
flow in the rectangular stormflow channel of Santa Anita
Wash in Arcadia, California. The concrete channel was 28 ft (8.5 m)
wide and had a slope of 0.0251. On the infrequent occasions when the
channel had carried storm runoff in the past, the flow had been ob-served
to be pulsating. For the test, water was released into the chan-nel
from an upstream reservoir at controlled rates of approximately
100 ft”/s (2.8 m3/s), 200 ft3/s (5.6 m3/s), 300 ft3/s (8.5 m3/s). Unstable
flow did not develop until the flow came out of a bend in the steep
storm channel and entered a straight reach of the channel. In other
words, the released flow was stable upstream from the bend and pul-sating
downstream from the bend. During the release of water, dis-

charge measurements were made continuously by current meter in
the stable flow upstream from the bend. The discharge hydrograph
based on those measurements is shown by solid line in figure 133.
Downstream from the bend a simultaneous attempt was made to
measure the unstable flow by the method described in this paper, for
the purpose of verifying the method.
At the test site, about 3,300 ft (1,000 m) downstream from the bend,
the equivalent of a series of staff gages, in the form of a grid, was
painted on one of the vertical channel walls so that water-surface
320
280
240
0
6
; 200
:
L
f
0 160
?
0
5
ri 120
2
::
E
80
40
-Measured discharge
CLOCK TIME. IN HOURS
-1
,
FIGURE 133.-Discharge hydrograph at Santa Anita Wash above Sierra Madre Wash,
Calif., April 16, 1965, and plot of discharges computed from observations of flow.

elevations could easily be read by a crew of observers. Some of the
observers were equipped with both still- and motion-picture cameras
to document the observations; others were equipped with stopwatches
to time wave velocity over a measured course of 102 ft (31 m) and to
obtain the elapsed time between the arrival of waves. The waves were
not evenly spaced and occasionally one wave would overtake another,
but in general the waves were fairly uniform in size, maintained their
spacing, and underwent little attenuation in the 3,300-ft reach above
the test site. For computation purposes the average volumes of five
consecutive waves and their average elapsed time between arrivals
CT,,) were used, and discharges were computed at 15 min intervals
using the procedure described earlier. For example, at the time of
greatest discharge, the average value of T,, was 9.6 s, and the average
wave dimensions wereD, = 0.42 ft (0.13 m), h, = 0.66 ft (0.20 m), and
L, = 158 ft (48.2 m). The computed value of Q, equaled 152 ft3/s (4.30
m%). No optical current meter was available at the time, and Q1 was
therefore computed by the Manning equation. The computed value of
Q, also equaled 152 ft3/s (4.30 m3/s), giving a computed total discharge
304 ft3/s (8.60 m3/s) at the time of observation. The values of discharge
that were computed at 15-min intervals are plotted as open circles in
figure 133 and show satisfactory agreement with the “true” discharge
hydrograph. The field test of the method was therefore considered a
success.
PROPOSED INSTRUMENTATION
There is as yet no instrumentation that is operational for automati-cally
recording the data required to compute discharge under condi-tions
of pulsating flow. Thompson concluded the above-cited report
(1968) by describing three types of automatic instrumentation-photographic,
depth sensing, and dye dilution-that might be devel-oped
for that purpose.
SELECTED REFERENCES
Buchanan, T. J., and Somers, W. P., 1969, Discharge measurements at gaging stations:
U.S. Geol. Survey Techniques Water-Resources Inv., book 3, chap. A8, p. 57-63.
Holmes, W. H., 1936, Traveling waves in steep channels: Civil Eng., v. 6, no. 7, p.
467-468.
International Standards Organization, 1969, Liquid flow measurement in open
channels-Establishment and operation of a gauging station and determination of
the stage-discharge relation: IS0 Recommendation RllOO, Geneva, 44 p.
Thompson, T. H., 1968, Determination of discharge during pulsating flow: U.S. Geol.
Survey Water-Supply Paper 1869-D, 22 p.
U.S. Bureau of Reclamation, 1971, Water measurement manual [2d ed.]: Water Re-sources
Tech. Pub., p. 157-159.
World Meteorological Organization, 1962, Field methods and equipment used m hy-drology
and hydrometeorology: Flood Control Ser. no. 22, p. 50-51.
-1971, Use of weirs and flumes in stream gauging:WMO-no. 280, Tech. Note no.
117, Geneva, 57 p.

9. INDIRECT DETERMINATION OF PEAK DISCHARGE 273
CHAPTER 9.- INDIRECT DETERMINATION OF
PEAK DISCHARGE
INTRODUCTION
During floods, it is frequently impossible or impractical to measure
the peak discharges when they occur because of conditions beyond
control. Roads may be impassable; structures from which current-meter
measurements might have been made may be nonexistent, not
suitably located, or destroyed; knowledge of the flood rise may not be
available sufficiently in advance to permit reaching the site near the
time of the peak; the peak may be so sharp that a satisfactory cur-rent-
meter measurement could not be made even with an engineer
present at the time; the flow of debris or ice may be such as to prevent
use of a current meter; or limitations of personnel might make it
impossible to obtain direct measurements of high-stage discharge at
numerous locations during a short flood period. Consequently, many
peak discharges must be determined after the passage of the flood by
indirect methods such as slope-area, contracted opening, flow-over-dam,
or flow-through-culvert.
Indirect determinations of discharge make use of the energy equa-tion
for computing streamflow. The specific equations differ for differ-ent
types of flow, such as unobstructed open-channel flow, flow over
dams, and flow through culverts. However, all the methods involve
these general factors:
1. Physical characteristics of the channel; that is dimensions and
conformation of the channel within the reach used and boundary
conditions.
2. Water-surface elevations at time of peak stage to define the upper
limit of the cross-sectional areas and the difference in elevation
between two or more significant cross sections.
3. Hydraulic factors based on physical characteristics, water-surface
elevations, and discharge, such as roughness coefficients and dis-charge
coefficients.
This chapter provides only a brief general discussion of the proce-dures
used in collecting field data and in computing discharge by the
various indirect methods. That highly specialized subject is treated in
detail in the several manuals of the series “Techniques of Water-
Resources Investigations of the United States Geological Survey”
that are listed as references at the end of this chapter.

It should be remembered that the discharge that is determined by
either direct measurement or by indirect methods includes not only
the water but also any substances suspended or dissolved in the water
(p. 79).
COLLECTION OF FIELD DATA
The data required for the computation of discharge by indirect
methods are obtained in a field survey of a reach of channel. The
survey includes the elevation and location of high-water marks cor-responding
to the peak stage; cross sections of the channel along the
reach; selection of a roughness coefficient; and description of the
geometry of dams, culverts, or bridges, depending on the type of
peak-discharge determination to be made. The selection of a suitable
site is a most important element in the application of the indirect
method of discharge determination.
It is recommended that a transit be used to make a “transit-stadia”
survey of the selected site. That method combines vertical and hori-zontal
control surveys in one operation and is accurate, simple, and
speedy.
Selection of a roughness coefficient remains essentially an “art”
that is developed through experience. The factors that exert the
greatest influence on the coefficient of roughness are the character of
the streambed material, cross section irregularity, the presence of
vegetation, and the alinement of the channel. In the Manning equa-tion
the roughness coefficient, n, ranges from as low as 0.012 for a
concrete-lined channel in excellent condition or for a smooth sand
channel of regular geometry to more than 0.1 for overbank areas
having a heavy cover of brush.
SLOPE-AREA METHOD
The slope-area method is the most commonly used technique of
indirect discharge determination. In the slope-area method, dis-charge
is computed on the basis of a uniform-flow equation involving
channel characteristics, water-surface profiles, and a roughness or
retardation coefficient. The drop in water-surface profile for a uniform
reach of channel represents energy losses caused by bed and bank
roughness.
In applying the slope-area method, any one of the well-known vari-ations
of the Chezy equation may be used. However the Manning
equation is preferred in most countries, including the U.S.A., because
it is simple to apply, and the many years of experience in its use have
shown that it produces reliable results.

