Macmillan International College Edition Titles of related interest: J A Fox: An Introduction to Engineering Fluid Mechanics B Henderson-Sellers: Reservoirs N T Kottegoda: Stochastic Water Resources Technology Essentials of Engineering Hydraulics JONAS M K DAKE B.Se (Eng.) (London); M.Sc.Teeh (Man.); Se.D (M.LT.) M ANSTI © Jonas M K Dake 1972,1983 All rights reserved No part of this publication may be reproduced or transmitted, in any form or by any means, without permission First edition 1972 Reprinted with corrections 1974 Second edition 1983 Published by THE MACMILLAN PRESS LTD London and Basingstoke Companies and representatives throughout the world In association with; African Network of Scientific and Technological Institutions P.O Box 30592 Nairobi Kenya ISBN 978-0-333-34335-7 ISBN 978-1-349-17005-0 (eBook) DOI 10.1007/978-1-349-17005-0 Typeset by MULTIPLEX techniques ltd Contents Foreword to the First Edition Preface to the Second (Metric) Edition Preface to the First Edition List of Principal Symbols IX X Xl XIII PART ONE ELEMENTARY FLUID MECHANICS Fundamental concepts of fluid mechanics 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Introduction The Continuum Units of Measurement Some Important Fluid Properties Transfer Phenomena Types of Flow Boundary Layer Concepts and Drag Fluids in Static Equilibrium Methods of analysis 2.1 Control Volume Concepts 2.2 The Basic Physical Laws of Mass, Energy and Momentum Transport 2.3 Conservation of Mass 2.4 The Linear Momentum Principle 2.5 The Principle of Conservation of Energy: First Law of 2.6 3 13 18 20 25 Thermodynamics The Moment of Momentum Concept 40 41 42 45 52 60 Steady incompressible flow through pipes 3.1 3.2 3.3 3.4 3.5 Introduction Enclosed Flow at a Low Reynolds Number Momentum and Energy Correction Factors Pipe Flow at a High Reynolds Number Analysis of Pipe Systems 63 64 70 71 87 Contents vi Flow in non-erodible open channels 401 402 403 404 405 406 95 107 113 123 133 137 Experimental fluid mechanics 501 502 503 504 505 Introduction Momentum Concepts Energy Concepts Gradually Varied Flow Open Channel Surges Miscellaneous Information Introduction Dynamic Similarity Physical Significance of Modelling Laws Models of Rivers and Channels Dimensional Approach to Experimental Analysis 142 143 146 160 165 Water pumps and turbines 601 602 603 604 605 606 Introduction The Pelton Wheel Turbine Reaction Machines Selection and Installation of Pumps and Turbines Cavitation Pumping from Wells 173 175 178 190 196 205 PART TWO SPECIALIZED TOPICS IN CIVIL ENGINEERING Flow in erodible open channels 701 702 703 704 Properties of Sediments Mechanics of Sediment Transport Design of Stable Alluvial Channels Moveable Bed Models 213 219 229 236 Physical hydrology and water storage 801 802 803 804 805 806 807 808 Introduction Precipitation Evaporation and Transpiration Infiltration Surface Run-off (Overland Flow) Stream Run-off Storage and Streamflow Routeing Design Criteria 242 244 249 252 254 258 266 276 Contents vii Groundwater and seepage 9.1 9.2 9.3 Introduction Fundamentals of Groundwater Hydraulics Some Practical Groundwater Flow Problems 282 285 298 10 Sea waves and coastal engineering 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 Introduction Wave Generation and Propagation Small Amplitude Wave Theory Finite Amplitude Waves Changes in Shallow Water Wave Reflection and Diffraction Coastal Processes Coastal Enginee ring 312 315 319 326 327 331 334 340 11 Fundamental economics of water resources development 11.1 Introduction 11.2 Basic Economic and Technological Concepts (Decision Theory) 346 349 Problems Appendix: Notes on Flow Measurement A.l Velocity-Area Methods A.2 Direct Discharge Methods 401 404 Index 412 Foreword to the First Edition by 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, a friend and former student of mine, has attempted to bring out the principles of physics which are likely to be of future importance to hydraulic engineering science, with particular reference to water resources problems With the greater importance and complexity of water resource exploitation likely to occur in the future, our analysis and design of engineering problems in this field must become more exact, and there are several parts of Dr Dake's book which introduce new ideas In the past half-century, the science of fluid mechanics has been largely dominated by the demands of aeronautical engineering; in the future it is not too much to believe that the efficient supply, distribution, drainage and re-use of the world's water supply for the benefit of an increasing population will present the most urgent of problems to the engineer I feel particularly honoured, too, in that this book must be among the first technical 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 help the establishment of degree courses at Kumasi, and to produce skilled technological manpower That a book of this standard should now come forward is a source of pleasure to all those who have helped, and an indication of future success J R D FRANCIS 1972 ix Preface to the Second Edition The Second Edition of Essentials ofEngineering Hydraulics has retained the primary