Essentials of Engineering Hydraulics

Macmillan International College Edition

Titles ofrelated interest:

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B Henderson-Sellers: Reservoirs

N T Kottegoda: Stochastic Water Resources Technology

Essentials of EngineeringHydraulics

JONAS M. K. DAKEB.Se (Eng.) (London); M.Sc.Teeh. (Man.); Se.D.(M.LT.)

MANSTI

© Jonas M. K. Dake 1972,1983

All rights reserved. No part of this publication maybe reproduced or transmitted, in any form or by any means,

without permission.

First edition 1972Reprinted with corrections 1974

Second edition 1983

Published byTHE MACMILLAN PRESS LTD

London and BasingstokeCompanies and representatives throughout

the world.

In association with;African Network of Scientific and Technological Institutions

P.O. Box 30592NairobiKenya

Typeset by MULTIPLEX techniques ltd

ISBN 978-0-333-34335-7 ISBN 978-1-349-17005-0 (eBook)

DOI 10.1007/978-1-349-17005-0

Contents

Foreword to the First EditionPreface to the Second (Metric) EditionPreface to the First EditionList of Principal Symbols

IX

X

Xl

XIII

PART ONE ELEMENTARY FLUID MECHANICS

1. Fundamental concepts of fluid mechanics

1.1 Introduction 31.2 The Continuum 31.3 Units of Measurement 41.4 Some Important Fluid Properties 81.5 Transfer Phenomena 131.6 Types of Flow 181.7 Boundary Layer Concepts and Drag 201.8 Fluids in Static Equilibrium 25

2 Methods of analysis

2.1 Control Volume Concepts 402.2 The Basic Physical Laws of Mass, Energy and Momentum

Transport 412.3 Conservation of Mass 422.4 The Linear Momentum Principle 452.5 The Principle of Conservation of Energy: First Law of

Thermodynamics 522.6 The Moment of Momentum Concept 60

3 Steady incompressible flow through pipes

3.1 Introduction 633.2 Enclosed Flow at a Low Reynolds Number 643.3 Momentum and Energy Correction Factors 703.4 Pipe Flow at a High Reynolds Number 713.5 Analysis of Pipe Systems 87

vi Contents

4 Flow in non-erodible open channels401 Introduction 95402 Momentum Concepts 107403 Energy Concepts 113404 Gradually Varied Flow 123405 Open Channel Surges 133406 Miscellaneous Information 137

5 Experimental fluid mechanics501 Introduction 142502 Dynamic Similarity 143503 Physical Significance of Modelling Laws 146504 Models of Rivers and Channels 160505 Dimensional Approach to Experimental Analysis 165

6 Water pumps and turbines601 Introduction 173602 The Pelton Wheel Turbine 175603 Reaction Machines 178604 Selection and Installation of Pumps and Turbines 190605 Cavitation 196606 Pumping from Wells 205

PART TWO SPECIALIZED TOPICS IN CIVILENGINEERING

7 Flow in erodible open channels701 Properties of Sediments 213702 Mechanics of Sediment Transport 219703 Design of Stable Alluvial Channels 229704 Moveable Bed Models 236

8 Physical hydrology and water storage

801 Introduction 242802 Precipitation 244803 Evaporation and Transpiration 249804 Infiltration 252805 Surface Run-off (Overland Flow) 254806 Stream Run-off 258807 Storage and Streamflow Routeing 266808 Design Criteria 276

Contents vii

9 Groundwater and seepage

9.1 Introduction 2829.2 Fundamentals of Groundwater Hydraulics 2859.3 Some Practical Groundwater Flow Problems 298

10 Sea waves and coastal engineering

10.1 Introduction 31210.2 Wave Generation and Propagation 31510.3 Small Amplitude Wave Theory 31910.4 Finite Amplitude Waves 32610.5 Changes in Shallow Water 32710.6 Wave Reflection and Diffraction 33110.7 Coastal Processes 33410.8 Coastal Enginee ring 340

11 Fundamental economics of water resourcesdevelopment

11.1 Introduction 34611.2 Basic Economic and Technological Concepts (Decision

Theory) 349

Problems

Appendix: Notes on Flow Measurement

A.l Velocity-Area Methods 401A.2 Direct Discharge Methods 404

Index 412

Foreword to the First Editionby

J. R. D. Francis, B.Sc. (Eng.), M.Sc., M.I.C.E., F.R.MeLS.Professor of Fluid Mechanics arid Hydraulic Engineering,Imperial College of Science and Technology, London

It is a pleasure to have the opportunity of commending this book. The author, afriend and former student of mine, has attempted to bring out the principles ofphysics which are likely to be of future importance to hydraulic engineeringscience, with particular reference to water resources problems. With the greaterimportance and complexity of water resource exploitation likely to occur in thefuture, our analysis and design of engineering problems in this field must becomemore exact, and there are several parts of Dr. Dake's book which introduce newideas. In the past half-century, the science of fluid mechanics has been largelydominated by the demands of aeronautical engineering; in the future it is nottoo much to believe that the efficient supply, distribution, drainage and re-useof the world's water supply for the benefit of an increasing population willpresent the most urgent of problems to the engineer.

I feel particularly honoured, too, in that this book must be among the firsttechnical texts to come from a young and flourishing university, and is, I think,the first in hydraulic engineering to come from Africa. Over many years,academics in Britain and elsewhere have attempted, with varying success, to helpthe establishment of degree courses at Kumasi, and to produce skilled techno­logical manpower. That a book of this standard should now come forward is asource of pleasure to all those who have helped, and an indication of futuresuccess.

J. R. D. FRANCIS1972

ix

Preface to the Second Edition

The Second Edition of Essentials ofEngineering Hydraulics has retained theprimary objectives and structure of the original book. However, the rationalmetric system of units (Systerne International d'Unites) has been adoptedgenerally although a few examples and approaches have retained the imperialunits.

The scope of the book has been increased by inclusion of section 1.8, 'Fluidsin Static Equilibrium' and sub-sections 8.7.3 and 9.3.5 'Routeing ofFloods inRiver Channels' and 'The Transient State of the WellProblem', respectively.There has been general updating.

A guide to the solution of the tutorial problems at the end of the book isavailable for restricted distribution to lecturers upon official request to thepublisher.

Jonas M. K. DakeNairobi 1982

x

Preface to the First Edition

Teaching of engineering poses a challenge which, although also relevant to thedeveloped countries, carries with it enormous pressures in the developingcountries. The immediate need for technical personnel for rapid developmentand the desire to design curricula and training methods to suit particular localneeds provide strong incentives which could, without proper control, compromiseengineering science and its teaching in the developing world.The generally accepted role of an engineering institution is the provision of thescientific foundation on which the engineering profession rests. It is also recog­nized that the student's scientific background must be both basic and environ­mental. In other words, engineering syllabuses must be such that, while notcompromising on basic engineering science and standards, they reflect sufficientbackground preparation for the appropriate level of local development.

This text has been written to provide in one volume an adequate coverage ofthe basic principles of fluid flow and summaries of specialized topics in hydraulicengineering, using mainly examples from African and other developing countries.

A survey of fluid mechanics and hydraulics syllabuses in British universitiesreveals that the courses are fairly uniform up to second year level but vary widelyin the final year. This book is well suited to these courses. Students in thoseuniversities which emphasize civil engineering fluid mechanics will also find thisbook useful throughout the whole or considerable part of their courses of study.

Essentials ofEngineering Hydraulics can be divided into two parts. Part I,Elementary Fluid Mechanics, emphasizes fundamental physical concepts anddetails of the mechanics of fluid flow. A good knowledge of general mechanicsand mathematics as well as introductory lectures in fluid mechanics coveringhydrostatics and broad definitions are assumed. Coverage in Part I is suitable upto the end of the second year (3-year degree courses) or third year (4-year degreecourses) of civil and mechanical engineering undergraduate studies. Part lIonSpecialized Topics in Civil Engineering is meant mainly for final-year civilengineering degree students. Treatment is concentrated on discussions of thephysics and concepts which have led to certain mathematical results. Equationsare generally not derived but discussions centre on the merits and limitations ofthe equations.

The general aim of the book is to emphasize the physical concepts of fluidflow and hydraulic engineering processes with the hope of providing a foundationwhich is suitable for both academic and non-academic postgraduate work. To-

xi

xii Preface to the First Edition

wards this end, serious efforts have been made to steer a middle course betweenthe thorough mathematical approach and the strictly down-to-earth empiricalapproach.