9. INDIRECT DETERMINATION OF PEAK DISCHARGE
The Manning equation, written in terms of discharge, is
275
Q = 1.486 AR@S”, (in English units), or (45)
n
Q = AR2k3~z (in metric units), (454
n
where
Q = discharge,
A = cross-sectional area,
R = hydraulic radius,
S = friction slope, and
n = roughness coefficient.
The Manning equation was developed for conditions of uniform flow
in which the water-surface profile and energy gradient are parallel to
the streambed and the area, hydraulic radius, and depth remain con-stant
throughout the reach. For lack of a better solution, it is assumed
that the equation is also valid for the nonuniform reaches that are
invariably encountered in natural channels, if the water-surface gra-dient
is modified by the difference in velocity-head between cross
sections. The energy equation for a reach of nonuniform channel be-tween
cross section 1 and cross section 2 shown in figure 134 is
(h, + h,,) = (h, + hUgI + &)I - 2 + NW, - 2, (46)
where
h = elevation of the water surface at the respective cross
sections above a common datum,
h,- = velocity head at the respective cross sections = (rV2/2g,
where (Y = velocity-head coefficient,
hf = energy loss due to boundary friction in the reach,
Ah,. = upstream velocity head minus the downstream velocity
head, used as a criterion for expansion or contraction
of reach, and
k(Ah,.) = energy loss due to acceleration or deceleration in a con-tracting
or expanding reach, where
k = energy loss coefficient.

I
- I
I
I
I

The friction slope (S) to be used in the Manning equation is thus
defined as
S = h,z Ah + M,, - k(Ah,) ,
L L (47)
where Ah is the difference in water-surface elevation at the two sec-tions
and L is the length of the reach.
In using the Manning equation the conveyance, K, is computed for
each cross section as (1.486/n)AR2/3 in English units, or (Iln)AR2~” in
metric units. The mean conveyance in the reach is then computed as
the geometric mean of the conveyance at the two sections. This proce-dure
is based on the assumption that the conveyance varies uniformly
between sections. The discharge is computed by use of the equation
Q=w, (48)
where S is the friction slope as previously defined.
CONTRACTED-OPENING METHOD
The contraction of a stream channel by a roadway crossing creates
an abrupt drop in water-surface elevation between an approach sec-tion
and the contracted section under the bridge. The contracted sec-tion
framed by the bridge abutments and the channel bed is in a sense
a discharge meter that can be utilized to compute floodflows. The head
on the contracted section is defined by high-water marks, and the
geometry of the channel and bridge is defined by field surveys.
In computations of peak discharge at a contraction, the drop in
water-surface level between an upstream section and a contracted
section is related to the corresponding change in velocity. The dis-charge
equation results from writing the energy and continuity equa-tions
for the reach between these two sections, designated as sections
1 and 3 in figure 135.
The discharge equation is
Q = CA,4 2g Ah + a, v,2 -hf
2.9 >
, (49)
in which
Q = discharge,
g = acceleration of gravity,
C = coefficient of discharge based on the geometry of the bridge
and embankment,
A:, = gross area of section 3; this is the minimum section parallel
to the constriction between the abutments, and it is not

necessarily located at the downstream side of the bridge,
Ah = difference in elevation of the water surface between sec-a1
2
tions 1 and 3,
- = weighted average velocity head at section 1, where V, is
the average velocity, Q/A,, and (Y, is coefficient that
takes into account the variation in velocity in that sec-tion,
and
h, = the head loss caused by friction between sections 1 and 3.
The friction loss, h,, as computed by the Manning equation, is only
(1) I
b
(3)
FIGURE 135.-Definition sketch of an open-channel contraction.

an approximation of the actual loss because of the rapid change in
velocity from section 1 to section 3. Therefore, satisfactory results are
attainable only if the term “/+” is small relative to the difference in
head, Ah.
FLOW OVER DAMS AND WEIRS
The term “dams,” as used here, also includes highway and railway
embankments that act as broad-crested dams during floods. The peak
discharge over a dam or weir can be determined on the basis of a field
survey of high-water marks and the geometry of the particular struc-ture.
(The terms “dam” and “weir” are used interchangeably.)
The basic equation for flow over a dam is
Q = CbH3/2, (50)
where
Q = discharge,
C = a coefficient of discharge having the dimensions of the
square root of the acceleration of gravity,
b = width of the dam normal to the flow, excluding the width of
piers, if any, and
H = total energy head (h + V,,‘/2g) referred to the crest of the
dam, where h = static head, and V,, = mean velocity at
the approach section to the dam.
It is apparent from equation 50 that the reliability of a computation
of flow over a dam is dependent primarily on using the correct dam
coefficient, C. Values of C vary with the geometry of the dam and with
the degree of submergence of the dam crest by tailwater. One of the
manuals referred to on page 273 (Hulsing, 1967) treats in detail the
coefficients associated with sharp-crested (thin-plate) weirs, broad-crested
weirs, round-crested weirs, and weirs of unusual shape. Be-cause
the technical details in that manual cannot be readily sum-marized
here, the reader is referred to the Hulsing report.
FLOW THROUGH CULVERTS
The peak discharge through culverts can be determined from
high-water marks that define the headwater and tailwater eleva-tions.
This indirect method is used extensively to measure flood dis-charges
from small drainage areas.
The placement of a roadway fill and culvert in a stream channel
causes an abrupt change in the character of flow. This channel transi-tion
results in rapidly varied flow in which acceleration, rather than
boundary friction, plays the primary role. The flow in the approach
channel to the culvert is usually tranquil and fairly uniform. How-ever,
within the culvert the flow may be tranquil, critical, or rapid if
the culvert is partially filled, or the culvert may flow full under pres-sure.

The physical features associated with culvert flow are illustrated in
figure 136. They are the cross section in the approach channel located
upstream from the culvert entrance at a distance that is equivalent to
the width of the culvert opening; the culvert entrance; the culvert
barrel; the culvert outlet; the farthest downstream section of the
barrel; and the tailwater downstream from the culvert barrel.
The change in the water-surface profile in the approach channel
reflects the effect of acceleration that results from the contraction of
cross sectional area. Loss of energy near the entrance is related to the
sudden contraction and subsequent expansion of the live stream
within the barrel, and entrance geometry has an important influence
on this loss. The important features that control the stage-discharge
relation at the approach section can be the occurrence of critical depth
in the culvert, the elevation of the tailwater, the entrance or barrel
geometry, or a combination of these elements.
The peak discharge through a culvert is determined by application
of the continuity equation and the energy equation between the ap-proach
section and a section within the culvert barrel. The location of
the downstream section depends on the state of flow in the culvert
barrel. For example, if critical flow occurs at the culvert entrance, the
headwater elevation is not a function of either the barrel friction loss
or the tailwater elevation, and the terminal section is located at the
upstream end of the culvert.
Information obtained in the field survey includes the peak eleva-tion
of the water surface upstream and downstream from the culvert
and the geometry of the culvert and approach channel. Reliable
high-water marks can rarely be found in the culvert barrel; therefore,
the type of flow that occurred during the peak flow cannot always be
determined directly from field data, and classification becomes a
trial-and-error procedure.
Culvert
barrel Outlet section
FIGURE 136.-Graphical presentation of the Bernoulli equation in culvert flow.

