Contents

Cover

Half Title page

Title page

Copyright page

Dedication

List of Symbols

Preface

Acknowledgments

Chapter 1: Introduction

1.1 Water Distribution Networks and Their Design

1.2 Feasibility For Gravity-Driven Water Networks

1.3 The Elements

1.4 Engineering Design

1.5 Gravity-Driven Water Network Distinguishing Characteristics

1.6 The Fundamental Problem

1.7 A Brief Background

1.8 Approach

1.9 Key Features of this Book

References

Chapter 2: The Fundamental Principles

2.1 The Problem Under Consideration

2.2 The Energy Equation for Steady Pipe Flow: Fluid Dynamics

2.3 A Static Fluid

2.4 Length Scales for Gravity-Driven Water Networks

2.5 Mass Conservation

2.6 Special Case of Reservoir At State 1

2.7 Single- and Multiple-Pipe Networks Revisited

2.8 The Role of the Momentum Equation

2.9 Forced Flows

2.10 Summary

References

Chapter 3: Pipe Materials and Dimensions

3.1 Introduction

3.2 Pipe Materials

3.3 The Different Contexts for Pipe Diameter

3.4 Systems for Specifying Pipe Dimensions

3.5 Choosing an Appropriate Nominal Pipe Size

References

Chapter 4: Classes of Pipe Flow Problems and Solutions

4.1 The Classes

4.2 An Illustrative Pipe Flow Problem of Class 4

4.3 The Problem Statement

4.4 Setting up the Problem

4.5 Different Approaches to the Solution

4.6 A Note of Caution

4.7 Summary

References

Chapter 5: Minor-Lossless Flow in A Single-Pipe Network

5.1 Introduction

5.2 Solution and Basic Results

5.3 Results for Limiting Case of A Vertical Pipe: Froude Number

5.4 Design Graphs for A Single Pipe for Minor-Lossless Flow

5.5 Comprehensive Design Plots for Gravity-Driven or Forced Flow

5.6 The Forgiving Nature of Sizing Pipe

References

Chapter 6: “Natural Diameter” For A Pipe: Local Static Pressure

6.1 Motivation

6.2 The Energy Equation Written for Local Static Pressure

6.3 An Illustration: The “Natural Diameter”

6.4 Commentary

6.5 Local Static Pressure for A Three Dimensional Network

6.6 Graphical Interpretations: Energy Line and Hydraulic Grade Line

6.7 Summary

References

Chapter 7: The Effects of Minor Losses

7.1 Nature of the Minor Loss

7.2 A Numerical Example

7.3 The Case For Uniform D

7.4 Importance Threshold for Minor Losses

7.5 Fixed and Variable Minor Losses

References

Chapter 8: Examples for A Single-Pipe Network

8.1 Introduction

8.2 A Straight Pipe

8.3 Format of Mathcad Worksheets for Single-Pipe Networks

8.4 A Circuitously Run Pipe with Atmospheric Delivery Pressure

8.5 A Circuitously Run Pipe with Specified Nonzero Delivery Pressure: “Sensitivity” Studies

8.6 The Effect of Local Peaks in the Pipe

8.7 A Network Designed from Site Survey Data

8.8 Draining A Tank: A Transient Problem

8.9 The Syphon

References

Chapter 9: The Energy Equation Based on Approximate Friction Factor

9.1 The Problem

9.2 A Recommendation

9.3 Energy Equation: Friction Factor from the Blasius Formula

9.4 Forced Flows

9.5 Summary

References

Chapter 10: Optimization

10.1 Fundamentals

10.2 The Optimal Fluid Network

10.3 The Objective Function

10.4 A General Optimization Method

10.5 Optimization Using Mathcad

10.6 Optimizing A Gravity-Driven Water Network

10.7 Minimizing Entropy Generation

10.8 Summary

References

Chapter 11: Multiple-Pipe Networks

11.1 Introduction

11.2 Background

11.3 Our Approach

11.4 A Simple-Branch Network: Flow From A Junction to Multiple Tapstands

11.5 Pipes of Different Diameters in Series: Controlled Dissipation Of Potential Energy

11.6 Multiple-Branch Network

11.7 Loop Network

11.8 Large, Complex Networks

11.9 Multiple-Pipe Networks with Forced Flow

11.10 Perspective: Conventional Approach To Solving Multiple-Pipe Network Problems

11.11 Closure

References

Chapter 12: Microhydroelectric Power Generation

12.1 Background

12.2 The System

12.3 Approach

12.4 Analysis

12.5 Hybrid Hydroelectric Power and Water Network

12.6 Summary

References

