[.B.S.E., M.I.E.T., F.H.E.A. Environment, Heriot-Watt University

Sixth edition JOHN F. DOUGLAS ".Sc, Ph.D., A.C.G.I., D.I.C., C.Eng., M.I.C.E., M.l.Mech.E. Fomieily of London South Bank University JANUSZ M. GASIOREK B.Sc, Ph.D., C.Eng., M.l.Mech.E., M.C.I.B.S.E. Formerly of London South Bank University JOHN A. SWAFFIELD F.R.S.E., B.Sc, M.PhiL, Ph.D., C.Eng., M.R.Ae.S., F.C.I.B.S. Emeritus Professor, School of the Built Environment, Heriot-Watt University, Edinburgh LYNNE B. JACK [.B.S.E., M.I.E.T., F.H.E.A. Environment, Heriot-Watt University Prentice Hall is an imprint of Harlow, England London New York Boston San Francisco Toronto Sydney Singapore Hong Kong Tokyo Seoul Taipei New Delhi Cape Town Madrid Mexico City Amsterdam Munich Paris Milan

Contents Preface to the Sixth Edition xix Preface to the Fifth Edition xxi Preface to the Fourth Edition xxiii Acknowledgements xxvi List of Computer Programs xxviii List of Symbols xxx PART I ELEMENTS OF FLUID MECHANICS xxxiv Chapter 1 Fluids and their Properties 2 1.1 Fluids 4 1.2 Shear stress in a moving fluid 4 1.3 Differences between solids and fluids 5 1.4 Newtonian and non-newtonian fluids 6 1.5 Liquids and gases 7 1.6 Molecular structure of materials 7 1.7 The continuum concept of a fluid 9 1.8 Density 10 1.9 Viscosity 11 1.10 Causes of viscosity in gases 12 1.11 Causes of viscosity in a liquid 13 1.12 Surface tension 14 13 Capillarity 15 14 Vapour pressure 16 15 Cavitation 17 16 Compressibility and the bulk modulus 17 17 Equation of state of a perfect gas 19 18 The universal gas constant 19 19 Specific heats of a gas 19 20 Expansion of a gas 20 Concluding remarks 22 Summary of important equations and concepts 22

Chapter 2 Pressure and Head 24 2.1 Statics of fluid systems 26 2.2 Pressure 27 2.3 Pascal's law for pressure at a point 28 2.4 Variation of pressure vertically in a fluid under gravity 29 2.5 Equality of pressure at the same level in a static fluid 30 2.6 General equation for the variation of pressure due to gravity from point to point in a static fluid 32 2.7 Variation of pressure with altitude in a fluid of constant density 33 2.8 Variation of pressure with altitude in a gas at constant temperature 34 2.9 Variation of pressure with altitude in a gas under adiabatic conditions 35 2.10 Variation of pressure and density with altitude for a constant temperature gradient 38 2.11 Variation of temperature and pressure in the atmosphere 39 2.12 Stability of the atmosphere 41 2.13 Pressure and head 43 2.14 The hydrostatic paradox 44 2.15 Pressure measurement by manometer 45 2.16 Relative equilibrium 51 2.17 Pressure distribution in a liquid subject to horizontal acceleration 51 2.18 Effect of vertical acceleration 52 2.19 General expression for the pressure in a fluid in relative equilibrium 52 2.20 Forced vortex 56 Concluding remarks 57 Summary of important equations and concepts 57 Problems 57 Chapter 3 Static Forces on Surfaces. Buoyancy 60 3.1 Action of fluid pressure on a surface 62 3.2 Resultant force and centre of pressure on a plane surface under uniform pressure 62 3.3 Resultant force and centre of pressure on a plane surface immersed in a liquid 63 3.4 Pressure diagrams 68 3.5 Force on a curved surface due to hydrostatic pressure 71 3.6 Buoyancy 73 3.7 Equilibrium of floating bodies 76 3.8 Stability of a submerged body 76 3.9 Stability of floating bodies 77 3.10 Determination of the metacentric height 78 3.11 Determination of the position of the metacentre relative to the centre of buoyancy 78 3.12 Periodic time of oscillation 81 3.13 Stability of a vessel carrying liquid in tanks with a free surface 82 Concluding remarks 85 Summary of important equations and concepts 85 Problems 85