objectives and structure of the original book However, the rational metric system of units (Systerne International d'Unites) has been adopted generally although a few examples and approaches have retained the imperial units The scope of the book has been increased by inclusion of section 1.8, 'Fluids in Static Equilibrium' and sub-sections 8.7.3 and 9.3.5 'Routeing of Floods in River Channels' and 'The Transient State of the Well Problem', respectively There has been general updating A guide to the solution of the tutorial problems at the end of the book is available for restricted distribution to lecturers upon official request to the publisher Jonas M K Dake Nairobi 1982 x Preface to the First Edition Teaching of engineering poses a challenge which, although also relevant to the developed countries, carries with it enormous pressures in the developing countries The immediate need for technical personnel for rapid development and the desire to design curricula and training methods to suit particular local needs provide strong incentives which could, without proper control, compromise engineering science and its teaching in the developing world The generally accepted role of an engineering institution is the provision of the scientific 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 not compromising on basic engineering science and standards, they reflect sufficient background preparation for the appropriate level of local development This text has been written to provide in one volume an adequate coverage of the basic principles of fluid flow and summaries of specialized topics in hydraulic engineering, using mainly examples from African and other developing countries A survey of fluid mechanics and hydraulics syllabuses in British universities reveals that the courses are fairly uniform up to second year level but vary widely in the final year This book is well suited to these courses Students in those universities which emphasize civil engineering fluid mechanics will also find this book 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 and details of the mechanics of fluid flow A good knowledge of general mechanics and mathematics as well as introductory lectures in fluid mechanics covering hydrostatics and broad definitions are assumed Coverage in Part I is suitable up to the end of the second year (3-year degree courses) or third year (4-year degree courses) of civil and mechanical engineering undergraduate studies Part lIon Specialized Topics in Civil Engineering is meant mainly for final-year civil engineering degree students Treatment is concentrated on discussions of the physics and concepts which have led to certain mathematical results Equations are generally not derived but discussions centre on the merits and limitations of the equations The general aim of the book is to emphasize the physical concepts of fluid flow and hydraulic engineering processes with the hope of providing a foundation which is suitable for both academic and non-academic postgraduate work Toxi 404 Essentials of Engineering Hydraulics submerged float is comparatively large so that the effect of the smaller surface float can be neglected Rod floats (or chain floats) are made from wooden poles or hollow metal cylinders weighted at one end so as to float in an approximately upright position with the unweighted end slightly above the water surface Chain floats are pieces of wood connected by a chain They also float approximately upright Rod or chain floats should reach as close as practicable to the bottom of the channel without touching it at any point on their path The velocity of the floats are generally multiplied by 0·92- 0·94 to get the mean velocity in the vertical of the path A,1.4 Salt-velocity Method A concentrated salt solution (or brine) is introduced into the flow This increases the electrical conductivity of the water Electrodes connected to an ammeter or any other electrical recorder are installed at one or two points of observation below the place where the salt solution is introduced An increase in the electric current is indicated when the prism of water containing salt passes the electrodes By registering the time of travel of the brine over a fixed distance the flow velocity can be calculated In a pipe or conduit of uniform cross sectional area the length of the reach divided by the time of travel gives the mean velocity and the discharge is the product of this mean velocity and the cross sectional area If the cross section of the conduit is not uniform, the volume of the reach must be determined This volume divided by the time of travel gives the discharge The main difficulties in the salt method are correction for dispersion or diffusion of the salt in solution and the volumetric effect of the solution on the normal flow rate A.2 Direct Discharge Methods A.2.1 Venturi Meter, OrificePlate and Dall Tube pipe pipe Fig A.2 Venturi meter The Venturi meter is appropriate for measuring discharges in pipes It is principally a short length of a pipe which tapers from a known diameter to a throat from where it again expands to a fixed diameter Appendix: Notes on Flow Measurement 405 With