Effect of staggered roughness elements on flow characteristics in rectangular channel

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 03 Issue: 08 | Aug-2014, Available @ http://www.ijret.org 359
EFFECT OF STAGGERED ROUGHNESS ELEMENTS ON FLOW
CHARACTERISTICS IN RECTANGULAR CHANNEL
Elnikhely E.A1
1
Lecturer, Water and Water Str. Eng. Dep., Faculty of Engineering, Zagazig University, Zagazig University, Zagazig,
Egypt
Abstract
Flow characteristics are measured experimentally on an artificially roughened bed in a horizontal flume. The pattern; of
roughness are staggered arrangements. The water surface profile is recorded at different sections. This paper investigated the
effects of using fiberglass sheets as roughness elements for staggered arrangement, on different flow characteristics. Compared to
the smooth bed, it is observed that the roughness bed decreases the relative jump depth by 22%, increases the relative energy loss
by 14%, and reduces the relative jump length by 8.1%. The experimental results achieved promising results regarding each of
dissipating energy; the relative jump length as well as the relative jump depth in addition to the coefficient of discharge. The
derived formulas for relative depth and the relative energy loss that satisfactorily agree with the experimental data are proposed.
Prediction equations were developed using the multiple linear regression (MLR) to model the hydraulic jump characteristics.
Keywords: Experimental, Theoretical, Flow characteristics, Bed roughness
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1. INTRODUCTION
Hydraulic jump is one subject which has extensively been
studied in the field of hydraulic engineering. It is an
intriguing and interesting phenomenon. The cost of the basin
which confines the whole length of free jump is very high.
As a result, roughness elements were usually installed in the
basin itself to reduce the jump length and to increase the
energy loss by increasing turbulence. It may play as
damping members for the jump. Characteristics of flow
under the effect of roughness were investigated by several
theoretical and experimental models include Rajaratnam
(1964), Pillai and Unny (1964), Rajaratnam (1968),
Leutheusser and Schiller (1975), Peterka (1978), Ranga
Raju (1980), Hughes and Flack (1984), and Abdelsalam et
al. (1986), Mohamed Ali (1991) and Negm et al. (1993).
Alhamid (1994) investigated experimentally different
hydraulic jump characteristics formed on an artificially
roughened bed. It was concluded that 12% roughness
density provides the optimal length of basin for the flow
conditions. Ead and Rajaratnam (2002) indicated that the
length of jumps on corrugated beds is less than its length
over smooth one. Evcimen (2005) determined the effect of
different roughness types and arrangements on hydraulic
jump characteristics in a rectangular channel. The bed
friction effect on the stability of a stationary hydraulic jump
was investigated by Defina and Susin(2008) in a rectangular
upward sloping channel through a combined theoretical and
experimental approach. A numerical scheme provided by
turbulence models was used by Abbaspour et al (2009) to
predict the 2-D water surface location, flow velocity
distribution, and the bed shear stress for jump on a
corrugated bed. Elsebaie and Shabayek (2010) studied the
effect of different shapes of corrugated beds on the
characteristics of hydraulic jumps for all shapes of
corrugated beds, they found that the length of the jump on
the different corrugated beds was less than half of that on
smooth beds and the integrated bed shear stress on the
corrugated beds was more than 15 times that on smooth
beds. The jump upon four adverse slopes in two cases of
rough and smooth bed was examined by Nikmehr and
Tabebordbar (2010). The results showed that the sequent
depth ratio and the length of jump upon smooth bed has
been more than rough bed for the same slopes and Froude
numbers. Tokyay et al. (2011) found that the roughness
elements considerably reduce the sequent depth and length
of the hydraulic jump. AboulAtta et al. (2011) used T-shape
roughness instead of the regular cubic one. They found that
the T-shape roughness save materials and reduce the
jumplength compared to the cubic one. Ezizah et al. (2012)
tested a new roughness shape (U-shap). Sun and Ellayn
(2012) found that the staggered roughness is more efficient
than strip roughness. Esfahani and Bejestan (2012) found
that the roughening bed of stilling basin can reduce the jump
length by about 40%. Thus the present study investigates
experimentally the effect of staggered sheets as roughness
elements on flow characteristics. The water surface profile is
recorded at different sections. Habib and Nassar (2013)
found that the apron of 90% staggered roughness length
increases the relative energy loss by 17%.
2. EXPERIMENTAL SETUP
Experiments were carried out in the Hydraulics Laboratory
of the Faculty of Engineering, Zagazig University, Egypt. It
was accompanied in a flume of 0.30 m wide, 0.50 m deep
with an overall length of about 12.0 m. The discharges were
measured using a pre-calibrated orifice meter fixed in the
main flow line. The tailgate was fixed at the end of the
experimental part of the flume which used to control the
tail-water depth. The water depths were measured by means
of point gauges. Figure (1) presents a typical arrangement of