PART II CONCEPTS OF FLUID FLOW 88 Chapter 4 Motion of Fluid Particles and Streams 90 4.1 Fluid flow 92 4.2 Uniform flow and steady flow 93 4.3 Frames of reference 93 4.4 Real and ideal fluids 94 4.5 Compressible and incompressible flow 94 4.6 One-, two- and three-dimensional flow 95 4.7 Analysing fluid flow 96 4.8 Motion of a fluid particle 96 4.9 Acceleration of a fluid particle 98 4.10 Laminar and turbulent flow 100 4.11 Discharge and mean velocity 102 4.12 Continuity of flow 104 4.13 Continuity equations for three-dimensional flow using Cartesian coordinates 107 4.14 Continuity equation for cylindrical coordinates 109 Concluding remarks 109 Summary of important equations and concepts 110 Problems 110 Chapter 5 The Momentum Equation and its Applications 112 5.1 Momentum and fluid flow 114 5.2 Momentum equation for two- and three-dimensional flow along a streamline 115 5.3 Momentum correction factor 116 5.4 Gradual acceleration of a fluid in a pipeline neglecting elasticity 119 5.5 Force exerted by a jet striking a flat plate 120 5.6 Force due to the deflection of a jet by a curved vane 123 5.7 Force exerted when a jet is deflected by a moving curved vane 124 5.8 Force exerted on pipe bends and closed conduits 126 5.9 Reaction of a jet 129 5.10 Drag exerted when a fluid flows over a flat plate 136 5.11 Angular motion 138 5.12 Euler's equation of motion along a streamline 141 5.13 Pressure waves and the velocity of sound in a fluid 143 5.14 Velocity of propagation of a small surface wave 146 5.15 Free surface wave speed in unconfined fluid volumes 148 5.16 Differential form of the continuity and momentum equations 150 5.17 Computational treatment of the differential forms of the continuity and momentum equations 153 5.18 Comparison of computational fluid dynamics (CFD) methodologies 158 Concluding remarks 164 Summary of important equations and concepts 165 Further reading 165 Problems 166

Chapter 6 The Energy Equation and its Applications 168 6.1 Mechanical energy of a flowing fluid 170 6.2 Steady flow energy equation 174 6.3 Kinetic energy correction factor 176 6.4 Applications of the steady flow energy equation 177 6.5 Representation of energy changes in a fluid system 180 6.6 The Pitot tube 182 6.7 Determination of volumetric flow rate via Pitot tube 183 6.8 Computer program VOLFLO 185 6.9 Changes of pressure in a tapering pipe 185 6.10 Principle of the venturi meter 187 6.11 Pipe orifices 189 6.12 Limitation on the velocity of flow in a pipeline 190 6.13 Theory of small orifices discharging to the atmosphere 190 6.14 Theory of large orifices 194 6.15 Elementary theory of notches and weirs 195 6.16 The power of a stream of fluid 199 6.17 Radial flow 200 6.18 Flow in a curved path. Pressure gradient and change of total energy across the streamlines 201 6.19 Vortex motion 204 Concluding remarks 210 Summary of important equations and concepts 211 Problems 211 Chapter 7 Two-dimensional Ideal Flow 214 7.1 Rotational and irrotational flow 216 7.2 Circulation and vorticity 218 7.3 Streamlines and the stream function 220 7.4 Velocity potential and potential flow 222 7.5 Relationship between stream function and velocity potential. Flow nets 226 7.6 Straight-line flows and their combinations 230 7.7 Combined source and sink flows. Doublet 238 7.8 Flow past a cylinder 243 7.9 Curved flows and their combinations 246 7.10 Flow past a cylinder with circulation. Kutta-Joukowsky's law 251 7.11 Computer program ROTCYL 254 Concluding remarks 255 Summary of important equations and concepts 255 Problems 256 PART III DIMENSIONAL ANALYSIS AND SIMILARITY 258 Chapter 8 Dimensional Analysis 260 8.1 Dimensional analysis 262 8.2 Dimensions and units 262

