Transient free surface flows in building drainage systems 1st Edition Swaffield
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- 5. Transient free surface flows in building drainage systems 1st Edition Swaffield Digital Instant Download Author(s): Swaffield, J. A ISBN(s): 9780415589154, 0415589150 Edition: 1 File Details: PDF, 6.37 MB Year: 2015 Language: english
- 7. Transient Free Surface Flows in Building Drainage Systems Climate change will present a series of challenges to engineers concerned with the provision of both building internal appliance drainage networks and rainwater sys- tems within the building boundary, generally identified as the connection to the sewer network. Climate change is now recognised as presenting both water shortage and enhanced rainfall design scenarios. In response to predictions about imminent climate change Transient Free Surface Flows in Building Drainage Systems addresses problems such as the reduction in water available to remove waste from buildings, and conversely, the increase in frequency of tropical-type torrential rain. Starting with introductory chapters that explain the theories and principles of solid transport, free surface flows within drainage networks, and attenuating appliance discharge flows, this book allows readers from a variety of backgrounds to fully engage with this crucial subject matter. Later chapters apply these theories to the design of sanitary and rainwater systems. Case studies highlight the applicability of the method in assessing the appropriateness of design approaches. In this unique book, research in modelling for free surface flows at Edinburgh’s Heriot-Watt University is drawn on to provide a highly authoritative, physics-based study of this complex engineering issue. John Swaffield was President of the Chartered Institution of Building Services Engineers for 2008–09, and Emeritus Professor of Building Engineering at Heriot- Watt University, Edinburgh, UK, until he tragically passed away in early 2011. The writing of this book was completed by his colleagues at Heriot-Watt University. Michael Gormley is a Senior Lecturer in Architectural Engineering in the School of the Built Environment at Heriot-Watt University. He has been an active researcher in the field of fluid flow modelling since 2000. His research interests include pressure transient propa- gation and suppression in high rise buildings, water conservation and the modelling and control of infection spread in hospitals. Grant Wright is a Lecturer in Civil Engineering in the School of the Built Environment at Heriot-Watt University. His research interests include fluid flow modelling at multiple scales, ranging from curtilage level drainage systems through to regional scale flood model- ling, as well as the performance of sustainable urban drainage systems and public percep- tion of flooding related issues. Ian McDougall is a Computing Officer in the School of the Built Environment at Heriot-Watt University. He has been responsible for the production and maintenance of drainage-related computer models since 1995. His research specialisms are solid transport in horizontal drains and water conservation.
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- 9. Transient Free Surface Flows in Building Drainage Systems John Swaffield with Michael Gormley, Grant Wright and Ian McDougall
- 10. First published 2015 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 711 Third Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2015 John Swaffield, Michael Gormley, Grant Wright and Ian McDougall The right of John Swaffield, Michael Gormley, Grant Wright and Ian McDougall to be identified as the author of this work has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Swaffield, J. A., 1943– Transient free surface flows in building drainage systems/John Swaffield, Michael Gormley, Grant Wright and Ian McDougall. pages cm Includes bibliographical references and index 1. Hydraulic transients. 2. Drainage. 3. Sewerage. 4. Runoff. 5. Drainage pipes. I. Title. TC171.S94 2015 696′.13—dc23 2014030683 ISBN: 978-0-415-58915-4 (hbk) ISBN: 978-0-203-84576-9 (ebk) Typeset in Sabon by Swales & Willis Ltd, Exeter, Devon, UK