GENERAL CLASSIFICATION OF FLOW
For convenience in computation, culvert flow has been classified
into six types on the basis of the location of the control section and the
relative heights of the headwater and tailwater elevations. The six
types of flow are illustrated in figure 137, and pertinent characteris-tics
of each type are given in table 15. From that information the
general classification of types of flow can be made.
1. If h,/D is equal to or less than 1.0 and (h, -2)/D is less than 1.5,
only types I, II, and III flow are possible.
2. If ha/D is greater than 1.0, only type IV flow is possible.
3. If h,lD is equal to or less than 1.0 and (h, - z)/D is equal to or
greater than 1.5, only types V and VI flow are possible.
A manual by Bodhaine (1968) discusses trial-and-error procedures
for further identification of the type of culvert flow and for the compu-tation
of discharge.
ESTIMATING DISCHARGE FROM SUPERELEVATION IN
BENDS
Situations exist where none of the four methods previously de-scribed
for determining peak discharge can be reliably applied. For
example, in a highly sinuous, steep canyon stream, there may be no
straight reaches of sufficient length for reliable application of the
slope-area method; no abrupt area contractions may exist; and no
manmade structures, such as dams or culverts, may have been built.
In the above situation the peak discharge may sometimes be esti-mated
from the superelevation in a bend of the stream (Apmann,
1973). The discharge should be estimated at each of several bends,
after which the several estimated discharges are averaged.
A fundamental characteristic of open channel flow is the deforma-tion
of the free surface in a bend because of the action of centrifugal
force. The water surface rises on the concave or outside bank of the
TABLE 15.-Characteristzcs of types of culvert flow
[D = maxnnum vertical height of barrel and dmmeter of circular culverts]
Flow BC3~~~l
type flow
I Partly ftill _-
II ____ do ____ _-
III _--- do __----
IV Full --______
V Partly full --
Location of
termmal
sectmn
Kind of
control
Inlet -----__--- Critical
depth.
---- do ---___-- ---_ do -----_
Inlet -----_---- Entrance
geometry.
Outlet---------- Entrance and
CUlVWt h,-r
slope ~ D
Steep __ <1.5
Mild _- cl.5
do -- cl.5
Any __ B1.0
__ do _- al.5
h, h,
--
h. D
Cl.0 s1.0
Cl.0 s1.0
>l.O Cl.0
- >l.O
- Cl.0
- s1.0
barrel
geometry.

bend and lowers along the convex or inside bank of the bend. The
difference in water-surface elevation between the banks is the
superelevation. Superelevation varies with angular distance in the
bend because of acceleration of the fluid entering and leaving the
curve and because of the varying curvature of streamlines within the
bend.
The discharge equation given by Apmann (1973) is
&=A &?.$k
/I-
(51)
where
Q = discharge,
A = average radial cross section in the bend,
g = acceleration of gravity,
h = superelevation, that is, the maximum difference in water-surface
elevation, measured along a radius of the bend,
between inner and outer banks of the bend, and
K = superelevation coefficient.
The value of K is determined from the equation
K = f tanh (9) ln($
p,C,(beginning
of curve)
Note: b=r,-r
FIGURE 138.-Ideahzed sketch of a bend (plan view).
(52)

(NOTE.-tanh is the hyperbolic tangent)
The symbols in equation 52 are shown in the sketch in figure 138.
The method described applies only to bends having no overbank
flow. The limited amount of work that has been done with the method
indicates that it should not be applied where superelevations are less
than 0.25 ft (0.076 m) because of uncertainties regarding the eleva-tions
of high-water marks at the banks. These uncertainties result
from wave action and from the thickness of the bank-deposited debris
that is often used as a high-water mark.
SELECTED REFERENCES
American Society of Civil Engineers, 1975, Sedimentation engineering, A S.C.E.
Manuals and Reports on Engineering Practice no. 54, 745 p.
Apmann, R. P., 1973, Estimating discharge from superelevation in bends: Am. Sot
Civil Engineers, Hydraulics Div. Jour., v. 99, no. HYl, p. 65-79.
Benson, M. A., and Dalrymple, Tate, 1967, General field and office procedures for
indirect discharge measurements: U.S. Geol. Survey Techniques Water-Resources
Inv., book 3, chap. Al, 30 p.
Bodhaine, G. L., 1968, Measurement of peak discharge at culverts by indirect methods:
U.S. Geol. Survey Techniques Water-Resources Inv., book 3, chap A3, 60 p
Dalrymple, Tate, and Benson, M. A., 1967, Measurement of peak discharge by the
slope-area method: U.S. Geol. Survey Techniques Water-Resources Inv., book 3,
chap. A2, 12 p.
Hulsing, Harry, 1967, Measurement of peak discharge at dams by indirect methods:
U.S. Geol. Survey Techniques Water-Resources Inv., book 3, chap. A5, 29 p.
Matthai, H. F., 1967, Measurement of peak discharge at wdth contractions: U.S. Geol.
Survey Techniques Water-Resources lnv.: book 3, chap A4, 44 p.

INDEX
The index covers the two volumes of this manual. Volume I contains
pages l-284 and Volume II contains pages 285-631
A
A-path sounding reel, 104
Acceleration head, 391,429,439
Accuracy of bubble-gage stage
recorders, factors
affecting, 71-14
Accuracy of current-meter
discharge measurements,
factors affecting, 179-181
standard error, 181-183
Accuracy of float measurements
of discharge, 262
Accuracy oE float-operated stage
recorders, factors
aEfecting, 68-70
Accuracy of nonrecording stage
gages I factors affecting,
chain gage, 67-68
electric-tape gage, 66-67
float-tape gage, 65-66
staff gage, 64
wire-weight gage, 64-65
Accuracy of tracer-dilution
factors affecting, 215-220
Acoustic velocity meter, 528-529
-S- ee also Velocity index,
acoustic meter
Air entrainment, effect on
acoustic velocity
metering, 456
Air line sounding correction for
vertical angles, 159-163,
166-168
Anchor ice, 361,364-366
Angle of current, measurement
of, 129-130,142-143
Annual published report,
discharge records in,
617.618.624.627-630
format of, 601-603
hydrologic-conditions bar
graph in, 616
index of, 631
introductory text of, 606-614
list of stations in, 605
rna~ of stations in. 615
reservoir records in, 619-623
revision of published records
in, 625
river-basin schematic diagram
in, 626
table of contents of, 604
Artificial controls
See Controls, artificial
Auxiliary gage, 3,23,53-54,400-
405,54i
Azimuth indicator, 129-130
B
Backwater, definition of, 393
Backwater, variable
See Variable backwater
Backwater from aquatic growth, 6
Backwater from ice
See ICC?, effect on stream
hydraulics
see Ice effect, discharge
computation for periods of
Base gage, 23,53-54,400,547
Bed configuration in sand-channel
streams, 377-379
Bench mark, 24
Bends, discharge determination
at,
in open channels, 281-283
in pipes, 526-527
Bernoulli energy equation, 322
Boat equipment for current-meter
discharge measurement by,
conventional method, 120-123
moving boat method, 187-197
-S- ee also Current-meter discharge measurements
from boats
Boundary effect on,
acoustic velocity-meter
operation, 454-456,459
surface velocity, 137-138
vertical-axis current-meter
operation, 82,87-88
Bayer method, 416-418
Braystoke current meter, 88
Bridge board, 119
Bridge equipment for current-meter
discharge
measurement, 117-120
-S- ee also Current-meter discharge measurements
from bridges
Bridge piers, 149-150
Brine-inJection system, 533
Bubble-gage Stage recorder,
accuracy of, factors
affect1nq. 71-74
bubble-feed Gate effect on,
72-74
description of sensor for, 32-
34
gas column, weight-variation
effect on, 74
gas-friction effect on, 71-72
operation of, 60-61
orifice installations for, 33-
34,52
shelter for, 51-52