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the staggered roughened bed to show the distribution of the
roughness element over the channel bed. The experimental
program is summarized in table (1), it is including two
stages. Stage I can be described as the base case. It includes
the case of smooth bed without any modifications. It
included about 39 experimental runs. Stage II explores the
effect of the staggered roughened elements on the flow
characteristics for different variable depths, (Hr=0.5, 0.75,
1.0, and 1.5 cm). It included about 24 experimental runs.
The test procedure consisted of the following steps:
The discharge and desired gate opening were set; the
position of the jump was adjusted; the flow rate and the
water surface profile were recorded; the length of jump, Lj,
was measured in each case. The Froude number ranges
between 3.3 and 8.6.
Fig 1: Schematic diagram of the experimental model
Table 1: Scheme of experimental work stages
3. THEORETICAL APPROACH
3.1 Dimensional Analysis
The flow field downstream of a roughened apron (bed with
staggered sheets) DS of the sluice gate depends on a large
number of flow variables as shown in figure (1). A
dimensional analysis is applied to correlate the different
variables affecting phenomena under study and the
following functional relationship is obtained:






 1
11
2
, F
y
H
f
y
y r
………………………….(1)






 1
11
, F
y
H
f
y
L rj
………………………..…(2)
And








1
11
, F
y
H
f
E
E r
…………………………(3)







G
H
y
H
fC r
d ,
1
…………………………..(4)
Stage Description Characteristics
Hman Hr G
(mm) (cm) (cm)
I (39 runs) The smooth case 40 2.1
35 0 2.3
30 2.6
25 3.0
3.3
3.5
II (24 runs) The effect of the depth of the staggered roughness elements 40 0.5 2.1
40 0.75 2.3
40 1.0 2.6
40 1.5 3.0
40 3.3
40 3.5

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in which 12 yy is the relative jump depth; 1yHr is the
relative depth of the roughened element; 1F is the initial
Froude number ;
5.0
111 )gy(vF  ; 1j yL
is the relative
length of the free jump; 1EE is the relative energy loss
through the free jump, and 𝐶𝑑 is the coefficient of discharge.
3.2 The Relative Depth of Jump (y2/y1)
Both the 1-D momentum and continuity equations are used to
develop a theoretical design model for computing the relative
depth ratio. The approach involves the following assumptions:
the flow is steady, the liquid is incompressible, and the
pressure distribution is hydrostatic at the beginning and at the
end of jump.
Also, the velocity distribution at the beginning and the end
of the jump is uniform. The turbulence effect and the air
entrainment are neglected. Actually, the main assumption of
the theoretical model is that it deals with the projection of
roughness elements. By applying the pressure-momentum
relationship in the longitudinal direction one gets (see
Fig.1):-
)VV(QF 2211  ……………………(5)
)VV(PPP 22111rough.2 

QQ
g
 ……..(6)
Where:
2
22 5.0P By ....................................................(7)
2
11 5.0P By ……………………….(8)




1
roughP
ni
i
roughr ByH …………….(9)
In which: B :channel width; P2 :hydrostatic pressure just
downstream of the jump; P1 :hydrostatic pressure just
upstream of the jump; Prough: the total hydrostatic pressure
on the roughness elements; y1 :initial depth of the jump;
y2:sequent depth of the jump; roughy : the diference between
water depths US and DS the roughness element; rH : the
height of the roughness element and n is the number of
roughness elements in the lateral direction. Substituting in
equation (6) yields.
)(5.05.0 2211
2
1
1
2
2 vQvQ
g
ByByHBy
ni
i
roughr 

  


…….(10)
For simplification of equation (10), it can be rewritten in the
following form.
)(5.05.0 2211
2
1
2
2 vQvQ
g
ByByHnBy avroughr 