- 11. Contents List of illustrations vi Foreword xix 1 Water is the new carbon 1 2 Fluid flow conditions in open channels and partially filled pipes 18 3 Solution of the governing equations of fluid flow conditions in open channels and partially filled pipes 64 4 Simulation of free surface unsteady flow in building drainage networks 129 5 Solid transport in building drainage networks 169 6 Rainwater drainage systems 217 7 Design applications 248 8 Afterword 270 References 274 Index 282
- 12. Illustrations 1.1 Levels of relative water stress in the UK 2 1.2 Water-based climate change issues 3 1.3 Reductions in w.c. flush volume since 1880 6 1.4 Solid transport dependence on w.c. design parameters, as well as both drain and waste solid dimensions 7 1.5 Solid transport depends primarily on the volume of flush water discharged behind the solid 7 1.6 Influence of number of co-habitants on per capita water consumption 9 1.7 Projected number of households by household type, England 9 1.8 Siphonic system on Stanstead Airport 11 1.9 Siphonic system unsteady inflow/storage/outflow 11 1.10 Grey water collected v. w.c. flushing requirements 12 1.11 Q/t graphs for a 6-litre flush w.c. (in black) and a bath discharge (in grey) 13 1.12 Critical solid transport distances for multi-house installation 14 2.1 Schematic definition of free surface flow descriptors 20 2.2 The superposition of the –c wave speed upon the system brings the wavefront to rest and allows the determination of the surface wave speed 22 2.3 Dependence of wave speed on flow depth, illustrated for a partially filled circular–cross section channel (100 mm diameter) 23 2.4 Dependence of attenuation on wave, flow and channel properties 24 2.5 Steady non-uniform free surface flow in a uniform conduit 25 2.6 Water and air velocity profiles in a partially filled pipe flow 27 2.7 The dependence of the Chezy coefficient on Reynolds Number and channel relative roughness 31
- 13. Illustrations vii 2.8 Values of the Chezy Coefficient based on Manning n for 50% full bore flow partially filled pipe flow for a range of typical building drainage diameters 31 2.9 Increased flow capacity, 50% full bore, as the pipe slope is increased, flow predictions based on Colebrook- White with a wall roughness k of 0.06 mm 32 2.10 50% full bore flow capacity comparison between Colebrook-White predictions, with a wall roughness k = 0.06 mm, and Chezy predictions with a Manning’s n of 0.009 33 2.11 Geometry of a circular–cross section drain 35 2.12 Geometrical variation of area, wetted perimeter, flow width and hydraulic mean depth for a circular cross section partially filled drain flow 35 2.13 Variation of flow mean velocity and flowrate with depth for a circular cross section 36 2.14 Variation of Normal depth with channel slope and applied flow for a 100 mm diameter drain 38 2.15 Variation of Normal and Critical depth with partially filled drain diameter and applied flow at a slope of 0.01 38 2.16 Variation of Normal and Critical depth with Manning n value for a 100 mm diameter drain at 0.01 slope 39 2.17 Relationships between flowrate Q, Specific Energy, SE, and the boundaries of subcritical and supercritical flow defined in terms of the flow Critical depth 40 2.18 Forces acting across a hydraulic jump in steady partially filled pipe flow 44 2.19 Hydraulic jump formed upstream of a junction or flow obstruction 45 2.20 Sequent depth across a hydraulic jump formed upstream of a junction or flow obstruction in a 100 mm diameter drain at 0.01 slope with a Manning n value of 0.009 46 2.21 Hydraulic jump formed downstream of a channel entry 46 2.22 Sequent depth across a hydraulic jump formed downstream of drain entry in a 100 mm diameter drain at 0.01 slope with a Manning n value of 0.025 47 2.23 Sequent depth across a hydraulic jump formed downstream of drain entry in a 100 mm diameter drain at 0.0025 slope with a Manning n value of 0.009 47 2.24 Gradually varied flow depth profile downstream of a vertical stack discharge to horizontal branch where the downstream flow is supercritical 48 2.25 Simpson’s Rule prediction of the gradually varied flow depth profile downstream of a vertical stack
- 14. viii Illustrations discharge to a horizontal branch under supercritical flow conditions 49 2.26 Gradually varied flow depth profile downstream of a vertical stack discharge to horizontal branch where the downstream flow is subcritical 49 2.27 Simpson’s Rule prediction of the gradually varied flow depth profile downstream of a vertical stack discharge to horizontal branch where the downstream flow is subcritical 50 2.28 Supercritical flow exits a free discharge at its normal depth as no indication of the presence of the exit can be transmitted upstream as the wave speed is less than the flow mean velocity 50 2.29 Subcritical flow exits a free discharge at its Critical depth as information concerning the presence of the exit is transmitted upstream as the wave speed exceeds the flow mean velocity 51 2.30 Simpson’s Rule predictions of the subcritical flow depth profile upstream of a free outfall at Critical depth 51 2.31 Hydraulic jumps established upstream of a multiple branch junction carrying supercritical flows 52 2.32 Simpson’s Rule prediction of the depth profiles upstream and downstream of a level invert junction in a supercritical flow network 52 2.33 Hydraulic jump established upstream of a top entry branch junction carrying supercritical flows 53 2.34 Backwater profiles established upstream of a multiple branch junction carrying subcritical flows 53 2.35 Mechanism establishing annular flow below each active vertical stack to branch junction 54 2.36 Forces acting on the annular film and the basis for a terminal flow condition once the annular water film reaches a terminal velocity 55 2.37 Flowrate in a smooth vertical stack from equation 2.35 with the maximum set when the annular flow area becomes 25% of the stack cross section 57 2.38 Terminal annular velocity and development distance in a vertical stack annular water flow for a range of stack diameters 58 2.39 Development of the Steady Flow Energy Equation 60 2.40 Development of Darcy’s Equation, the full bore steady flow frictional relationship in a constant cross section conduit 61 3.1 Derivation of the continuity equation for unsteady flow in a general conduit 65 3.2 Derivation of the momentum equation for unsteady flow in a general conduit 65
- 15. Illustrations ix 3.3 General free surface flow conduit properties 67 3.4 Wave speed in full bore water flow in a range of pipe materials to demonstrate impact of fluid and pipe properties 71 3.5 Method of Characteristics representation of unsteady free surface and full bore flow conditions 77 3.6 Characteristic equations available in full bore transient simulation, partially filled subcritical and supercritical conduit flows and mixed regime supercritical and subcritical flows across a hydraulic jump upstream of a junction or obstruction 79 3.7 Linear interpolation errors demonstrated within the backwater profile upstream of a subcritical free outfall 86 3.8 Time line interpolation avoids interpolation errors inherent in the linear interpolation scheme 86 3.9 Impact of TFAC > 1 on the predicted surge downstream of a sudden stoppage in a siphonic rainwater system 87 3.10 Potential for linear interpolation errors increases as the time step decreases relative to its initial value as the flow velocities within the network vary with appliance discharge 88 3.11 Cubic interpolation technique 89 3.12 Interpolation to yield MoC node depths introduces initial errors as distance increments do not match 90 3.13 Network illustrating the need to monitor branch flows and adjust the network time step to satisfy the Courant Criterion 94 3.14 Attenuation of an appliance discharge along a 20 m length of 100 mm diameter branch set at a 0.01 slope, illustrating the decrease in wave height 96 3.15 Influence of time step choice on the predicted wave attenuation along the 20 m branch drain 97 3.16 Influence of interpolation scheme on the retention of the branch drain exit Critical depth value ahead of the arrival of the appliance discharge wave 98 3.17 Influence of the chosen interpolation scheme on the rate of change of depth following the arrival of the incident appliance discharge wave 98 3.18 Time step variation based on both initial base flow, 0.1 or 1.0 litres/second, and TFAC value, 1 or 3 99 3.19 Flow depth 4 m from entry as predicted by both the LIN and NGE interpolation schemes 100 3.20 Space-time grid as a basis for a finite difference scheme, where n represents time progression and j represents the nodal number, increasing in the initial flow direction 103