Contents xi 8.3 Dimensional reasoning, homogeneity and dimensionless groups 262 8.4 Fundamental and derived units and dimensions 263 8.5 Additional fundamental dimensions 265 8.6 Dimensions of derivatives and integrals 267 8.7 Units of derived quantities 268 8.8 Conversion between systems of units, including the treatment of dimensional constants 268 8.9 Dimensional analysis by the indicial method 271 8.10 Dimensional analysis by the group method 273 8.11 The significance of dimensionless groups 281 Concluding remarks 282 Summary of important equations and concepts 282 Further reading 282 Problems 283 Chapter 9 Similarity 284 9.1 Geometric similarity 288 9.2 Dynamic similarity 288 9.3 Model studies for flows without a free surface. Introduction to approximate similitude at high Reynolds numbers 293 9.4 Zone of dependence of Mach number 295 9.5 Significance of the pressure coefficient 296 9.6 Model studies in cases involving free surface flow 297 9.7 Similarity applied to rotodynamic machines 299 9.8 River and harbour models 301 9.9 Groundwater and seepage models 307 9.10 Computer program GROUND, the simulation of groundwater seepage 312 9.11 Pollution dispersion modelling, outfall effluent and stack plumes 313 9.12 Pollutant dispersion in one-dimensional steady uniform flow 316 Concluding remarks 321 Summary of important equations and concepts 321 Further reading 322 References 322 Problems 323 PART IV BEHAVIOUR OF REAL FLUIDS 324 Chapter 10 Laminar and Turbulent Flows in Bounded Systems 326 10.1 Incompressible, steady and uniform laminar flow between parallel plates 328 10.2 Incompressible, steady and uniform laminar flow in circular cross-section pipes 333 10.3 Incompressible, steady and uniform turbulent flow in bounded conduits 337

xii Contents 10.4 Incompressible, steady and uniform turbulent flow in circular cross-section pipes 340 10.5 Steady and uniform turbulent flow in open channels 344 10.6 Velocity distribution in turbulent, fully developed pipe flow 345 10.7 Velocity distribution in fully developed, turbulent flow in open channels 354 10.8 Separation losses in pipe flow 354 10.9 Significance of the Colebrook-White equation in pipe and duct design 361 10.10 Computer program CBW 362 Concluding remarks 363 Summary of important equations and concepts 364 Further reading 364 Problems 364 Chapter 11 Boundary Layer 366 11.1 Qualitative description of the boundary layer 368 11.2 Dependence of pipe flow on boundary layer development at entry 370 11.3 Factors affecting transition from laminar to turbulent flow regimes 371 11.4 Discussion of flow patterns and regions within the turbulent boundary layer 372 11.5 Prandtl mixing length theory 374 11.6 Definitions of boundary layer thicknesses 377 11.7 Application of the momentum equation to a general section of boundary layer 378 11.8 Properties of the laminar boundary layer formed over a flat plate in the absence of a pressure gradient in the flow direction 379 11.9 Properties of the turbulent boundary layer over a flat plate in the absence of a pressure gradient in the flow direction 384 11.10 Effect of surface roughness on turbulent boundary layer development and skin friction coefficients 388 11.11 Effect of pressure gradient on boundary layer development 388 Concluding remarks 391 Summary of important equations and concepts 391 Further reading 392 Problems 392 Chapter 12 Incompressible Flow around a Body 394 12.1 Regimes of external flow 396 12.2 Drag 397 12.3 Drag coefficient and similarity considerations 401 12.4 Resistance of ships 403 12.5 Flow past a cylinder 407 12.6 Flow past a sphere 411 12.7 Flow past an infinitely long aerofoil 418

Contents xiii 12.8 Flow past an aerofoil of finite length 426 12.9 Wakes and drag 430 12.10 Computer program WAKE 435 Concluding remarks 436 Summary of important equations and concepts 436 Problems 436 Chapter 13 Compressible Flow around a Body 438 13.1 Effects of compressibility 440 13.2 Shockwaves 445 13.3 Oblique shock waves 455 13.4 Supersonic expansion and compression 457 13.5 Computer program NORSH 459 Concluding remarks 459 Summary of important equations and concepts 460 Problems 460 PART V STEADY FLOW IN PIPES, DUCTS AND OPEN CHANNELS 462 Chapter 14 Steady Incompressible Flow in Pipe and Duct Systems 464 14.1 General approach 466 14.2 Incompressible flow through ducts and pipes 467 14.3 Computer program SIPHON 470 14.4 Incompressible flow through pipes in series 471 14.5 Incompressible flow through pipes in parallel 473 14.6 Incompressible flow through branching pipes. The three-reservoir problem 475 14.7 Incompressible steady flow in duct networks 478 14.8 Resistance coefficients for pipelines in series and in parallel 486 14.9 Incompressible flow in a pipeline with uniform draw-off 489 14.10 Incompressible flow through a pipe network 489 14.11 Head balance method for pipe networks 490 14.12 Computer program HARDYC 491 14.13 The quantity balance method for pipe networks 493 14.14 Quasi-steady flow 495 Concluding remarks 501 Summary of important equations and concepts 502 Further reading 502 Problems 502 Chapter 15 Uniform Flow in Open Channels 506 15.1 Flow with a free surface in pipes and open channels 508 15.2 Resistance formulae for steady uniform flow in open channels 510