Chapter 13: Network Design

13.1 The Design Process

13.2 Overview

13.3 Accurate Dimensional Data for the Site

13.4 Calculating Design Information from Site-Survey Data

13.5 Estimating Water Supply and Demand

13.6 The Reservoir Tank

13.7 The Tapstand

13.8 Estimating Peak Water Flow Rates

13.9 Source Development

13.10 Hydrostatic Pressure Issues

13.11 The Break-Pressure Tank

13.12 The Sedimentation Tank

13.13 Flow Speed Limits

13.14 Dissipation of Potential Energy

13.15 Designing for Peak Demand: Pipe Oversizing

13.16 The Composite Pipeline

13.17 Water Hammer

References

Chapter 14: Air Pockets in the Network

14.1 The Problem

14.2 The Physics of Air/Liquid Pipe Flows: Flow in A Straight Pipe

14.3 Flow in A Pipe with Local High Points

14.4 The Effect of Air Pockets on Flow Rate

14.5 An Example

14.6 Summary

References

Chapter 15: Case Study

15.1 Engineering Design: Science and Art

15.2 Design Process Revisited

15.3 The Case

References

Chapter 16: Exercises

16.1 Comments

16.2 The Problems

References

16.3 The Solutions

Appendix A: List of Mathcad Worksheets

Appendix B: Calculating Pipe Length and Mean Slope from GPS Data

B.1 The Basics: Northing and Easting

B.2 An Example

References

Appendix C: Mathcad Tutorial

Index

Author Index

GRAVITY-DRIVEN WATER FLOW IN NETWORKS

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

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Library of Congress Cataloging-in-Publication Data:

Jones, Gerard F.
Gravity-driven water flow in networks : theory and design / Gerard. F. Jones.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-28940-2 (hardback)
1. Hydrodynamics. 2. Water—Distribution. 3. Drainage. I. Title.
TC171.J66 2010
628.1’44—dc22 2010031088

oBook ISBN: 978-0-470-93965-9
ePDF ISBN: 978-0-470-93964-2
ePub ISBN: 978-1-118-00208-7

To Nicki, Lauren,
and Chris, and in loving
memory of Eric

List of Symbols

English Symbols

A | area, m2
a | cost-per-length coefficient, US$/m
aw | wave speed in liquid, m/s
B | bulk modulus for liquid, Pa
b | exponent
C | coefficient
C’ | cost per unit length, US$/m
CT | total cost, US$
| constant in inequality constraint
cv | specific heat at constant volume,
D | inside, or nominal, diameter of pipe, m
E | elastic modulus of pipe, Pa
e | internal energy per unit mass, J/kg
F | dimensionless static pressure at delivery location, p2/pgz1
| dimensionless static pressure at a pipe end, p/ρg(z1 – z2)
Fr | Froude number
f | Darcy friction factor (friction factor)
f* | factor in Eqn (2.16)
g | gravitational acceleration, 9.807 m/s2
| inequality constraint function
H | head, (m/s)2
h | head, m
| height, m
i | growth rate, %/100
K | minor loss coefficient
L | pipe length, m
| pipe length from inlet to outlet measured in horizontal plane, m
| equality constraint function
M | number of minor-loss elements accounted for using Le/D values
m | integer
| mass flow rate, kg/s
N | number of minor-loss elements accounted for using K values
n | integer
p | static pressure, Pa
P | population
PF | peak factor
Q | volume flow rate, L/s
| heat transfer rate to system, W
Re | Reynolds number
r | radius, m
s | mean slope between source and delivery points
S | hydraulic gradient
š | slack variable
T | temperature, °C
t | time
| dummy variable
u | local velocity in the direction of fluid flow, m/s
| cross-sectional average flow speed, m/s
V | volume, L
| rate of work done by system, W
x, y | horizontal coordinates (x is alternately a pipeline coordinate), m
| independent parameters in optimization
| objective function
z | vertical coordinate, m

Greek Symbols

α | kinetic energy correction factor
β | factor in Eqn (11.55)
γ | r / z1 for syphon geometry
Δ | change
| roughness of pipe wall, m
| efficiency
λ | tortuosity; ratio of actual length of pipe to pipe length if run straight
| Lagrange multiplier
v | kinematic viscosity, m2/s
ρ | density, kg/m3
| dummy variable of integration