- 16. x Illustrations 3.21 Schematic representation of one version of the MacCormack method 106 3.22 Illustration of the Preismann slot to allow simulation of pressurised pipe flow 107 3.23 Typical quasi-steady bath discharge profile to a horizontal branch drain via an appliance trap seal 108 3.24 Entry to a branch drain from an appliance trap seal 109 3.25 Idealised w.c. discharge to a branch drain to represent the energy content of the inflow 110 3.26 Depth at a level invert junction 112 3.27 Depth relationships determined experimentally for two level invert junctions 113 3.28 Depth at a top entry junction 114 3.29 Flow depths upstream and downstream of an obstruction or a badly made in-line pipe junction 115 3.30 Flow depths upstream and downstream of a slope defect in a horizontal branch 116 3.31 Discharge profiles accumulate at the base of a vertical stack to establish a combined discharge to the downstream drain 117 3.32 Transition from annular to free surface horizontal flow at a stackbase 119 3.33 Flow accumulation in a vertical stack serving a number of upper floors 123 3.34 Boundary conditions necessary to simulate the movement of a hydraulic jump within branches terminating at a junction or a drain defect 124 3.35 Hydraulic jump response to an increasing approach flow and subsequent junction backflow, followed by a return to initial conditions as appliance discharge abates 125 4.1 Mechanism of wave attenuation in a partially filled channel 130 4.2 The attenuation mechanism is dependent upon the form of the applied wave 131 4.3 Schematic of DRAINET graphical user interface that allows multi-storey systems to be modelled 133 4.4 Illustrative discharge profiles to demonstrate dependence of wave attenuation on channel and appliance discharge parameters 134 4.5 Influence of pipe diameter on the attenuation in a 20 m, 100 mm diameter glass drain at a slope of 1/100 in response to a ‘Plateau’ format appliance discharge 135 4.6 Influence of wall roughness on the attenuation in a 20 m, 100 mm diameter drain at a slope of 1/100 in response subject to a ‘Plateau’ format appliance discharge 135
- 17. Illustrations xi 4.7 Influence of pipe slope on the attenuation in a 20 m, 100 mm diameter glass drain at slopes of 0.02, 0.015, 0.01 and 0.005 in response subject to a ‘Plateau’ format appliance discharge 136 4.8 Influence of appliance discharge profile on the attenuation in a 20 m, 100 mm diameter coated cast iron drain at a slope of 1/100 in response subject to either a ‘Plateau’ or ‘Peak’ format appliance discharge 136 4.9 Influence of leading edge rise time on the attenuation in a 20 m, 100 mm diameter coated cast iron drain at a slope of 0.01 in response subject to a ‘Plateau’ format appliance discharge with rise times of 0.5 and 2.0 seconds 137 4.10 Influence of baseflow on the attenuation of a ‘Peak’ profile format discharge in a 20 m, 100 mm diameter glass drain at a slope of 0.01 in response subject to a ‘Plateau’ format appliance discharge 137 4.11 Summary of attenuation dependencies 138 4.12 Peak flowrate profiles along a 20 m long, 100 mm diameter drain in response to a ‘Peak’ profile discharge 138 4.13 Peak flow velocity, wave speed and Froude Number profiles along a 20 m long, 100 mm diameter drain in response to a ‘Peak’ profile discharge 139 4.14 Peak flow velocity, depth and specific energy profiles along a 20 m long, 100 mm diameter drain in response to a ‘Peak’ profile discharge 139 4.15 Comparison of DRAINET predictions of wave attenuation, in terms of flowrate and wavelength, to the measurements presented by Burberry 140 4.16 Graphical representation of the predicted increasing length of the appliance discharge as it progresses along a 20 m, 100 mm diameter drain set at a slope of 1/140 141 4.17 Comparison of Wyly (1964) observation of horizontal drain flow surge capacity with DRAINET simulations (Swaffield and Galowin 1992) 141 4.18 Validation of the energy entry condition representing a w.c. discharge to a horizontal branch drain 142 4.19 Validation of the Normal and Critical depth boundary conditions representing the more tranquil discharge to a horizontal branch drain from appliances such as baths, showers or downstream of a junction or defect 143 4.20 Summed flow at the base of a two-storey vertical stack at NBS Washington, DC 144 4.21 Comparison of flow depth — the observed and predicted flow depths downstream of the vertical stack to sewer connection, NBS test installation 145 4.22 Schematic of the vertical stack and sewer connection network used to demonstrate the DRAINET simulation