15.3 Optimum shape of cross-section for uniform flow in open channels 515 15.4 Optimum depth for flow with a free surface in covered channels 519 Concluding remarks 521 Summary of important equations and concepts 522 Further reading 522 Problems 522 Chapter 16 Non-uniform Flow in Open Channels 524 16.1 Specific energy and alternative depths of flow 526 16.2 Critical depth in non-rectangular channels 528 16.3 Computer program CRITNOR 530 16.4 Non-dimensional specific energy curves 531 16.5 Occurrence of critical flow conditions 532 16.6 Flow over a broad-crested weir 533 16.7 Effect of lateral contraction of a channel 534 16.8 Non-uniform steady flow in channels 537 16.9 Equations for gradually varied flow 538 16.10 Classification of water surface profiles 540 16.11 The hydraulic jump 543 16.12 Location of a hydraulic jump 545 16.13 Computer program CHANNEL 546 16.14 Annular water flow considerations 547 Concluding remarks 550 Summary of important equations and concepts 551 Further reading 551 Problems 551 Chapter 17 Compressible Flow in Pipes 554 17.1 Compressible flow. The basic equations 556 17.2 Steady isentropic flow in non-parallel-sided ducts neglecting friction 557 17.3 Mass flow through a venturi meter 558 17.4 Mass flow from a reservoir through an orifice or convergent-divergent nozzle 561 17.5 Conditions for maximum discharge from a reservoir through a convergent-divergent duct or orifice 562 17.6 The Laval nozzle 563 17.7 Normal shock wave in a diffuser 567 17.8 Compressible flow in a duct with friction under adiabatic conditions. Fanno flow 572 17.9 Isothermal flow of a compressible fluid in a pipeline 576 Concluding remarks 579 Summary of important equations and concepts 580 Problems 580

PART VI FLUID MECHANICS FOR ENVIRONMENTAL CHANGE 582 Chapter 18 Environmental Change and Renewable Energy Technologies 584 18.1 Environmental change 586 18.2 The application of wind turbines to electrical power generation 603 18.3 Wave energy conversion for electrical power generation 616 18.4 Tidal power 632 Concluding remarks 633 Summary of important concepts 634 Further reading 634 References 635 Chapter 19 Environmental Change and Rainfall Runoff Flow Modelling 636 19.1 Gradually varied unsteady free surface flow 638 19.2 Computer program UNSCHAN 646 19.3 Implicit four-point scheme 648 19.4 Flood routeing 650 19.5 The prediction of flood behaviour 652 19.6 Time-dependent urban stormwater routeing 657 19.7 Rainwater and grey water reuse 662 19.8 Combined free surface and pressure surge analysis. Siphonic rainwater systems 670 Concluding remarks 679 Summary of important equations and concepts 679 Further reading 680 References 680 PART VII UNSTEADY FLOW IN BOUNDED SYSTEMS 682 Chapter 20 Pressure Transient Theory and Surge Control 684 20.1 Wave propagation velocity and its dependence on pipe and fluid parameters and free gas 692 20.2 Computer program WAVESPD 698 20.3 Simplification of the basic pressure transient equations 700 20.4 Application of the simplified equations to explain pressure transient oscillations 700 20.5 Surge control 705 20.6 Control of surge following valve closure, with pump running and surge tank applications 706 20.7 Computer program SHAFT 714 20.8 Control of surge following pump shutdown 716 Concluding remarks 721