Subscripts

a | actual
a, b, c, … | pipe labels for multiple-pipe networks
b | pertaining to branch
app | approximate
atm | atmospheric
1,2 | inlet and outlet states
1,2,3, … | node numbers for multiple-pipe networks
d | demand
D | discharge
del | delivery
e | equivalent
entry | at entry of pipe
f | final
F | future
fr | friction
g | generator
high | high point
i, j | indices
j | at a junction
in | in
L | loss
low | low point
| local
m | pertaining to main
mod | modified
out | out
p | peak
P | present
R | souRce
ref | reference
S | storage tank
s | start
sys | system
sc | scale
shaft | shaft
T | total
t | turbine
th | theoretical
u | unit
| refers to surroundings or terminal conditions
99% | 99% of total

Superscripts

n | natural
new | most-recent result from an iterative procedure
old | result before most-recent from an iterative procedure
opt | optimal
’ | measured from a peak
* | refers to a liquid-filled pipe segment

Preface

Several of the key elements of the mission statement for the Nicaraguan-aid organization, Agua Para la Vida (www.aplv.org), follow:

Help small, rural communities of Nicaragua develop and maintain access to safe drinking water.

Provide training and education to local people in all aspects of designing, building, and maintaining drinking water systems so that they can achieve autonomy in rural drinking water development.

Develop design tools and teaching methods for use by other groups involved in village water system construction.

Even with the considerable aid of the many organizations like Agua Para la Vida and Youth Action For Rural Development (YARD) in Kenya (www.wsp.org), much of the population of these countries and others like them lack access to clean water. In Nicaragua it is most ironic that this deficit occurs in mountainous regions where the wet-season lasts 8 months of the year or more and rain water is plentiful! The need for the careful design of gravity-driven clean water networks in these, and many other similar parts of the world community is well established. This book is a small attempt to help in this worthy endeavor by presenting information to support technologists, engineers and engineering students, and practitioners who carry out these designs.

When the topic of analysis and design for water flow in pipes is raised, the saying “… there is nothing new under the sun” likely comes to mind. Certainly, many references on this are readily available. I began to teach this subject as a part of service learning projects at Villanova University in early 2004. The focus of the projects was to provide clean water for the people of central Nicaragua who had no easy access to this and often drank nearby, but contaminated water with dire consequences. With the guidance of faculty, the mostly mechanical engineering students assessed, analyzed, and designed the networks, and in some cases followed up by helping to install the network they or others had designed. I found teaching the analysis of gravity-driven water networks to the students to be a challenge. Most had already taken a course in fluid mechanics and had learned some things about pipe flow. However, gravity-driven flow in a closed pipe is very different than the flow problems to which they had been exposed. In my lectures that stressed fundamentals related to the importance of mean slope in a single-pipe network, local static pressure distributions near low and high points, and cost-minimization to determine unique solutions to the energy equation, it was as if I were teaching an entirely new subject. After some reflection, I would recall from my own teaching of fluid mechanics that the elevation change in nearly all problems was neglected (certainly for gases) or assumed negligible compared with a specified pressure difference between the pipe ends. The important elements of gravity-driven pipe flow are, in fact, never taught! I recognized a clear need for a good learning and teaching tool on this topic.

The literature was of little help. The treatment of gravity-driven flow in the existing text, trade, and hand books, if presented at all, is technology based so there were few, if any, fundamentals to which the students could relate and use as a sound basis for understanding and insight. In short, in the literature where gravity-driven flow appeared there was little educational value, and in sources like textbooks where the educational value is high, there was little or no treatment of gravity-driven flow networks. Simple and fundamentally sound design tools and algorithms using modern-day software were also missing.

Thus, this book is written in an attempt to place the analysis and design of gravity-driven water networks on a sound fundamentals footing and to provide easy-to-use algorithms and charts for analysis and design computations. In this way, I have attempted to bridge the gap between fundamental fluid mechanics and the applied and useful technology-based material in the various existing references on gravity-driven water networks. In particular, the topics have been chosen to add clarity, a sound technical basis, and support to many of those contained in the currently popular handbook by Thomas Jordan, Jr. (2004), which is cited in many places in this text. A benefit of the fundamentals approach is the production of original design graphs, formulas, and computational algorithms for the correct, sustainable designs of single-and multiple-pipe gravity-driven water networks.

