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

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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.

1 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

2 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 Fluids Shear stress in a moving fluid Differences between solids and fluids Newtonian and non-newtonian fluids Liquids and gases Molecular structure of materials The continuum concept of a fluid Density Viscosity Causes of viscosity in gases Causes of viscosity in a liquid Surface tension Capillarity Vapour pressure Cavitation Compressibility and the bulk modulus Equation of state of a perfect gas The universal gas constant Specific heats of a gas 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.

3 Chapter 2 Pressure and Head Statics of fluid systems Pressure Pascal's law for pressure at a point Variation of pressure vertically in a fluid under gravity Equality of pressure at the same level in a static fluid General equation for the variation of pressure due to gravity from point to point in a static fluid Variation of pressure with altitude in a fluid of constant density Variation of pressure with altitude in a gas at constant temperature Variation of pressure with altitude in a gas under adiabatic conditions Variation of pressure and density with altitude for a constant temperature gradient Variation of temperature and pressure in the atmosphere Stability of the atmosphere Pressure and head The hydrostatic paradox Pressure measurement by manometer Relative equilibrium Pressure distribution in a liquid subject to horizontal acceleration Effect of vertical acceleration General expression for the pressure in a fluid in relative equilibrium Forced vortex 56 Concluding remarks 57 Summary of important equations and concepts 57 Problems 57 Chapter 3 Static Forces on Surfaces. Buoyancy Action of fluid pressure on a surface Resultant force and centre of pressure on a plane surface under uniform pressure Resultant force and centre of pressure on a plane surface immersed in a liquid Pressure diagrams Force on a curved surface due to hydrostatic pressure Buoyancy Equilibrium of floating bodies Stability of a submerged body Stability of floating bodies Determination of the metacentric height Determination of the position of the metacentre relative to the centre of buoyancy Periodic time of oscillation 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.

4 PART II CONCEPTS OF FLUID FLOW 88 Chapter 4 Motion of Fluid Particles and Streams Fluid flow Uniform flow and steady flow Frames of reference Real and ideal fluids Compressible and incompressible flow One-, two- and three-dimensional flow Analysing fluid flow Motion of a fluid particle Acceleration of a fluid particle Laminar and turbulent flow Discharge and mean velocity Continuity of flow Continuity equations for three-dimensional flow using Cartesian coordinates 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 Momentum and fluid flow Momentum equation for two- and three-dimensional flow along a streamline Momentum correction factor Gradual acceleration of a fluid in a pipeline neglecting elasticity Force exerted by a jet striking a flat plate Force due to the deflection of a jet by a curved vane Force exerted when a jet is deflected by a moving curved vane Force exerted on pipe bends and closed conduits Reaction of a jet Drag exerted when a fluid flows over a flat plate Angular motion Euler's equation of motion along a streamline Pressure waves and the velocity of sound in a fluid Velocity of propagation of a small surface wave Free surface wave speed in unconfined fluid volumes Differential form of the continuity and momentum equations Computational treatment of the differential forms of the continuity and momentum equations 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.

5 Chapter 6 The Energy Equation and its Applications Mechanical energy of a flowing fluid Steady flow energy equation Kinetic energy correction factor Applications of the steady flow energy equation Representation of energy changes in a fluid system The Pitot tube Determination of volumetric flow rate via Pitot tube Computer program VOLFLO Changes of pressure in a tapering pipe Principle of the venturi meter Pipe orifices Limitation on the velocity of flow in a pipeline Theory of small orifices discharging to the atmosphere Theory of large orifices Elementary theory of notches and weirs The power of a stream of fluid Radial flow Flow in a curved path. Pressure gradient and change of total energy across the streamlines Vortex motion 204 Concluding remarks 210 Summary of important equations and concepts 211 Problems 211 Chapter 7 Two-dimensional Ideal Flow Rotational and irrotational flow Circulation and vorticity Streamlines and the stream function Velocity potential and potential flow Relationship between stream function and velocity potential. Flow nets Straight-line flows and their combinations Combined source and sink flows. Doublet Flow past a cylinder Curved flows and their combinations Flow past a cylinder with circulation. Kutta-Joukowsky's law 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 Dimensional analysis 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 Contents xi 8.3 Dimensional reasoning, homogeneity and dimensionless groups Fundamental and derived units and dimensions Additional fundamental dimensions Dimensions of derivatives and integrals Units of derived quantities Conversion between systems of units, including the treatment of dimensional constants Dimensional analysis by the indicial method Dimensional analysis by the group method The significance of dimensionless groups 281 Concluding remarks 282 Summary of important equations and concepts 282 Further reading 282 Problems 283 Chapter 9 Similarity Geometric similarity Dynamic similarity Model studies for flows without a free surface. Introduction to approximate similitude at high Reynolds numbers Zone of dependence of Mach number Significance of the pressure coefficient Model studies in cases involving free surface flow Similarity applied to rotodynamic machines River and harbour models Groundwater and seepage models Computer program GROUND, the simulation of groundwater seepage Pollution dispersion modelling, outfall effluent and stack plumes 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 Incompressible, steady and uniform laminar flow between parallel plates Incompressible, steady and uniform laminar flow in circular cross-section pipes 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.