- 18. xii Illustrations of vertical stack entry flow to a horizontal sewer connection or multi-stack collection network 146 4.23 Comparison of the horizontal sewer connection drain entry flow profile following simultaneous and staggered w.c. discharges on the four upper floors 147 4.24 Comparison of the maximum flow depth and flowrate profiles along the 20 m, 100 mm diameter glass sewer connection branch set at 0.01 slope 148 4.25 Development and attenuation of the discharge wave along the 20 m, 100 mm diameter glass sewer connection at a 0.01 slope 148 4.26 Comparison of the horizontal sewer connection drain entry flow profile following 1.0 and 1.45 second increment staggered w.c. discharges on the four upper floors 149 4.27 Comparison of the maximum flow depth and flowrate profiles along the 20 m, 100 mm diameter glass and uncoated cast iron sewer connection branches set at 0.01 slope 150 4.28 Development and attenuation of the discharge wave along the 20 m, 100 mm diameter uncoated cast iron sewer connection at a 0.01 slope, following the 1.45 second staggered upper floor w.c. discharges 150 4.29 Comparison of the maximum flow depth and flowrate profiles along the 20 m, 100 mm diameter uncoated cast iron sewer connection branch set at 0.01 slope 151 4.30 Comparison of the entry flow profiles to the glass and uncoated cast iron sewer connections 152 4.31 Comparison of the maximum flow depth and flowrate along a 20 m sewer connection of 100 mm and 150 mm diameter at a slope of 0.01 152 4.32 Comparison of the entry flow profile generated by upper floor w.c. discharges staggered by 2 seconds in a 100 mm and a 150 mm diameter sewer connection 153 4.33 Wave attenuation along the 20 m, 150 mm, diameter uncoated cast iron sewer connection following the 2.0 second staggered set of upper floor w.c. discharges 153 4.34 Demonstration of the effect of increasing the horizontal sewer connection diameter from 100 mm to 150 mm on the full bore flow established following a series of 2 second delay upper floor w.c. discharges 154 4.35 Propagation of the full bore flow condition along the 100 mm uncoated cast iron drain in response to the inflow profile generated by upper floor w.c. discharges at a 2 second stagger 155 4.36 Initial propagation of the full bore flow condition along the 100 mm uncoated cast iron drain 155
- 19. Illustrations xiii 4.37 Historic definition of flow conditions downstream of a stack to collection drain interface compared to the flow profile predicted by DRAINET for the 100 mm diameter uncoated cast iron drain 156 4.38 Level invert and top entry junction geometry utilised in the demonstrations of MoC simulations of junction–flow interaction 158 4.39 Maximum and minimum flow velocity and water depth for a 90° level invert branch junction 159 4.40 Interaction of flows from a 90° branch junction 160 4.41 Flow velocity and depth profile along the 12 m collection pipe with a 45° level invert junction at 10 m 161 4.42 Interaction of flows at a 45° level invert junction 161 4.43 Flow depths along the main collection drain (pipes 2 and 3) illustrating development of the jump position at different times for a top entry junction 162 4.44 Interaction of flows for top entry junction 163 4.45 Flow velocity and water depth at the junction for a 45° top entry junction 163 4.46 Flow velocity and water depth along the main drain line with discharge from top entry 45° junction 164 4.47 Experimental test rig used to test junction effects 165 4.48 Effect of 90° top entry junction on solid transport 166 4.49 A 45° top entry junction showing solids travelling with the predominant flow 166 4.50 Potential for higher risk of blockages from level invert junctions 167 4.51 Laboratory confirmation of potential blockage risk from level invert junction 167 5.1 Zonal description of the mechanism of solid transport in attenuating flows in a branch drain following a w.c. discharge 180 5.2 Deformable solid velocities measured in a 100 mm diameter branch drain at a range of gradients and w.c. flush volumes 182 5.3 Experimental variable slope and cross section test rig to determine the solid transport characteristics under reduced flush volume conditions 184 5.4 Branch drain cross-sectional shapes and dimensions, including the likely cross-sectional shape of the solid during transport 185 5.5 Solid velocities recorded along the circular and parabolic cross section branch drains tested at a 1/60 slope subjected to a 6 litre flush 186 5.6 Predicted peak depths and specific energy values along the various branch drains considered as an example of the effect of wave attenuation 187