Both theory and design are covered in this work, along with the analysis that must join the two. It is a considerable challenge to span this range effectively. For the theory I have, of course, relied on past work from classical fluid mechanics in which the focus may be thought of as the discipline of engineering. The design and practical content, that is, the practice of engineering, comes from reflection on past written works and our team’s experience in the field with actual gravity-driven water networks and with industry applications.

In addition to practitioners, this book is written for engineers, technologists, and scientists and for students preparing for these fields. To help the readers relate to the technical material, the presentation style has been chosen to be consistent with what students normally encounter in an undergraduate college-level course in the United States. In some cases, an advanced-level high school physics course that covers the energy equation for a moving fluid and the topic of flow in a pipe may suffice as adequate background to understand much of the material presented in this text.

Most of this book can be covered in about half of a 14-week term. This is the time that could perhaps be allotted for a college or high school level design course. The main Chapters 1–13, and 15 should be coverable in 7 weeks, along with most of the relevant problems in Chapter 16. Chapters 10 and 14, on optimization and air blocks, may be added at the discretion of the instructor.

Double-outlined textboxes, like this one, will be employed to provide periodic breaks for the reader where there is an extended amount of technical material and will include examples, clarifying and reinforcing comments, supplemental information, and questions for exploration.

Fundamental equations and final forms of the most useful ones will be boxed.

This should not be confused with the double-outlined textboxes.

In addition to textboxes, annotations in the form of footnotes appear very frequently throughout the text. This is a personal preference of the author1.

Other than the chapter on optimization and local static pressure, the mathematics required to understand the material in this book is algebra including the solution of single and simultaneous nonlinear algebraic equations using numerical methods. Many chapters require this. For readers who have forgotten or are not familiar with nonlinear algebraic equations, a section in Chapter 4 is included to refresh memories or introduce the basics of this topic. References to integrals and to ordinary differential equations are made in several chapters including those on local static pressure and minor losses, so it is worthwhile for the reader to recall some of the basics surrounding the calculus when covering this material. Some understanding of the calculus is needed for optimization, which always requires the derivative to determine so-called “stationary” points for a function. Of course, it is assumed that the reader has, at least, a familiarity with fluid mechanics.

Most pipe-flow problems of the types considered in this book require numerical solutions carried out on a computer. The traditional way of solving the systems of nonlinear algebraic equations that arise in pipe flows is iteration and linearized scaling (often referred to as “Regula Falsi” in texts on numerical methods), covered in Chapter 11, which for simple problems, could be executed by hand. A similar method that “compartmentalizes” the terms from the energy equation and then uses trial-and-error to determine pipe diameter is the normal method of solution where just a single pipe is involved (Chapter 4). However, computer programs to quickly and efficiently solve the equations of pipe flow are well developed and have been for very many years. These fall into two classes. Nearly all are “opaque” in that the user is not made aware, or chooses not to be aware, of the program’s basis. This means that an executable file is run on a computer, which is the result of a compilation of a source program written in perhaps Fortran or C++ (see comments below).

The other class is composed of “transparent” computer programs that present the solution in an easy-to-read manner, and appear as if written on paper. The solution for a given design is obtained by modifying an already-developed program for a closely related one. The commercial package Mathcad2 is chosen for use in this book. In particular, the root and Given … Find constructs in Mathcad are very valuable for the solution of nonlinear algebraic equations. There are frequent references to these. Mathcad is also the only commercial package that explicitly includes units in equations. The conversion from one unit to another, say inches to mm, as required by the problem is accomplished automatically and is transparent. For various reasons, the use of units and the associated need to include them when solving engineering problems are a challenge for students today. Mathcad worksheets that solve the equations for many types of gravity-driven water networks are supplied with this text (downloaded from http://www.wiley.com/WileyCDA/WileyTitle/
productCd-0470289406,descCd-DOWNLOAD.html). If familiarization with Mathcad is needed, a brief tutorial is presented in Appendix C.

As is the case with all technological tools, the lifetime of Mathcad may be finite. That is, at some time in the future it may be replaced with a “new and improved” version or it may even disappear. This is not a concern because the fundamental equations for analysis and design appearing in this text remain unchanged and can be solved with any programming language or tool, such as C++, Matlab3, Microsoft’s Excel, or a new and improved Mathcad. Even a programmable hand-held calculator is sufficient for some problems. More-senior engineers may recall a similar discussion in the 1970s concerning Fortran, then the dominant programming language in engineering, as to what the computational tool of the future will be. The answer that was often given was that no one knew for certain, but it would probably be called Fortran. Presently, after numerous revisions over the years, Fortran continues to be used by scientists and engineers worldwide.