C -S- ee also Stage-discharge
relatlo", natural controls
Controls, partial, definltlon
Of, 11
Controls, section, definition
of, 10,286-287
-S- ee also Stage-discharge
relation, artlflclal
co"trols
relation, natural controls
See also Shifting control
CoTGCrTZG Eactors, XIV
Conveyance-slope method, 334-337
Counter, electric, for current
meter, 130
Cranes for current-meter
measurements, 117-120
Cable cars, 110-115
pullers for, 111
sounding-reel seats for, 111
Cableway, carrier (bank-operated),
115-117
Csbleway equipment for current-meter
discharge
measurement. 110-117
-S- ee also Current-meter
discharge measurements
from cableways
Canfleld sounding reel, 102-104
Chain gage,
affecting, 67-68
descrlotion oE. 31-32
Cha"gl"gLdischarge, effect of
See Unsteady flow
Channel control,
See Controls, channel
Coaxial rating-curve method,
481-484
Colorlmetrlc analysis, 249-250
Columbus-type control, 312
Columbus weights, 102
Conductance meter, 252-255
Connectors in current-meter
assembly, 102
Constant rating-fall
method, 396-400
Contracted-opening method of
peak-discharge
determination, 277-279
Co"trols,
attrlbutes desired I",
11-12.15-16
sensitivity of, 12
stability of, 11-12
types of, 10-11
Co"trols, artificial,
attributes desired I", 12,
15-16
choice of, 17-20
definition of, 10
design of, 21-22
for sand channels, 387-388
precalibcatlon of, 16-
17.21.260
purpose of, 3
types of, 12-13
relation, artificial
co"trols
See also Shifting control
Controls. channel
deflnltion of, 10.286-287
rating for, 328-332.382-385
rating shifts for, 354-
360,385-387
Controls, complete, definition
Of, 10
Controls, compound, definition,
10
Controls, natural
attributes desired in, 11-12
deflnltion of, 10
Crest-stage gages,
description of, 77-78
location of, 9
Crump weir, 307
Cubatures, method of, 476-479
Culvert discharge,
characteristics of, 281
determlnatlon of, 279-280
types of, 281,282
Current angularity, measurement
of, 142-143
Current-direction Indicator,
129-130
Current meter, conventional,
care of, 93-94
comparison of performance of
vertical-axls and
horizontal-axls types of,
89-90
prlnclple of operation of, 84
rating of, 94-96
types of, 85
-S_e_e also Velocity index,
standard current meter
current meter, horizontal-axis,
Braystoke meter, 88
comparlso" with vertical-axis
meter. 89-90
Haskell meter, 88-89
Hoff meter, 88-89
Neypric meter, 88-89
Ott meter, 88-90,142
Current meter, optical,
care of, 94
characterlstlcs oE. 91-93
rating of, 96-97
use of, 137,170,175,270
Current meter, vertical axIs,
comparison with horizontal-axls
meter, 89-90
performance characteristics,
87-88
Price AA meter, 85-88,88-
90,143-145
Price pygmy meter, 86,143-145
USGS vane meter, 86-87,154
Current-meter discharge
measurement,
description, general, 80-82
general informatlon to be
recorded, 140-141
Volume 1, p. l-284
Volume 2, p. 285-631

mean-section method, 82 meter-setting. comoutatlo"
measurement of horizontal
angle of flow, 142-143
measurement notes, 83
midsection method, SO-82
observations to be recorded,
141-142
precautions in subfreezlng
weather, 148
precautions when debris 1s
present, 148
preparation of equipment, 141
procedure, general, 139-143
ielectlon of cross sectlo",
7.139-140.149.151.153
selectlon of observation
verticals, 140,149,153,
174,175
sounding correction for
vertical angles, 159-168
standard error, 181-183
storage correction, 177-179
summary of factors affecting
accuracy, 179-181
velocitv determination, 131-
139-
-S- ee also Velocity measurements
Current-meter discharge measure-ments
Erom boat;, con-ventional
method,
equipment assembly for, 120-
123
limiting factors, 155.157-158
position of boat for obser-vations
during, 156-157
procedure for, 158
stringing of tag line for, 155
-S- ee also Discharge measure-ments
by movlnq-boat
method
from bridges,
choice of upstream or down-stream
side oE bridge, 149
depth corrections for deep,
swift streams, 159-168
equipment assembly for, 117-
120
footbrldge and rod suspens~o",
use of, 150
handline, use of, 150-151
meter-setting, computation
for, 147
piers I" measurement section,
82,149-150
sounding weight, selection of,
146-147
tags for meter setting, use
of, 147-148
velocity-observation method,
selectlo" OE, 147,148
from cableways,
depth correction Eor deep,
swift streams, 159-168
equipment assembly for, llO-
117
handllne, use of, 150-151
for, 147
sounding weight, selection of,
146-147
tags for meter setting, use
Of, 147-148
selectlo" of, 147,148
of deep, swift
streams,
when depth can be sounded,
159-168
when depth cannot be sounded,
168-169
when meter cannot be
submerged. 170
from 1c.e cover,
effective depth, measurement
Of, 153-154
equipment assembly, 124-129
measurement cross section,
selectlon of, 151,153
measurement notes, 155,156
meter setting, 153,155
observation holes, number of,
153
partial ice cover, method used
for, 155
precautions, 151,155
vane meter, use of, 154
vertical-velocity distrl-butlo",
154
Current-meter discharge measure-merits,
mea" gage height
of,
discharge-weighted mean, 171-
173
frequency of gage-height
readings, 170-171
time-weighted mea", 171,173
Current-meter discharge measure-ments,
procedures for,
during rapidly changing
stage
on large streams, 174-175
below powerplants, 140
on small streams, 174,175-177
current-meter discharge measure-ments,
types of
boat, 155-158
-S- ee also Discharge
measurements. movinq-boat
method
bridge, 149-151
cableway, 146-148
ice cover, 151-155
network of meters, 158-159
wading, 143-146
by wading,
cross sectlon, modification
of, 144-146
current-meter type, selection
of, 143-144,145
position of hydrographer, 146
Volume 1, p. l-284
Volume 2, p. 285-631