Chapter 11 gives an introduction to the fundamental economics of waterresources development which is a very important topic at postgraduate level. Ifeel that economics and decision theory must be given more prominence inundergraduate engineering curricula especially in countries where young graduatessoon find themselves propelled to positions of responsibility and decisionmaking.

In an attempt to make this book comprehensive and yet not too bulky andexpensive, I have resorted to a literary style which uses terse but scientific wordswith the hope of putting the argument in a short space. I have also followedrather the classroom 'hand-out' approach than the elaborate and sometimes long­winded approach found in many books.

'The author of any textbook depends largely upon his predecessors' - Francis.Existing books and other publications from which I have benefited are listed atthe end of each chapter in acknowledgement and as further references for theinterested reader. The tutorial problems have been derived from my own classexercises, homework and class tests at M.I.T. and from other sources, all of whichare gratefully acknowledged. In the final chapter, problems 3.18, 4.23, 4.24,5.18,5.19,6.3,6.14,8.1,8.2 and 8.3 have been included with the kind per­mission of the University of London. All statements in the text and answers toproblems, however, are my responsibility.

I wish to thank Prof. J. R. D. Francis of Imperial College, London andDr. J. O. Sonuga of Lagos University and other colleagues who read the manu­script in part or whole and made many useful suggestions. The encouragement ofProf. Francis, a former teacher with continued interest in his student and theexternal examiner in Fluid Mechanics and Hydraulics as well as the moderatorfor Civil Engineering courses at U.S.T., has been invaluable. Mr. D. W. Prah ofthe Department of Liberal and Social Studies, U.S.T., made some useful com­ments on the use of economic terms in Chapter 11. The services of the clericalstaff and the draughtsmen of the Faculty of Engineering, U.S.T., especially ofMessrs. S. K. Gaisie and S. F. Dadzie during the preparation of the manuscriptand drawings are also gratefully acknowledged.

Finally, I wish to express my sincere gratitude to the University of Scienceand Technology, Kumasi, whose financial support has made the production ofthis book possible.

University ofScienceand Technology, Kumasi, Ghana Jonas M. K. Dake1972

list of Principal Symbols

Bb

CCGCpC.R.F.C vC

CoCdCfc.s.c.v.ev

E

FF'

f

J:g

go

cross-section area of a jet (L 2)area (L 2)

acceleration (L/t 2) , area (L 2), wave amplitude (L)

amplitude of wave beat envelope (L)

top width of a channel (L)bottom width of a channel (L)

I

Chezy coefficient (L 2/t); wave velocity (L /t)group velocity (waves) (L/t)specific heat at constant pressure (L 2 /Tt 2 )

Capital Recovery Factorspecific heat at constant volume (L 2 /Tt 2

)

concentration of mass, surge wave speed (L/t) , speed of sound (L/t)coefficient of dragcoefficient of dischargecoefficient of drag (friction)control surfacecontrol volumecoefficient of velocity

molecular mass conductivity (M/Lt), pipe diameter (L), drag (ML/t 2)

sieve diameter which pass N% of soil sample (L)median sand particle size (L)geometric mean size (sand) (L), depth (L), drawdown (L)geometric mean size (sand) (L)diameter of a nozzle (L)

energy (ML2/t2) , specific energy (L), Euler number, rate of evaporation (L/t);

wave energy (M/t 2) , modulus of elasticity (M/Lt 2

)

rate of transmission of wave energy (ML/t 3)

thermal eddy diffusivity (L2 /t )mass edd y diffusivity (L2/t)kinetic energy (ML2 /t2

)

potential energy (ML2 /t2)

exponential constant (= 2.71828)vapour pressure (mmHg), void ratio

force (ML/t 2) , Froude number, fetch (L)

densimetric Froude numberfriction factorinfiltration capacity (L/t or L3/t)silt factor

acceleration due to gravity (L/t 2)

constant - 32.174 Ibm/slug

enthalpy (L 2/t2), total head (L), wave height (L)head developed or consumed by a rotodynamic machine (L)pum p head (L)theoretical head of a rotodynamic machine (L)

xiii

xiv List of Principal Symbols

n, static lift (L)Hsv net positive suction head (NPSH) (L)HT turbine head (L)h head of water above spillway crest (L), hydraulic head (L)hf friction head loss (L)

I moment 0 f inertia (ML"), infiltration amount (L 3), rate of interestseepage (hydraulic) gradient (LIL)

io rainfall intensity (Lit)