G. F. JONES

Villanova, Pennsylvania
September, 2006

1 It is hoped that the readers will find the history, clarifications, and extensions presented by these aids useful without distracting from the principal thrust of the material.

2Mathcad, Parametric Technology Corporation, 140 Kendrick Street, Needham, Massachusetts

3Matlab, The MathWorks, Inc. 3 Apple Hill Drive, Natick, Massachusetts 01760, USA.

Acknowledgments

I want to acknowledge the support from and stimulating discussions with James O’Brien and Jordan Ermilio of Villanova University. The three of us began a service-learning project at Villanova in 2003 and the book is an outgrowth of this initiative that continues today. Also due thanks are the mechanical engineering students at Villanova, whose interest and dedication in helping those less-fortunate than themselves over the past 7 years in their travels to central Nicaragua were the principal motivation for writing this book. The author also appreciates the thoughtful comments of Gary Gabriele, Ron Parise, Louis Velez, and Kevin Woods who, along with Jim and Jordan, reviewed the text and added their insight. Jordan also co-authored Chapters 13 and 15 and supplied many of the photographs for which I am very grateful.

I also wish to thank Villanova University for giving the time for me to finish a large part of this book during a sabbatical in the fall of 2007.

I am grateful to the staff at Wiley including my editor Bob Esposito, production manager Christine Punzo and her production staff, and LATEX guru Amy Hendrickson, for their persistence and patience in seeing this project through to completion.

Lastly, I thank my wife, Nicki, for her patience, love, and support during the brief, but intense, period of time spent writing this book and during my travels to Central America.

G. F. J.

CHAPTER 1

INTRODUCTION

“Give a Man a Fish, and Feed Him for a Day. Teach Him to Fish, and Feed Him for Life“

– Traditional

1.1 WATER DISTRIBUTION NETWORKS AND THEIR DESIGN

It is generally recognized that water distribution networks date to thousands of years BC. Those in Greece, Syria, Jordan, Turkey (Mays, 2000), Palestine, Persia (Salzman, 2006), and Crete (Trifunovic, 2006), as well as Rome (Chanson, 2002; Salzman, 2006; Trifunovic, 2006), Machu Picchu (Wright et al., 1997) and, later, New York City (Koeppel, 2000) have been extensively documented in print and the visual media. The networks consisted of “aqueducts,” open channels and lead and wooden pipes, that used gravity to move water over large distances with reasonable losses. Despite these very early successful efforts at the design and construction of water distribution networks, it is estimated that today nearly 1 billion people live without access to clean drinking water throughout the world (Trifunovic, 2006); more than 15% of the total population. In particular, the probability of access to clean water in rural populations in South and Central America and Africa ranges from a scant 40–60%.

The design of water networks has undoubtedly had a much shorter history, at least in terms of what we now know as engineering design. Consider evidence of the different elements used in the aqueducts in Rome in the first century, AD (Chanson, 2002). Culverts,1 flow regulation with overflow and underflow gates,2 and dropshafts to dissipate energy in steep regions using vortical motion appeared frequently. The relatively high levels of technical and construction expertise for this time period are remarkable. However, design was carried out by rules-of-thumb, based on simple observations and experiences, passed down through generations and across vast regions by word of mouth or perhaps script, not through the understanding of mass, momentum, and energy conservation that we use today. Certainly, there were no fast computational tools in ancient times to carry out the sophisticated calculations for the design and performance of these networks.3

In contrast to the likely design of the Roman aqueducts, imagine the following exchange that may occur on a day this week in the District Engineer’s Office in a remote town in a developing country.

Community Member: Good morning Sr. Engineer. Last year, our community of San Pedro identified clean water as a priority development concern. In addition to this, we understand that your office has also been promoting small hydroelectric facilities for rural areas such as ours. There are currently 23 families living in the main section of San Pedro, which also has a school, a church, and a community center. There are an additional 80 families who live in more isolated areas of San Pedro and we believe that these families will start to build their homes closer to the village center once we have completed a water supply system and have reliable access to electricity.

District Engineer: Well, the local government is very interested in assisting areas, such as San Pedro, and we hope to be able to work with your community in the near future. Perhaps you can help us by providing some more information. For example; how many sources of water are there in San Pedro? Where will you get the water?

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!