selection of, 143,145
zero flow, gage helqht of, 146
D
Dams
inflatable, 510-511
-S~e e also Weirs
Dams with movable gates, 486-488
-S- ee also Gates
Dat”llJ.
definition of, 23
maintenance of, 23-24,63-64
Datum corrections, 545-583
level notes for, 545-546
Deflection meter
See Velocity index, deflection
meter
Depth corrections for deep,
swift streams,
meter-position correction,
167-168
tags, use of, 147-148.150,
160,163
total-depth correction, 159-
167
Depth, measurement of,
handline method, 150-151
rod method. 97-101.150
sonic-sounder method, 108-110
sounding-reel method, 147-
148,159-167
under ice, 153-154
.-S- ee also Sounding equipment Dlfferentlal-head meter, 522-528
Digital stage recorder, 36-39
servicing of, 59-60,63
Directlon of curcent, 129-130,
142-143
Discharge, changing
See Unsteady flow
Discharge, defined, 79,273-274
Discharge measurements,
below hvdroelectric power-plants,
140 -
correction for storage, 177-
179
frequency of, 79
llstinq of, 287-288,547-549
mean gage height of, 170-173
mean gage height of
plotting of, 287
review of, 547-549
Discharge measurements by con-ventional
current meter
See Current-meter discharge
measurements
Discharge measurements by float
method, 170,261-262
accuracy of, 262
Discharge measurements by
fluorescent-dye dilution,
discharge, computation of,
mean velocity adlustment,
208-210
total width and area
adjustment, 207-208
unadjusted discharge, 204.
207
discharqe-computation notes,
244-
field procedures, 237-240
fluorometer analvsis. 240-241
sample computatlbn, 241-246
simplified procedures for
making numerous measure-ments.
246-248
moving-boat method,
angle observer, function of,
202
battery charger, 193
boat, 195-196
boat operator, function of,
201-202
current meter, 188-189
description, general, of
measurement method, 183-
184
204-211
equipment,
assembly of, 199-200
mounting of, 195-197
removal of, 197
field procedures, 197-204
instrument setting,
for rate Indicator, 201
for sonic sounder, 200
measurement site, preparation
Of, 197-198
notekeeper, function of, 203-
204
rate Indicator and counter,
190-193
sonic sounder, 193-195
theory of measurement method,
184-187
vane and angle lndlcator, 187-
188
Discharge measurements by radio-active-
tracer dilution,
256-258
radIoactIve tracers, 212,257
Discharge measurements by salt
dilution,
advantages of, 212,237,250
concentrated solution,
preparation of, 251-252
255-256
injectlon of concentrated
solution, 252
measurement reach, selection
Of, 251
sampling by conductance meter,
252-255
sodium dichromate
240-246 dilution, 212,249-250
Volume 1, p. l-284
Volume 2, p. 285-631

Discharge measurements by timing
drift, 170,261-262
Discharge measurements by tracer
dilution, constant-rate
Injection,
advantages of, 212,219,237
concentration-time curve,
213,214
fluorescent dye, use of, 223-
248
sodium dlchromate, use of,
249-250
theory, 212,213
dilution, general,
calibration of measurement
reach, 220-222
inflow or outflow, effect of,
222-223
loss of tracer, 216,239
mixing lenqth, 217-219
mixing of tracer in reach,
216-219
percentage of mixing, 219-220
tracer criteria, 211-212
turbidity, effect on, 215-216
when used, 212
dilution, sudden
injection,
advantages of, 212
concentration-time curve, 214-
215
radioactive tcacecs, use of,
212.256-258
salt, use of, 212.250-256
theory, 212-213,214-215
-S_e_e also Dye-ln]ection
apparatus, fluorescent
dye, fluorometer
Discharge measurements, types
of,
current-meter (conventional)
method, 79-183
float method, 261-262
moving-boat method, 183-211
peak discharge, indirect
methods Ear, 273-284
portable Parshall flume
method, 265-267
portable-weir method, 263-265
tracer-dilution method, 211-
259
unstable flow, method for,
268-272
volumetric method, 262-263
Discharge rating for hydraulic
facilities. 486-543
-S- ee also Stageidischarge
relation
Discharge-record, daily,
digital-recorder statlon,
automated-computation sequence
for, 592-597
computation-progress form for,
597,599-600
general procedure for, 587
input to computer for, 588,589
output from computer for,
588,590-592
statlon-analysis document
for, 597,599
Discharge record, daily,
estimates for
periods oE indeterminate
stage-discharge relation,
572-573
periods of no gage-height
record, 573-579
graphic-recorder statlon,
computation form for, 569-
571,579-580
computation method for, 571-
572
computation procedure Ear 3-
parameter discharge rela-tlon,
586-587
computation-progress Eorm for,
580
station-analysis document for,
580-585
tabulation form for, 570
nonrecording station, 559-
560
Discharge records, daily,
hydrographic comparison
of. 572-573.575-576
Discharge relation, thcee-parameter,
558-559,586
Drift, dischacge measurement by
timing, 261-262
Dry-line soundrng correction for
vertical angles, 159-
162,163,166-168
Dye
See Fluorescent dye
Dye-in]ection apparatus,
floating siphon, 233-234
Mariotte vessel, 232-233
pressure tank, 234-235
E
Earth Resources Technology
Satellite (ERTS). 57-59
Electric heaters.in stilling
wells, 48
Electric-tape gage,
affecting, 66-67
description of, 28,30
Electromaqnetic velocitv meter
for;
open channels, 528
-s-e e also Velocity index,
electromaqnetic meter
pressure cond;its, 528
Equipment assemblies for
current-meter discharge
measurements,
boat equipment, conventional,
120-123
bridge equipment, 117-120
Volume 1, p. l-284
Volume 2, p. 285-631

cableway equipment, 110-117
ice equipment, 124-129
moving-boat equipment, 187-197
velocity-azimuth-depth
assembly, 129-130
F
Fall, 393,394-395
Fall-rating method
See Stage-fall-discharge
relation
Float measurement of velocity,
260-262
accuracy of, 262
Float-operated stage recorder,
effect on accuracy of,
counterweight submergence, 69-
7.-"
float lag, 68-69
line shift. 69
temperature change, 70
Float sensor, description of, 32
Float-tape gage,
affectinq. 65-66
description of, 26.28
Flood routing, 344
Flood wave, velocity of, 415
Flume,
choice of, 17-20
design of, 21-22
types of, 13,312-314
use of for a control, 12-13
Flume, crltlcal-flow, choice of,
20
See also Parshall flume
Flume, portable, 265-267
Flume eatlngs, shifts in, 351-
352
Flume, supercritical-flow type,
choice of, 20
ratings for, 322-326
Fluorescence, defined, 223
Fluorescent dye,
calibration of standard
solutions of, 228-230
characteristics of, 223
Fluorescein, 223
quantity for constant-rate
injection of, 235-236
quantity for sudden injection
of, 236-237
Rhodamine B, 223
Rhodamlne BA, 223
RhodamIne WT, 223
sensitlvlty of measurement of,
212,223
storage of, 230
-S- ee also Discharge measure-ments
by tracer dilution,
constant-rate injection
Fluorometer, 212,223-232
background samples for, 231,
240-241
calibration characteristics
Of, 226-228
effect of temperature changes
226-228,240
flelz";se of, 225-226
operation of, 231-232
precautions in use of, 229,
231-232,238,239-240
Frazil ice, 360-361
Froude number, 549
G
Gage
See Stage gage
GaFdatum
See Datum
Gage height,
definition of, 22-23
documentation of record, 583
indicator of minimum, 61
Indicator of -p eak. 39.60-61
mean for discharge measure-ment,
170-173
discharge measurements.
mean gage height of
zero flow, 23,146,291,333-334,
549
Gage-height record, digital
recorder. 588-592
Gage-height record, graphic
recorder,
569
determination of dally mean
gage height from, 564
gage-height correctlons for,
563-564
subdIvIsion of dally gage
heights from, 564-569
time corrections for, 560-562
Gage-height record, nonrecordlng
station, 24-25
560
Gage-height record, uses of, 23
Gage well
See Stilling well
Gaqlnq cars
&-Cable cars
Gaging statlon
&es Stream-gaging station
Gates,
bear trap, 509,511-512
discharge rating of, 536-538
drum, 488-496
flashboards, 512-513
hinged-leaf, 509,511-512
needles, 514
radial,
on curved dam crest or
still. , 496.499-507
on horizontal surface, 496-
499
roller, 508
stop logs, 514
Talnter (See radial)
Volume 1, p. l-284
Volume 2, p. 285-631