7 xii Contents 10.4 Incompressible, steady and uniform turbulent flow in circular cross-section pipes Steady and uniform turbulent flow in open channels Velocity distribution in turbulent, fully developed pipe flow Velocity distribution in fully developed, turbulent flow in open channels Separation losses in pipe flow Significance of the Colebrook-White equation in pipe and duct design Computer program CBW 362 Concluding remarks 363 Summary of important equations and concepts 364 Further reading 364 Problems 364 Chapter 11 Boundary Layer Qualitative description of the boundary layer Dependence of pipe flow on boundary layer development at entry Factors affecting transition from laminar to turbulent flow regimes Discussion of flow patterns and regions within the turbulent boundary layer Prandtl mixing length theory Definitions of boundary layer thicknesses Application of the momentum equation to a general section of boundary layer Properties of the laminar boundary layer formed over a flat plate in the absence of a pressure gradient in the flow direction Properties of the turbulent boundary layer over a flat plate in the absence of a pressure gradient in the flow direction Effect of surface roughness on turbulent boundary layer development and skin friction coefficients 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 Regimes of external flow Drag Drag coefficient and similarity considerations Resistance of ships Flow past a cylinder Flow past a sphere 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.

8 Contents xiii 12.8 Flow past an aerofoil of finite length Wakes and drag Computer program WAKE 435 Concluding remarks 436 Summary of important equations and concepts 436 Problems 436 Chapter 13 Compressible Flow around a Body Effects of compressibility Shockwaves Oblique shock waves Supersonic expansion and compression 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 General approach Incompressible flow through ducts and pipes Computer program SIPHON Incompressible flow through pipes in series Incompressible flow through pipes in parallel Incompressible flow through branching pipes. The three-reservoir problem Incompressible steady flow in duct networks Resistance coefficients for pipelines in series and in parallel Incompressible flow in a pipeline with uniform draw-off Incompressible flow through a pipe network Head balance method for pipe networks Computer program HARDYC The quantity balance method for pipe networks 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 Flow with a free surface in pipes and open channels 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.

9 15.3 Optimum shape of cross-section for uniform flow in open channels 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 Specific energy and alternative depths of flow Critical depth in non-rectangular channels Computer program CRITNOR Non-dimensional specific energy curves Occurrence of critical flow conditions Flow over a broad-crested weir Effect of lateral contraction of a channel Non-uniform steady flow in channels Equations for gradually varied flow Classification of water surface profiles The hydraulic jump Location of a hydraulic jump Computer program CHANNEL 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 Compressible flow. The basic equations Steady isentropic flow in non-parallel-sided ducts neglecting friction Mass flow through a venturi meter Mass flow from a reservoir through an orifice or convergent-divergent nozzle Conditions for maximum discharge from a reservoir through a convergent-divergent duct or orifice The Laval nozzle Normal shock wave in a diffuser Compressible flow in a duct with friction under adiabatic conditions. Fanno flow 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.

10 PART VI FLUID MECHANICS FOR ENVIRONMENTAL CHANGE 582 Chapter 18 Environmental Change and Renewable Energy Technologies Environmental change The application of wind turbines to electrical power generation Wave energy conversion for electrical power generation 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 Gradually varied unsteady free surface flow Computer program UNSCHAN Implicit four-point scheme Flood routeing The prediction of flood behaviour Time-dependent urban stormwater routeing Rainwater and grey water reuse 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 Wave propagation velocity and its dependence on pipe and fluid parameters and free gas Computer program WAVESPD Simplification of the basic pressure transient equations Application of the simplified equations to explain pressure transient oscillations Surge control Control of surge following valve closure, with pump running and surge tank applications Computer program SHAFT 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.

11 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 Development of the St Venant equations of continuity and motion The method of characteristics Network simulation Computer program FM5SURG. The simulation of waterhammer Computer programs FM5WAVE and FM5GUTT. The simulation of open-channel free surface and partially filled pipe flow, with and without lateral inflow Simulation of low-amplitude air pressure transient propagation Computer program FM5AIR. The simulation of unsteady airflowin pipe and duct networks 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 Introduction One-dimensional theory Isolated blade and cascade considerations Departures from Euler's theory and losses 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 The concept of performance characteristics Losses and efficiencies Dimensionless coefficients and similarity laws Computer program SIM PUMP Scale effects Type number 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.

12 Contents xvii 23.8 Axial flow pumps and fans Mixed flow pumps and fans Water turbines The Pelton wheel Francis turbines Axial flow turbines Hydraulic transmissions 863 Concluding remarks 870 Summary of important equations and concepts 870 Problems 871 Chapter 24 Positive Displacement Machines Reciprocating pumps Rotary pumps Rotary gear pumps Rotary vane pumps Rotary piston pumps Hydraulic motors 892 Concluding remarks 892 Summary of important equations and concepts 893 Problems 893 Chapter 25 Machine-Network Interactions Fans, pumps and fluid networks Parallel and series pump operation Fans in series and parallel Fan and system matching. An application of the steady flow energy equation Change in the pump speed and the system Change in the pump size and the system Changes in fan speed, diameter and air density Jet fans Computer program MATCH Cavitation in pumps and turbines Fan and pump selection Fan suitability Modelling and simulation of network air flow distribution Ventilation and airborne contamination as a criterion for fan selection Computer program CONTAM 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

13 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 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

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific