Mechanics of Fluids The English Language Book Society is funded by the Overseas Development Administration of the British Government. It makes available low-priced, unabridged editions of British publishers' textbooks to students in developing countries. Below is a list of some other books on mechanical engineering published under ELBS imprint. Benham and Crawford Mechanics of Engineering Materials Longman Collett and Hope Engineering Measurements Longman Douglas Solving Problems in Fluid Mechanics Vols 1 and 2 Longman Douglas, Gasiorek and Swaffield Fluid Mechanics Longman Grosjean Principles of Dynamics Stanley Thornes Harrison and Nettleton Principles of Engineering Mechanics Edward Arnold Hughes and Martin Basic Engineering Mechanics Macmillan Joel Basic Engineering Thermodynamics Longman Rogers and Mayhew Engineering Thermodynamics Longman Spalding and Cole Engineering Thermodynamics Edward Arnold Mechanics of Fluids Sixth Edition B. S. MASSEY Reader (Emeritus) in Mechanical Engineering, University College London Springer-Science+Business Media, B.V. © B. S. Massey 1968, 1970, 1975, 1979, 1983, 1989 Originally published by Chapman and Hall in 1989. ISBN 978-0-412-36770-0 ISBN 978-1-4899-3126-9 (eBook) DOI 10.1007/978-1-4899-3126-9 All rights reserved. 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 or otherwise, without the prior written permission of the publishers. First published 1968 Second edition 1970 Third edition 1975 Fourth edition 1979 Fifth edition 1983 Reprinted 1984 (twice), 1986, 1987 (twice), 1988 Sixth edition 1989 ELBS edition first published 1970 ELBS edition of third edition 1975 ELBS edition of fourth edition 1979 Reprinted 1980 ELBS edition of fifth edition 1983 Reprinted 1988 ELBS edition of sixth edition 1989 To the generations of engineering students of University College London, from whom I have leamt so much Contents Preface xiii Prologue Units and related matters xv Dimensional analysis xx Further reading xxvii 1 Fundamental Concepts Relating to Fluids 1.1 The characteristics of fluids 1 1.2 Properties of fluids 4 1.3 The perfeet gas: equation of state 10 1.4 Compressibility 11 1.5 Viscosity 12 1.6 Surface tension 22 Reference 25 Further reading 26 Problems 26 2 Fluids in Equilibrium (Fluid 'Staties') 2.1 Introduction 27 2.2 Variation ofpressure with position in a fluid 27 2.3 The measurement of press ure 32 2.4 Hydrostatic thrusts on submerged surfaces 41 2.5 Buoyancy 49 2.6 The stability of bodies in fluids 52 2.7 Equilibrium of moving fluids 60 Further reading 64 Problems 64 3 The Principles of Fluid Motion 3.1 Introduction 69 3.2 Variation of flow parameters in time and space 69 3.3 Describing the pattern of flow 70 3.4 Continuity 74 3.5 Bernoulli's equation 76 3.6 General energy equation for steady flow of any fluid 80 3.7 Press ure variation perpendicular to streamlines 90 3.8 Simple applications of Bernoulli's equation 92 References 110 Further reading 111 Problems 111 4 The Momentum Equation 4.1 Introduction 113 4.2 The momentum equation for steady flow 113 vii viii CONTENTS 4.3 Applications of the momentum equation 117 Further reading 131 Problems 131 5 Two Kinds of Flow 5.1 Introduction 134 5.2 Reynolds's demonstration of the different kinds of flow 134 5.3 The criterion of flow 137 5.4 Laminar and turbulent flow in pipes 141 5.5 Eddy viscosity and the mixing length hypo thesis 146 5.6 The boundary layer and the viscous sub-Iayer 148 5.7 Distribution of shear stress in a circular pipe 150 Further reading 152 Problems 152 6 Laminar Flow between Solid Boundaries 6.1 Introduction 154 6.2 Steady laminar flow in circular pipes: the Hagen-Poiseuille law' 154 6.3 Steady laminar flow between parallel planes 160 6.4 Steady laminar flow between paral1el planes, one of which is moving 165 