vertical-lift, 507-508
wickets, 509-510.511-512
Geiaer counter. 258
Gibson method,.533-536
Graphic stage recorder, 39-41
servlclng of, 59-60,63
-S_e_e also Stage gage, recording
H
Handline, sounding,
description of, 104,106-108
use of, 150-151
Haskell current meter, 88,t?9
Headphones for counting meter
revolutions, 130
Heaters for stilling wells, 48
High-water marks,
at crest-stage gage, 77-70
at stream-gaging statlons, 60-
61
Hoff current meter, 88,89
Horizontal-axis current meters,
88-90
Horizontal-axis deflectior vane,
435-437
Hydraulic facilities
dams with gates, 486-514
navigation locks, 514-515
Hydroelectric powerplants,
discharge measurements below,
140
discharge ratings for, 536-
538
Hvdroqraphlc comparison of dailv
.dl&.charge iecords,
572,575-576
I
Ice, consideration of, in
gaging-statlon site
selectlo", 8
Ice, discharge measurement from,
151-155
Ice, effect on shifts, 553-554
Ice, effect on stream hydraulics
descrlptlon of, 360
Erom anchor ice, 361
Erom frazil, 361
Erom surface Ice, 363-364
Ice, formatlo"
of anchor Ice, 361
of frazll, 360-361
of surface ice, 362-363
ICC! cover, effect on tracer
mixing, 216
Ice creepers, 131
Ice effect, discharge compu-tations
for periods of,
anchor ice, 364-366
discharge-rat10 method, 368-
369
hydrographic- and climatic-comparison
method,
368,370-375
proposed method, 375-376
shifting-control method,
368,369-370
surface ice, 366-376
Ice equipment,
ice chisel, 125
ice drill, 124-125
ice-measuring stick, 125-128
reel support, collapsible, 128
weight assembly, 128-129
-s-e e also current-meter
from Ice cover
Ice in measurement section,
effect on accuracy, 180
Inclined stafE gage, 26.64
Indirect determination of peak
discharge, 2,273-284
-S- ee also Peak discharge, lndlrect determination of
Inflatable dams, 510
Instrument shelters for stage
recorders, 51-52
Intakes for stiiling wells,
drawdown at, 47
flushing system for, 44,50
lag of, 45-47,60
location of, 8, 43-44
static tubes for, 47,50
J
Jones method, 416
L
Laboratory rating of controls,
16-17,21,260
Laser flowmeter, 529
Leveling, checking of gages by,
545-546
Lewis method, 416
Locks, navigation,
leakaae throuah. 515-520
lockage discharge, 514-515
Logarithmic plotting, 289-294
Loop rating curve
for rlgld-boundary channels,
390,413-414
for sand channels, 378-379
M
Manning equation. 274-277,
329,342
Marlotte vessel, 232-233
Maximum-stage indicator, 39,60-
61
Measurement section, selection
of, 7,139-140,149,151-153
Mechanical meters. 521-522
Meters, pipe,
bend, 526-527
Volume 1, p. l-284
Volume 2, p. 285-631

displacement, 521
flow-nozzle, 525-526
inferential, 521-522
orifice, 526
unaltered-conduit, 527
variable-area, 522
venturi. 522-525
Minimum-stage indicator, 61
Model T stage recorder, 74-75
Motion of current meter, effect
of, 180-181
Moving-boat discharge-measurement
method
See Discharge measurement,
movlnq-boat method
Moving-boat-equipment assembly,
187-197
N
Neyprlc current meter, 88-90
NonrecordIng gage
gee Stage gage, nonrecording
0
Observer for gaging statlon, 24-
25
Oil for prevention of freezing
In,
bubble-gage vent pipe, 33-34
stilling wells, 48,51,60,66-67
Open-water discharge, 368
Optical current meter
See Current meter, optical
Ott current meter, 88-90
Orifice flow
free, 501-503
submerged, 503-505
Piers in discharge-measurement
section, 82,149-150,179
Pipe meters
See Meters, pipe
See pressure-conduit meterlng
Pltometer, 529-532
Pltot-static tube, 529-532
Portable flume, 265-267
Portable weir, 263-265
Pressure-conduit metering by,
acoustic-velocity meter, 528-
529
dlfferentlal-head meter, 522-
528
electromagnetic-velocity
meter, 528
laser flowmeter, 529
mechanical meters, 521-522
-S- ee also Meters, pipe
Pressure-conduit meter rating
by,
Gibson method, 533-536
pitometer, 529-532
pltot-static tube, 529-532
salt-velocity method, 533
Price current meter,
pygmy. 86-88,143-145
standard, 85-90,143-145
Protractor, measurement of cable
anc~ll e. 118-119
PublIshed reports
See Annual publlshed reports
Pulsating flow
See Unstable flow
Pulsations, horizontal, during
84-85
Pulsations, vertical, in holes
cut through ice, 153,155
Pumps, discharge rating of, 536-
537
Pygmy current meter, 86.87-88,
143-145
P
R
Palmer-Bowlus flume, 538
Parshall flume,
portable, 260,265-267
standard,
ratlnas for. 316-317
PartiaL-record statlons, purpose
of, 3
Peak discharge, IndIrect
determination of,
bend-superelevatlon method,
218,283
contracted-opening method,
277-279
culvert-dlscharqe method, 279-
281,282
dam-discharae method. 279
factors in,.273-274
field data for, 274
slope-area method, 274-277
weir-discharae method. 279
Peak-runoff comparison, 337-338
Peak-stage lndlcator, 39,60-61
Radial gate flow-over, 506
RadIoactIve tracers, 212,256-258
See also Discharge measure-ments
by radioactive
tracer dilution
Rating
See Stage-discharge relation
Rating curve,
analvsls of. 550-555
extrapoLati& of, 332-344
graphical plotting of, 287-294
"e" vaLue determlnatlon.
289-293
preparation of, 549-550,559
Rating-fall method
See Stage-fall-discharge
relation
Rating table,
exDanded. 557
preparation of, 555-559
standard, 556
VoLume 1, p. l-284
Volume 2, p. 285-631