J mechanical equivalent of heat, (ML"It 2)

K thermal molecular conductivity (MLITt 3) , coefficient of hydraulic resistances,

modulus of compressibility (MILt")Kn nozzle (loss) coefficientKr coefficient of wave refractionk coefficient of permeability (superficial) (Lit); wave number (21TIL)ks size of roughness (L)

L length (L), wavelength (L)L o wavelength in deep water (L)1 length (L)Ibm pound mass (M)lbf pound force (MLlt")M mass (M), Mach numberMB marginal benefitMe marginal costMP marginal productivityMRS marginal rate of substitutionMRT marginal rate of transformationm mass (M), mass rate of flow (Mit), hydraulic mean depth or radius (L)

N speed of rotation (rev/min)Ns specific speed (turbines)Nu unit speed (rotodynamic machines)n porosity, ratio of wave group velocity to phase velocity (CalC)n s specific speed (pumps)

o outflow (L 3 It)l5 average outflow (L 3 It)OMR operation, maintenance and repairs

P force (MLlt") , wetted perimeter (L), power (ML"lt 3 ) , principal investment,precipitation (rainfall)

Pu unit powerp pressure (MILt")ppm parts per millionPat atmospheric pressure (MILt")Pv vapour pressure (MILt 2

)

Q discharge rate (L31t) , heat (ML2It2 )

Qu unit dischargeq discharge per unit width (L"It)q velocity vector (Lit)lib rate of bed load transport per unit width (L2 It)qs rate of suspended load transport per unit width

SSfSFSFSos,

uu

list of Principal Symbols

universal gas constant (L21t2 T), Reynolds number, rainfall amount (L 3)

Reynolds number based on shear velocity (v'd/v)Richardson numberdegrees Rankineradius (L), (suffix) ratio of model quantity/prototype quantity

specific gravity, storage (L 3) , degree of saturation, storage constant

slope of energy grade line (LIL)shape factor (sand grains)flow net shape factorbed slope (LIL)specific gravity of solids

temperature (1), wave period (t), torque (ML 2/t2), transmissibility (L 2/t)time (t), wind duration (t)time of concentration (t)recurrence interval (t)duration of rainfall (t)

internal energy (ML 2 It 2) , wind speed (Lit)

specific internal energy (L 2 I t 2)

xv

YYcYnYoyY'6.Z or z;~

am{3

'Y'Ys6e€s

8

volume (L 3)

volume of voids (L3)velocity (Lit)time average velocity (turbulent flow) (Lit) (sections 1.5.4,4.1.3,7.2.3);sectional average velocity (sections 3.1, 3.2, 3.3, 3.4.1, 3.4.2)radial (flow) component of velocity in a rotodynamic machine (Lit)velocity of nozzle jet (Lit)seepage velocity (ch, 9) (Lit)shear velocity V(To/ p) (Lit)absolute surge wave speed (Lit), rotodynamic whirl component of velocity (Lit)

weight (MLlt 2) , Weber number, work (ML 2It2

)

work against pressure (ML 21t2)

work against shear (ML 21t2)

shaft work (ML 2It2)

settling velocity (sand particles) (Lit)

distance measured from wall (L)critical depth (L)uniform (normal) depth (L)depth (generally) in an open channel (L)centroid of section measured from water surface (L)centre of pressure measured from water surface (L)height of weir (L)summation ofapproaches (equivalent or equal to)

thermal molecular diffusivity (L2 It), anglemass molecular diffusivity (L2 It)angle, constant of proportionality in es =(3especific (unit) weight (MIL2t2

)

specific weight of solid matter (MIL2 t 2)

boundary layer thickness (L)eddy kinematic viscosity (L2 It)eddy diffusity for suspended load (L 2 It)angle, temperature (1)

xvi

1111h11mJ..L

vPPs(J

acag

"Tc

"0wornt;

list of Principal Symbols

efficiency, small amplitude wave form (L)hydraulic efficiencymechanical efficiencydynamic molecular viscosity (MILt), discharge factorkinema tic molecular viscosity (L 2 It)density (MIL3)density of solid matter (MIL3

)

surface tension (Mlt 2) , standard deviation, wave number (2n/T)

critical cavitation numbergeometric standard deviationshear stress (MILt 2

)

critical shear stress (MILt 2)

wall shear stress (MILt 2)

angular velocity (rad/t)Cauchy number