reference to Fig A.2,let the pipe cross-sectional area be a1 and the venturi throat area be a2 Also let the pressure head at inlet to the venturi tube be h and at the throat be h The corresponding velocities are V1 and V2 respectively Applying the energy equation, v~/2g + h1 =v~/2g + h (A.3) Combining equation (A.3) with the continuity equation yields Q = a2v2 = Cda1a2 y'[2g(h - h 2)/(ai - a~)] (A.4) where the coefficient of discharge Cd (less than unity) corrects for losses due to resistance to flow, flow contraction in the meter and other minor effects By measuring (h - h2 ) on a differential manometer and knowing Cd from a previous calibration, the discharge through the pipe can be calculated from equation (A.4) Other instruments for measuring flow through pipes which are based on the same principle of flow contraction through a section are the orifice plate and the Dall tube Discharge through them is also given by equation (A.4) In general their coefficient of discharge depends on the shape of the instrument, the form of orifice edge, the ratio of orifice diameter to the pipe dimensions and the roughness of the pipe walls On the whole the orifice plate is simple and cheap and occupies a small length but produces a large degradation of energy The venturi meter is relatively complex and expensive but produces a much smaller degradation of energy The Dall tube is of moderate cost, givesa greater head difference and provides less energy degradation than either the orifice plate or the venturi tube It is accordingly much more efficient All three instruments are suitable for measurement of discharge of a liquid or a gas in a closed conduit However, they are unsuitable for measurement in the laminar flow range since their coefficients of discharge are extremely variable in this range A.2.2 The Venturi Flume The venturi flume is based on the venturi principle discussed in subsection 4.3.4· and is used for flow measurement in open channels The value of its coefficient of discharge, which accounts for friction and contraction effects, ordinarily lies between 0·95 and 1·00 It can be kept at 0·98 or above if care is taken to have smooth surfaces and to round off all corners so as to lead the flow to the throat of the flume without contractions or unnecessary turbulence The venturi flume is suitable for measuring flow in small rivers in which the discharge does not exceed 20 m3ts (710 ft /s) However, the largest known was reported to have been suitable for measuring 50 m Is ( 1800 ft Is) One type of a standard design which combines the principle of the venturi with that of the broad-crested weir is the Parshall flume in which geometrical ratios and other conditions of installation are specified 406 Essentials of Engineering Hydraulics A.2.3 Weirs Weirs, especially sharp-crested ones, are commonly used to measure small quantities of water flow, generally less than about 0·25 m 3/s (9 ft 3/s) However, although sharp-crested weirs are primarily thought of in connection with water flow measurement, they appear in many structures as channel control and also serve as the basis of spillway design The nappe, immediately after leaving the sharp crest, suffers a contraction which corresponds to the contraction of a jet issuing from an edged orifice According to test results the shape of the nappe can be determined as a function of the overflow head Generally given data in this regard and for flow measurement are valid only if the upper and lower nappe are subject to full atmospheric pressure Insufficient aeration causes a reduction of pressure beneath the nappe due to removal of air by the over-falling jet and a change in the form of the.jet Many formulae for the overflow coefficient for sharp-crested weirs with a horizontal crest have been developed However few are accurate One of the most accurate seems to be that given by Rehbock This gives discharge Q(m 3/s) as: (A.5) where h o = height of the vertical weir plate (m) he = h + 0·0011 (m) h = overflow head above weir crest (m) B = width of the weir (m) Equation (A.5) is valid only within the limits 0·15 < h o < 1·22 (m) and h < 4ho and under the condition that the lower as well as the upper nappe is fully exposed to atmospheric pressure Triangular (or V-notch) weirs permit a more accurate measurement of smaller discharges because the discharge of a V-notched weir increases more rapidly with head in comparison with a horizontal crest weir The equation for discharge over a V-notched weir is given by theory as: 85 Q = ,j(2g) tan () /2 h / (A.6) where () is the included angle and h is the water head above the vertex Equation (A.6) has to be corrected by a factor expressing the influence of the deviations from ideal conditions assumed by theory Thus Q = J1 • 15 ,j(2g) tan () /2 h / (A.7) Appendix: Notes on Flow Measurement 407 where p = 0.565 + 0.0087 h- / (A.8) when metric units are used The coefficient for weirs with a crest made of a circular arc can be computed from Rehbock's empirical formula: p.=0.312+y[0·3-0.01 (5-h/r)2] +0·09h/h o (A.9) where r is the radius of curvature of the rounded top Equation (A.9) is valid within the limits 0·02 < r< h o (m) and h