Recording stage gage
See Stage gage, recording
Rectangular-coordinate plotting,
294,333-334
Ret?!1
for soundlnq line, 102-104
for width-measurement tag
line. 110.111.120-121
Reference gage. 53-54
inside gage, 53
outside gage, 53
-S_e_e also Base gage
Reference mark. 24.54
Reference point, 54
Relative concentration, 228
Reversal errors, for graphic
recorders, 563
Roll waves
See Unstable flow
Roller Clates, 508
Roughness coefficient, selection
of, 214,342,341,549
S
Salt (N&l), 212,237,250
See also Discharge measure-ments
by salt dilution
Salt-velocity measurement I"
pressure conduits, 533
Sand-channel streams,
bed conflguratlons for, 377-
379
depth-discharge relation for,
379-382
evidence of bed forms in, 384-
385
flow regime of, 377-379
sites for gaging stations on,
377
stage-discharge relation for,
376-377,382-384,385-387
Sand-channel streams, currer.t-meter
measurements of,
observation of configuration
of streambed and water
surface, 146
position of stream gager, 146
Sand-channel streams, gaging
stations on,
artlflclal controls for, 22,
387-388
sites for, 6,377
"se of bubble gage for, 33-34
Satellite data-collection
system, 57-59
Scintillation counter, 258
Section control
See Co"trols, sectlo"
Section-control ratings
See Stage-discharge relation,
artificial controls
See Stage-discharge relation,
natural co"trols
See Shifting control
S&L principle af wave
velocity, 415
Sediment, l"clus1o" of, I"
measured discharge, 273-
274
Sediment concentration, effect
on,
acoustic-velocity meterlng,
456-457
sand-bed configuration, 377-
378
Sediment trap for stilling well,
51
Sedimentation effect on,
channel-control ratings, 354-
359
flume ratings, 351-352
natural section-control
ratings, 352
weir ratings, 348-350
Servo control, 32
Servomanometer, 32
Sewer flowmeter,
USGS-type, 538-541
wenze1. 541-542
Shiftlng'control, 344-345
channel-control ratings, 354-
360,385-387
detection of rating shifts,
345-348
ratinas. 352-353
sand-channel ratings, 385-387
stage-fall-discharge ratings,
422-423
Shifts, application to rating
C"r"BS, 553-554
Slope-area determination of peak
discharge, 274-277
Slope stations, 390-412
criteria for establishment,
390-391
proposed analysis method, 423-
425
theoretical considerations,
391-392
variation from true slope,
394-395
-S_e_e also Stage-fall-discharge
relation
Sl"4 flow
7S ee Unstable flow Sodium dlchromate, 212,249-250
Sonic sounder, 108-110,193-195,
200-201
Sounding equipment,
handline, 104,106-108,150-151
reel. 102-104
sonic sounder, 108-110,193-
195.200-201
wading rod, 97-101
weights and accessories, lOl-
102
Sounding weights
See Weights, sounding
SR stage recorder, 76-77
Staff gage,
as auxiliary gage, 53
Volume 1, p. l-284
Volume 2, p. 285-631

Staff gage, vertical and
inclined,
affecting, 64
Stage, deflnltion of, 22
See also Gage height
Stage-discharge relation.
defined, 79
required, 285
extraoolation of hiclh flow.
2i5-286,334-344-
by conveyance-slope method,
334-337
by flood routing, 344
by peak-runoff comparlso",
337-338
by step-backwater method,
338-344
extrapolation 0E low flow,
333-334
graphical analysis, 287-294
See also Ice effect
-S- ee also Logarithmic plotting
_S-e e also Rectangular-coordinate
plotting
Stage-discharge relation,
artificial controls
flumes, 294-295,312-314
-S~e e also Flume,
supercritical-flow type
See also Parshall flume
general description of, 2&6-
287
transferrablllty of laboratory
ratings, 295
weirs. broad-crested, 295,306-
307
-S- ee also Columbus-type
control
See also Crump weir
_S-e e also Trenton-type
control
-S~e e also Weir, rectangular
flat-crested
-S_e_e also Weir, rectangular
flat-crested. notched
weirs, thin-plate, 294-306
-S_e_e also weir, rectangular
thin-elate
-S7e e also Weir, submerged thin-plate
-S- ee also Weir, trapezoidal
thin-plate
-S~e e also Weir, triangular
thin-plate
Stage-discharge relation,
natural controls,
channel control, 328-332,382-
384,385-387
general descrlptlo" of, 286-
287
section control, complete,
326-327
section control, compound,
327-328
_S-e e also Shifting control
Stage-discharge relation, sand
channels, 376-377,382-
384,385-387
Stage-discharge relation, shifts
in
See Shifting control
Stage-discharge relation, tidal
streams
See Tidal streams, discharge
catlng of
Stage-fall-discharge relation,
392-413,479
discharge determination from,
412-413
intermittence of, 396,402,405-
408
rating fall constant, 396-400
rating fall variable, 400-412
shift in rating, 422-423
types of, 395-396
variable backwater combined
with changing discharge,
421-422
variable slope caused by
changing discharge, 413-
421
variable slope caused by
variable backwater, 392-
396
-S- ee also Slope stations
Stage gage, "onrecordlng,
advantaqes of. 23
reports-of readings of. 24-
types of,
chain, 31-32
electric tape, 28-30
float tape, 26.29
staff, 26,27
wire weight, 26.28
25
Stage gage, recording,
advantages of, 23
instrument shelters for, 51-52
intakes for, 43-47
See also Intakes for
stilling wells
model T, 74-75
SR model, 76-77
types of recorder,
digital, 36-39
graphic, 39-41
types of sensor,
bubble gage, 32-34
_S-e e also Bubble-gage stage
recorder
float, 32
-S_e_e also Float-operated
stage recorder
Stage-velocity-discharge
relation,
acoustic velocity-meter
method, 439-459
deflectlon-meter method, 432-
439
electromagnetic velocity-meter
method, 459-469
standard current-meter method,
430-432
velocity Index, types of, 429-
430
Volume 1, p. l-284
Volume 2, p. 285-631