 
…….(11)
In which: avroughy
: the average difference between water
depths upstream and downstream the roughness elements.
Assuming that 1 = 2= 1.0 and applying the continuity
equation between section (1) and section (2):
)/)(/(5.05.0 211111
2
1
2
2 yyvvgyvyyHny avroughr  
…………(12)
Dividing Eq. (12) by
2
15.0 y , Let, rr hyH 1 ,and
rr1avrough yyy 
where : 12 yy :relative depth of jump; hr: relative
roughness element's height; yrr: relative water depth over the
roughness element.
)(1
2V
12)(
2
1
1
2
12
1
2
y
y
gy
ynh
y
y
rrr 
………….(13)
Equ. (13) can be written as:
)1(212)(
2
12
1
2
1
2
y
y
Fynh
y
y
rrr 
………………………...(14)
3.3. Energy Approach
The energy loss can be obtained by applying the energy
equation as follows:
21 EEE  ……………………(15)
Where 1E is the specific energy just upstream the free
jump, (i.e., gVyE 2
2
1111  ) and 2E is the specific
energy downstream the free jump (i.e.,
gVyE 2
2
2222  ), 1 is the energy coefficient at
beginning of the jump and 2 is the energy coefficient at end
of the jump. Assuming that; 1 = 2= 1.0.

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 )21()2(1
2
2
11
1
2
11
2
212
2
11
2
22
1
2
1
gyVgyVyy
gVy
gVy
E
E
E
E






………(16)

















2
1
)(2
1
2
1
2
1
2
1
2
1
2
2
1
1
2
2
1
1
2
2
22
1
2
1
2
1
2
1
F
y
y
F
y
y
F
gyyBVyB
y
y
E
E
…………………………(17)








)
2
1/()(
2
1
)(1
2
12
2
12
1
1
2
1
F
y
y
F
y
y
E
E
…………………………(18)
4. VERIFICATION OF THE DEVELOPED
EQUATIONS
Experimental data are used to evaluate the developed
equations, (Eqs. 14 and 18). Figures 2a and 2b show the
relationship between the theoretical results and the measured
experimental data. It can be said that the developed
equations prove an acceptable agreement as compared to the
observations (R2
= 0.91, 0.96) respectively.
2(a)
2
4
6
8
10
2 4 6 8 10
F1Theo.
F1 Exp.

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2(b)
Fig 2: Relationship between developed equations and experimental measurements (a) 1F model Eq. (14) (b) 1EE model Eq.
(18)
5. EXPERIMENTAL RESULTS AND
DISCUSSION
5.1 Effect of the Relative Depth of the Staggered
Roughened Elements
There is an interaction between the flow body and the
roughness elements. This interaction depends upon three
parameters, which can be listed as follows: 1- the flow
velocity, 2- projection area of the roughness elements and 3-
the percentage of the flow which can be reflected in the
adverse direction by the roughness elements. The relations
between the initial Froude number; 1F and each of the
relative jump depth y2/y1; the relative jump length Lj/y1 and
the relative energy loss 1EE for different roughened
depths (Hr=0.5, 0.75, 1.0, and 1.5cm) are shown in figures
(3a, 3b, and 3c). The figures show also the same relation for
the case of smooth bed. It clears from Fig. (3) that the values
of the relative jump characteristics including y2/y1, Lj/y1,
1EE increase with the increase of the initial F1. The
relative roughened depth (Hr =1.5 cm) gives the minimum
values of y2/y1. It reduces the average values of y2/y1 by
about 22 %. the case of (Hr=1.5 cm) increases the lost
energy in comparison with the smooth case by about 14%,
morever in comparison with the smooth case, it reduces the
values of Lj/y1 by about 8.1%.
Fig. (4) Shows the relation between H/G and the coefficient
of discharge Cd for the different values of Hr. The case of Hr
=0.5 cm gives the maximum values of Cd in comparison
with the smooth case. It increases the average values of Cd
by about 21%.
As seen in the experimental results, the jump characteristics
have been improved as the relative depth of the roughness
elements, Hr increased.
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.3 0.4 0.5 0.6 0.7 0.8 0.9
∆E/E1Theo.
∆E/E1 Exp.

_______________________________________________________________________________________
Fig 3a: Relations between F1 and y2/y1 for different relative staggered roughened depths
Fig 3b: Relations between F1 and Lj/y1 for different relative staggered roughened depths
0
2
4
6
8
10
12
0 2 4 6 8 10
y2/y1
F1
No-roughness
Hr=0.5
Hr=0.75
Hr=1.0
Hr=1.5
0
0.2
0.4
0.6
0.8
0 2 4 6 8 10
ΔE/E1
F1
No-roughness
Hr=0.5
Hr=0.75
Hr=1.0
Hr=1.5