xvi Contents Summary of important equations and concepts 721 Further reading 722 Problems 723 Chapter 21 Simulation of Unsteady Flow Phenomena in Pipe, Channel and Duct Systems 726 21.1 Development of the St Venant equations of continuity and motion 728 21.2 The method of characteristics 734 21.3 Network simulation 747 21.4 Computer program FM5SURG. The simulation of waterhammer 749 21.5 Computer programs FM5WAVE and FM5GUTT. The simulation of open-channel free surface and partially filled pipe flow, with and without lateral inflow 759 21.6 Simulation of low-amplitude air pressure transient propagation 765 21.7 Computer program FM5AIR. The simulation of unsteady airflowin pipe and duct networks 766 21.8 Low-amplitude air pressure transient propagation and simulation 773 Concluding remarks 787 Summary of important equations and concepts 787 Further reading 788 References 788 PART VIII FLUID MACHINERY. THEORY, PERFORMANCE AND APPLICATION 790 Chapter 22 Theory of Rotodynamic Machines 792 22.1 Introduction 794 22.2 One-dimensional theory 796 22.3 Isolated blade and cascade considerations 804 22.4 Departures from Euler's theory and losses 812 22.5 Compressible flow through rotodynamic machines 818 Concluding remarks 822 Summary of important equations and concepts 822 Further reading 822 Problems 823 Chapter 23 Performance of Rotodynamic Machines 824 23.1 The concept of performance characteristics 826 23.2 Losses and efficiencies 827 23.3 Dimensionless coefficients and similarity laws 833 23.4 Computer program SIM PUMP 839 23.5 Scale effects 840 23.6 Type number 841 23.7 Centrifugal pumps and fans 844

Contents xvii 23.8 Axial flow pumps and fans 846 23.9 Mixed flow pumps and fans 849 23.10 Water turbines 850 23.11 The Pelton wheel 851 23.12 Francis turbines 855 23.13 Axial flow turbines 860 23.14 Hydraulic transmissions 863 Concluding remarks 870 Summary of important equations and concepts 870 Problems 871 Chapter 24 Positive Displacement Machines 874 24.1 Reciprocating pumps 876 24.2 Rotary pumps 887 24.3 Rotary gear pumps 888 24.4 Rotary vane pumps 889 24.5 Rotary piston pumps 890 24.6 Hydraulic motors 892 Concluding remarks 892 Summary of important equations and concepts 893 Problems 893 Chapter 25 Machine-Network Interactions 896 25.1 Fans, pumps and fluid networks 898 25.2 Parallel and series pump operation 905 25.3 Fans in series and parallel 907 25.4 Fan and system matching. An application of the steady flow energy equation 912 25.5 Change in the pump speed and the system 916 25.6 Change in the pump size and the system 919 25.7 Changes in fan speed, diameter and air density 921 25.8 Jet fans 923 25.9 Computer program MATCH 931 25.10 Cavitation in pumps and turbines 932 25.11 Fan and pump selection 937 25.12 Fan suitability 941 25.13 Modelling and simulation of network air flow distribution 944 25.14 Ventilation and airborne contamination as a criterion for fan selection 959 25.15 Computer program CONTAM 966 25.16 Influence of air change rate and free air volume on contamination concentration levels 968 Concluding remarks 977 Summary of important equations and concepts 978 Further reading 979 Problems 979

xviii Contents Appendix 1 Some Properties of Common Fluids 984 A 1.1 Variation of some properties of water with temperature 984 Al.2 Variation of bulk modulus of elasticity of water with temperature and pressure 985 A1.3 Variation of some properties of air with temperature at atmospheric pressure 985 Al.4 Some properties of common liquids 985 Al.5 Some properties of common gases (at/? = 1 atm, T= 273 K) 986 Al.6 International Standard Atmosphere 986 Al.7 Solubility of air in pure water at various temperatures 987 Al.8 Absolute viscosity of some common fluids 987 Appendix 2 Values of Drag Coefficient C D for Various Body Shapes 988 Index 989 Supporting resources Visit www.pearsoned.co.uk/douglas to find valuable online resources Companion Website for students Simulations and computer programs for students, with clear instructions on how to use them to enhance study For instructors Complete, downloadable Solutions Manual For more information please contact your local Pearson Education sales representative or visit www.pearsoned.co.uk/douglas