Static tubes for Intakes, 47,50
Statlon analysis, 544-559
documentation of, 580-588,
597,599
Step-backwater method, 338-344
Stillina well.
auxiliary and reference gages
for, 51,53-54,287
dimensions of, 42
intakes for, 43-47
prevention of freezing in, 47-
48,51
sediment trap for, 51
types Of, 41
StopLatch for discharge measure-ments,
130
Storage corrections for dis-charge
measurements, 177-
179
Storm-drain metering
See Urban storm-drain metering
Streamflow, defined
See Discharge, defined
streamflow records,
general, 2-3
processing,
by digital computer, 2
of digital stage record,
544-559,587-600
of graphic stage record,
544-559.560-587
oE nonrecordlng stage
record, 544-558,559-560,
569-587
Stream gaging, sand channels
See Sand-channel streams,
current-meter measurements
See Sand-channel streams,
gaaina stations on
streakgaging procedures,
general, 3-4
Stream-gaging statlons,
nonrecording, 24
recording, 32,59-79
Stream-gaging station location,
field reconnaissance, 6
general site selection, 4-5
specific site selection, 4-
9,12
Stream-gaging station network,
design oE, 4
purpose of, 3
Stream-gaging station operation,
determination of peak stages,
60-61
frequency of Vlslts, 59
inspectlon and servicing
equipment and stage
record, 59-60,61-63
maintenance operations, 63
observer, 25
Strip-chart, 59-60
See also Graphic stage
recorder
Subfloors in stilling wells, 47-
49
Submerged broad-crested weirs,
312
Submerged thin plate weirs, 305
306
T
Tag lines (width measurement),
110.120-121
reels, 110
Tags on sounding line, use of,
107,147-148,150,160,163
Telemark, 55-56
Telemetering, 23,54-59
impulse system of, 55
position-motor system of, 55
resistance-system of, 57
satellite data-collectlon
system of, 57-59
Telemark system of, 55-56
Temperature effect on,
acoustic-velocity metering,
454
current-meter measurement
accuracy, 180
float-operated stage
recorder, 70
Eluorometer analysis,
226.227.240
sand-bed conflguratlon, 378
Tidal streams, discharge rating
of,
calibration of relation, 471
empirical methods, 475-484
unsteady-flow equation
methods, 471-475
variable control, 392
velocity-Index method, 471
Tidal streams, methods for
computing discharge, 2
Tide-correction method, 479-481
Timers for stage recorders,
34,37-39,59-60,473
Timing drift, discharge measure-ment
by, 261-262
Tracer dilution,
concentration, 228
relative concentration, 228
Tracer dilution, measurement of
discharge by
See Discharge measurements by
tracer dilution
Tracers
See Fluorescent dye
See Radioactive tracers
m Salt
See Sodium dichromate
Trenton-type control, 311-312
Turbines, -bischarge rating of,
536-537
Turbulence, 84-85
u
Unit rating-fall method, 396-400
Unstable flow,
description of, 260,268-269
examples of, 270-272
volume 1, p. l-284
Volume 2, p. 285-631

method of discharge deter
mlnatlon during, 269-270
proposed instrumentation for
measurement of, 272
Unsteady flow,
effect on stage-discharge
relation, 390,413-428
loop rating curve of, 413-414
rating-adjustment methods for,
416-421
Bayer method, 416-418
Jones method, 416
Lewis method, 416
Wiggins method, 418-421
theoretical considerations,
414-416
Unsteady flow combined with
variable backwater, 421-
422
Unsteady-flow equations, method
of solution,
characteristics method, 474-
475
Fourier series, 475
implicit method, 475
power series, 473-474
Urban storm-drain metering by,
538-542
USGS sewer flowmeter, 539-
541
Wenzel asymmetrical flow-meter,
541-542
Wenzel symmetrical flow-meter,
541-542
V
Valves, discharge rating of,
536-538
Vane current meter, 86-87.154
Variable backwater,
discharge determination, 412-
413
effect on stage-discharge
relation, 390,392-413
Influence on stage-gage
location, 7-8
rating fall, constant, 396-400
rating fall, variable, 400-412
Variable backwater combined with
changing discharge, 421-
422
Variable rating-fall method,
400-412
Variable slope, 390
-S- ee also Variable backwater Vegetation, effect on,
acoustic-velocity metering,
457,459
channel-control ratings,
359-360
ratings, 353
Velocity, wave, 415
Velocity area method of dls
charge determination, 334
Velocity-azimuth-depth assembly,
129-130
Velocity distribution I" a
vertical
under ice cover, 154-155
in own water. 132-133
Velociiy Index,' acoustic meter,
description, 439-441
effect of orientation on, 448-
454
effect of tidal-flow reversal
on, 448
factors affecting operation
Of, 454-459
in pressure conduits, 528-529
theory, 441-448
use of for tidal streams, 471
Velocity index, deflection
meter,
examples of use of, 437-
439,471
horizontal-axis vane, 435-437
locatlon of, 432
vertical-axls van$j,432-435
Velocity index, electromagnetic
meter,
Integrated-velocity Index,
a!xxsisal of method. 468
instrumentation, 465-468
theory of, 464-465
point-velocity index,
analysis of data, 461-464
instrumentation, 460-461
use of for tidal streams, 471
Velocity-Index, standard current
meter,
discharge relation, call-bration
of, 430-431
location of, 430
operation of, 430,432
Velocity measurement, mean in a
vertical by,
five-point method, 138
integration method, 138
six-point method, 138-139
six-tenths depth method,
134-135,174,175
subsurface-velocity method,
108,136-137,169,174,208-
211
surface-velocity method,
137-138,175
three-point method, 135
two-Doint method. 134
two-tenths depth method,
108,135-136,169,174,175
vertical-velocity curve
method, 132-133
Velocity near vertical wall,
82.87.137-138
Velocity'puisations, 84-85
Venturi flume
See Parshall flume
Venturi meter. 522-525
Vertical-axis'current meter
See Current meter, vertical
axis
Volume 1, p. l-284
Volume 2, p. 285-631

Vertical-axis deflectlo" vane,
432-435
v-rtical lift gates, 507-508
'vertical staff gage, 26,27,64
vert1ca1 ve1oc1ty curve, 133
Verticals, spacing of, I"
measurements, 140,149,
153,174,175
Volumetric measurement of
discharge, 260,262-263
w
Wading measurement of discharge
see Current-meter discharge
measurements by wading
Wading rod,
Ice, 100-101
round, 97,99,100
top-setting, 97,98
Water-stage recorder
See Stage gage, recording
Water year, 544
wave velocity, 415
Weights, sounding,
hancrers for, 102
hanger plns'for, 102
Weir, rectangular flat-crested,
307-308
notched, 309-311
WelK, rectanqular thin-plate,
graphical rating analysis of,
299
theoretical ratinq analysis
of, 295-299
Weir, trapezoidal thin-elate.
299:302-303
.
Weir, triangular or V-notch
thin-plate, 303-305
-S_e_e also Columbus-type control
-S- ee also Trenton-type control
Weirs,
broadcrested, 12
submerged, 312
choice between flumes and, la-
20
computations of peak discharge
over, 279
design oi, 21-22
thin-plate, 12-13
submerged, 305-306
weir flow
free, SOS-506
submerged, 506
Weir plate, portable, 260,263-
265
ratings. shifts in, 348-351
Wenzel flowmeter, 541-542
Wet-line sounding correction for
vertical angles, 159,160,
163-168
Width-measuring equipment, 110
WiggIns method, 418-421
Wind effect on,
chain-gage readings, 68
measurements, 180-181
staff-gage readings, 64
wire-weight gage readings,
65
Wire-weight gage,
affecting, 64-65
as auxiliary gage, 53
2
zero flow, 23,146,291-292,333-
334,549-550
Volume 1, p. l-284
Volume 2, p. 285-631

Water Supply Paper 2175, Vol. I, Table 8 on page 165 should be
replaced by the following table:
- -- -_ - -_ - -- .-
FPsr-
“$
3
: :
:: ” ,: .:;, :
,,‘, j: : :
_ -. -.-_- ~- . . -- - --- - -

c .
Water Supply Paper 2175, Vol. I, Table 6 on page 162 should be
replaced by the following table:

Measurement and Computation of Streamflow: Volume 1 Measurement of Stage and DischargePaper 2175 1982

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Measurement and Computation of Streamflow: Volume 1 Measurement of Stage and DischargePaper 2175 1982