- 20. xiv Illustrations 5.7 Solid velocities for all branch drain cross sections, BS w.c. flush volumes and slopes, demonstrating the result of the regression analysis for one test case 189 5.8 Solid velocities for all branch drain cross sections, w.c. type, flush volumes and drain slopes, demonstrating the result of the regression analysis for all the cases considered 190 5.9 Solid deposition data compared to the predicted mean travel distance to deposition indicated by Figure 5.8 191 5.10 Branch drain slope to achieve a particular solid transport performance, indicating the steepening necessary as flush volume is decreased 192 5.11 C1 and C2 defined in terms of the solid and drain parameters as identified in equations 5.10 and 5.11 194 5.12 Dependency of deformable solid transport on a range of solid, appliance discharge and branch drain dimensionless groups 195 5.13 Experimental solid velocities for a deformable sanitary product solid discharged to a branch drain set at a range of gradients 196 5.14 Tissue deformable solid transport in a hospital interfloor void branch drain set at 1/200 slope 198 5.15 Faecal and tissue deformable solid transport in a hospital interfloor void branch drain set at 1/200 slope, illustrating the importance of tissue as a trailing solid in the continuation of faecal solid transport, previously unpublished data from Bokor (1984) 198 5.16 Stages of solid transport from inception of motion to subsequent deposition 199 5.17 Forces acting on a solid during inception of motion, subsequent motion and deposition 200 5.18 Development of the solid transport characteristic solution and identification of the solid track 202 5.19 Method of characteristics solution for unsteady free surface flows, including the representation of solid track within the x-t plane 203 5.20 Comparison of observed and predicted solid transport from rest using the boundary equations developed to describe the forces acting on the solid and the leakage flow past the solid 204 5.21 Flow depth profiles observed along the length of a cylindrical solid as the solid velocity increases from zero to the local flow velocity 204 5.22 Comparative solid transport velocity predictions for two pads differing only in base area and saturated mass 205
- 21. Illustrations xv 5.23 Solid velocity simulation derived from floating solid observations using a constant velocity decrement factor 206 5.24 Water depth difference across a solid 208 5.25 Solid velocity measurement 209 5.26 Interacting solids 210 5.27 General form of the model 212 5.28 Water depth history along pipe showing dHS 213 5.29 Variation in dHS with VS when solids interact 214 5.30 Solid deposition showing stop/start motion 214 5.31 Variation in distance between solids as they travel along pipe 215 6.1 Schematic of conventional and siphonic rainwater drainage systems 218 6.2 Typical siphonic roof outlets 218 6.3 Typical gutter outlet illustrating entrained airflow exclusion baffle 218 6.4 Typical composition of a green roof 220 6.5 Typical gutter water surface profiles 221 6.6 Typical siphonic rainwater drainage system 222 6.7 Siphonic rainwater system establishment and cyclic operation 223 6.8 Impact of roof construction on runoff to gutters 228 6.9 Steady initial gutter depth profile established following imposition of a zero upstream inflow boundary condition 230 6.10 Schematic representation of the Method of Characteristics applied to full bore flow conditions 231 6.11 Gutter flow depths in a trapezoidal gutter in response to a varying rainfall intensity 233 6.12 Measured and predicted conditions for a standard gutter 234 6.13 Measured and predicted conditions for a wide gutter 235 6.14 Predicted gutter depths and overtopping rates for a 75 m section of Gutter B connected to four 110 mm diameter downpipes (roof area = 650 m2 ) 236 6.15 Schematic view of the Heriot-Watt siphonic roof drainage test rig 239 6.16 Measured and predicted conditions for design criteria rainfall 240 6.17 Measured and predicted conditions for a rainfall event below the design criteria 240 6.18 Measured and predicted gutter depths and system pressures from the MacCormack/MoC hybrid simulation 241 6.19 Predicted pressure surge generated by an instantaneous gutter outlet blockage 242