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Fig 3c: Relations between F1 and 1EE for different relative staggered roughened depths
Fig 4: Relations between H/G and Cd for different relative staggered roughened depths
6. STATISTICAL REGRESSION
Using a regression tool, this simplifies the regression tasks
and statistical analysis. The statistical analysis was used to
relate the dependent parameters including y2/y1, Lj/y1;
1EE ; and Cd and other independent ones under the basis
of non-liner regression. the statistical equations (19, 20, 21
and 22) were built to predict the different relative jump
characteristics including the relative jump depth y2/y1, the
relative jump length Lj/y1 and the relative energy loss
1EE for the flow of the studied roughened bed. Figures
(6, 8, 10 and 12) show a comparison between the measured
y2/y1, Lj/y1; 1EE ; and Cd and the predicted ones using
statistical models Equations (19, 20, 21 and 22), respectively
for all experimental measurements. The comparison
indicated an acceptable agreement between the model
prediction and experimental data. R2
= 0.98, 0.99, 0.94 and
0.96, respectively. The residuals of the pervious equations
are plotted versus the predicted values as shown in Figs (7,
9, 11, and 13).
0
10
20
30
40
50
60
0 2 4 6 8 10
Lj/y1
F1
No-roughness
Hr=0.5
Hr=0.75
Hr=1.0
Hr=1.5
0.5
0.6
0.7
0.8
0 5 10 15 20
Cd
H/G
N0-roughness
Hr=0.5
Hr=0.75
Hr=1.0
Hr=1.5

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134.1549.1043.1
1
1
1
2

y
H
F
y
y r
……………(19)
780.8896.3945.5
1
1
1

y
H
F
y
Lj r
…………………..(20)
166.0089.0062.0
1
1
1


y
H
F
E
E r
………….(21)
404.0046.0014.0
1

y
H
G
H
Cd r
…………….(22)
Fig 6 Relation between the measured y2/y1 and the predicted ones
Fig 7 Variations of residuals for different data sets with predicted data Eq. (20)
2
4
6
8
10
2 4 6 8 10
y2/y1Peridected
y2/y1 Exp.
-0.6
-0.4
-0.2
-1 E-15
0.2
0.4
0.6
2 4 6 8 10
Residuals
y2/y1 Perdicted
R2
=0.98

_______________________________________________________________________________________
Fig 8 Relation between the measured Lj/y1 and the predicted ones
Fig 10 Relation between the measured ∆E/E1 and the predicted ones
10
15
20
25
30
35
40
10 20 30 40
Lj/L1Perdicted
Lj/L1 Exp.
-2
-1
0
1
2
0 10 20 30 40 50
Residuals
Lj/L1 Perdicted
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.3 0.5 0.7 0.9
ΔE/E1perdicted
ΔE/E1 Exp.
R2
=0.99
R2
=0.94

_______________________________________________________________________________________
Fig 12 Relation between the measured Cd and the predicted ones
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.2 0.4 0.6 0.8 1
Residuals
ΔE/E1 Perdicted
0.6
0.7
0.8
0.9
1
0.6 0.7 0.8 0.9 1
CdPredicted
Cd Exp.
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.6 0.7 0.8 0.9 1
Residuals
Cd Perdicted
R2
=0.96

_______________________________________________________________________________________
7. CONCLUSIONS
The experimental work was accompanied to study the
characteristics of flow under the effect of staggered
roughness elements with different variable depths. To
improve the efficiency of the hydraulic jump
characteristics, a new roughness shape was tested in the
present study. It investigated the effect of the depth of the
roughness elements on the Flow characteristics in a
rectangular flume. The following conclusions can be listed.
 The case of staggered roughness elements of
roughened depth (Hr=1.5 cm) achieves minimum
values of y2/y1, reducing the average relative depth
of the jump by 22% in comparison with the case of
the smooth bed,
 It gives also the minimum values of the relative
jump length Lj/y1, reducing the average relative
length of the jump by 8.1% in comparison with the
smooth bed,
 In addition, it gives the maximum values of the
relative energy loss ∆E/E1, increasing the average
relative energy loss of the jump by 14%.
 The case of staggered roughness elements of
roughened depth (Hr=0.5 cm) increases the
coefficient of discharge Cd by 21%.
 The developed theoretical equations prove an
acceptable agreement as compared to the
experimental results.
 Prediction equations were developed using the
multiple linear regression (MLR) to model the H.J.
characteristics and an acceptable agreement was
obtained between the predicted and the measured
values.
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Elements as bed Roughness on Hydraulic Jump

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Effect of staggered roughness elements on flow characteristics in rectangular channel

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Effect of staggered roughness elements on flow characteristics in rectangular channel