6.5 The measurement of viscosity 169 6.6 Fundamentals of the theory of hydrodynamic lubrication 176 6.7 Laminar flow through porous media 193 References 196 Further reading 197 Problems 197 7 Turbulent Flow in Pipes 7.1 Introduction 199 7.2 Head lost to friction in a pipe 199 7.3 Variation of friction factor 201 7.4 Friction in non-circular conduits 207 7.5 Other head losses in pipes 208 7.6 Total head and pressure Iines 217 7.7 Combination of pipes 220 7.8 Conditions near the entry to the pipe 225 7.9 Quasi-steady flow in pipes 227 References 230 Further reading 230 Problems 231 8 Boundary Layers and Wakes 8.1 Introduction 235 8.2 Description of the boundary layer 235 8.3 The thickness of the boundary layer 238 8.4 The momentum equation applied to the boundary layer 239 8.5 The laminar boundary layer on a flat plate with zero pressure gradient 242 CONTENTS ix 8.6 The turbulent boundary layer on a smooth flat plate with zero press ure gradient 246 8.7 Friction drag for laminar and turbulent boundary layers together 249 8.8 Etfect of press ure gradient 251 8.9 Boundary layer control 269 8.10 Etfect of compressibility on drag 270 8.11 Distribution of velocity in turbulent flow 272 8.12 Free turbulence 280 References 281 Further reading 281 Problems 282 9 Physical Similarity 9.1 Introduction 285 9.2 Types of physical similarity 286 9.3 Ratios of forces arising in dynamic similarity 288 9.4 The application of dynamic similarity 294 9.5 Ship resistance 297 Further reading 302 Problems 302 10 The Flow of an Ideal Fluid 10.1 Introduction 304 10.2 The stream function 305 10.3 Circulation and vorticity 307 10.4 Velocity potential 310 10.5 Flow nets 312 10.6 Combining flow patterns 315 10.7 Basic patterns of flow 317 10.8 Combinations of basic flow patterns 326 10.9 Elementary aerofoil theory 339 References 345 Further reading 345 Problems 346 11 Flow with a Free Surface 11.1 Introduction 349 11.2 Types of flow in open channels 349 11.3 The steady-flow energy equation for open channels 351 11.4 Steady uniform flow - the Chezy equation 354 11.5 The boundary layer in open channels 358 11.6 Optimum shape of cross-section 359 11.7 Flow in closed conduits on"ly partly full 361 11.8 Simple waves and surges in open channels 362 11.9 Specific energy and jllternative depths of flow 365 11.10 The hydraulicjump 370 11.11 The occurrence of critical conditions 375 11.12 Gradually varied flow 386 11.13 Oscillatory waves 394 x CONTENTS 11.14 Conclusiop 406 References 407 Further reading 407 Problems 407 12 Flow with Appreciable Changes of Density 12.1 Introduction 410 12.2 Thermodynamic concepts 410 12.3 Energy equation with variable density: static and stagnation temperature 413 12.4 Elastic waves 415 12.5 Shock waves 420 12.6 Supersonic flow round a corner 431 12.7 The Pitot tube in flow with variable density 436 12.8 One-dimensional flow with negligible friction 438 12.9 High-speed flow past an aerofoil 446 12.10 Flow with variable density in pipes of constant cross-section 448 12.11 Analogy between flow with variable density and flow with a free surface 458 References 459 Further reading 460 Problems 460 13 Unsteady Flow 13.1 Introduction 463 13.2 Inertia pressure 463 13.3 Pressure transients 466 13.4 Surge tanks 490 Reference 493 Further reading 493 Problems 493 14 The Principles of Fluid Machines 14.1 Introduction 496 14.2 Reciprocating pumps 497 14.3 Rotodynamic machines 501 14.4 Rotodynamic pumps 532 14.5 Hydrodynamic transmissions 550 14.6 The effect of size on the efficiency of fluid machines 554 References 555 Further reading 555 Problems 556 Appendix 1 First and Second Moments and Centroids 561 Al.1 First moments and centroids 561 A1.2 Second moments 562 Appendix 2 Measurements and Flow Visualization 565 A2.1 Measurement ofvelocity 565