- 22. xvi Illustrations 6.20 Predicted conditions for design criteria rainfall event, with gradually submerging system exit 243 6.21 Predicted flow rates for a siphonic system experiencing exit submergence and outlet blockage 244 6.22 Gutter depth and pipe network pressures during an extreme rainfall event at the National Archive of Scotland test site installation 245 6.23 Blockage of a siphonic roof outlet 246 7.1 Distribution of w.c. to junction distances likely in current practice 252 7.2 Demonstration three pipe network and a comparison of the transport distances achieved in 75 mm, 100 mm and 150 mm diameter pipes by a 6 litre w.c. discharge at a slope of 1/100 253 7.3 Diurnal w.c. usage patterns 254 7.4 Assumed dwelling usage pattern morning ‘rush hour’ 254 7.5 Layout of sanitary fittings and drainage 255 7.6 Flow rate profiles for house types 1, 2 and 3 256 7.7 Assumed pattern for a series of nine dwellings connected to common drainage 256 7.8 Simulated nine dwelling group and cumulative flow rate at end of system for 100 mm diameter pipes 257 7.9 Solid transport comparison for overall slopes of 1/60 and 1/100 illustrating the percentage of solids to clear the network and the percentage deposited in either the house to collector section or in the collector drain. 258 7.10 Simple installation to test maximum travel distance 263 7.11 Domestic installation used to test the applicability of 4 litre/2.6 litre w.c. installation 265 7.12 Importance of adjoining flows 267
- 23. Tables 1.1 Water resources index classes 5 1.2 Global water challenges 6 2.1 Values of surface roughness, k mm, appropriate to the Colebrook-White expression, for a range of drainage pipe materials 29 2.2 Values of Manning n appropriate to the Chezy equation for a range of conduit, channel and pipe surface roughness 30 2.3 Values of surface roughness, k, appropriate to the Bazin expression, for a range of general channel materials 30 2.4 Use of the Colebrook-White 50% full bore flow capacity variation with pipe slope and diameter as a basis for design tables indicating the maximum rating for any slope diameter combination 33 3.1 Relevance of each term identified within the St Venant unsteady flow equations of continuity and momentum 67 3.2 Values of Young’s Modulus for possible pipe materials 70 3.3 Values of water Bulk Modulus and density 70 3.4 Identification of dependent variables and coefficients in the equations of continuity and motion developed for unsteady building drainage applications 75 3.5 Identification of the coefficients in the finite difference equations applicable to the building drainage applications considered 75 3.6 C+ and C– characteristic equations for each of the free surface and siphonic system full bore flow cases considered 76 3.7 Comparative depth and flowrate predictions as the number of nodes per m is increased from 1 to 16 100 3.8 Summary of the boundary equations developed for the MoC simulation of unsteady free surface flows in building drainage systems and rainwater gutters 126 4.1 Summary of the dependence of wave attenuation on drain and flow parameters 134
- 24. xviii Tables 4.2 Wall roughness values used in the determination of an appropriate friction factor within DRAINET 134 5.1 Dimensionless group indices (equation 5.8) 189 5.2 Volume discharged ahead of solid at each reduced flush volume setting 190 5.3 Velocity decrement laboratory observations for the transport of latex water filled sheath solids 207 6.1 Prevailing flow conditions in a rainwater drainage system 219 7.1 Summary of simulation results for 6 litre/4 litre flush volume w.c. 264 7.2 Summary of simulation results for 4 litre/2.6 litre flush volume 264 7.3 Appliances and associate volume of water used 265 7.4 Appliance usage data for house simulation 266
- 25. Foreword My husband John died before this book was completed, and I am grate- ful that members of the Drainage Research Group (DREG) at Heriot-Watt University agreed to take on the task to complete and publish it. I am indebted to them. John was always a ‘research fellow’ at heart and wanted to leave his research and books based on his life’s work as a legacy to his new found knowledge. This has now been secured. But not only has he left his research to posterity – he has also left a team of researchers that have been inspired by his work and will take this forward in the future. I hope this book will also stimulate your interest in fluid mechanics applied to drainage systems as well. Dr Jean Swaffield February 2014 Edinburgh
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