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
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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
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
13
14
15
16
17
18
19
20
Fluids and their Properties 2
Fluids 4
Shear stress in a moving fluid 4
Differences between solids and fluids 5
Newtonian and non-Newtonian fluids 6
Liquids and gases 7
Molecular structure of materials 7
The continuum concept of a fluid 9
Density 10
Viscosity 11
Causes of viscosity in gases 12
Causes of viscosity in a liquid 13
Surface tension 14
Capillarity 15
Vapour pressure 16
Cavitation 17
Compressibility and the bulk modulus 17
Equation of state of a perfect gas 19
The universal gas constant 19
Specific heats of a gas 19
Expansion of a gas 20
Concluding remarks 22
Summary of important equations and concepts 22
Chapter 2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
Statics of fluid systems 26
Pressure 27
Pascal's law for pressure at a point 28
Variation of pressure vertically in a fluid under gravity 29
Equality of pressure at the same level in a static fluid 30
General equation for the variation of pressure due to gravity from
point to point in a static fluid 32
Variation of pressure with altitude in a fluid of constant density 33
Variation of pressure with altitude in a gas at constant temperature 34
Variation of pressure with altitude in a gas under adiabatic conditions 35
Variation of pressure and density with altitude for a constant
temperature gradient 38
Variation of temperature and pressure in the atmosphere 39
Stability of the atmosphere 41
Pressure and head 43
The hydrostatic paradox 44
Pressure measurement by manometer 45
Relative equilibrium 51
Pressure distribution in a liquid subject to horizontal acceleration 51
Effect of vertical acceleration 52
General expression for the pressure in a fluid in relative equilibrium 52
Forced vortex 56
Concluding remarks 57
Summary of important equations and concepts 57
Problems 57
Chapter 3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
Pressure and Head 24
Static Forces on Surfaces. Buoyancy 60
Action of fluid pressure on a surface 62
Resultant force and centre of pressure on a plane surface under
uniform pressure 62
Resultant force and centre of pressure on a plane surface immersed in
a liquid 63
Pressure diagrams 68
Force on a curved surface due to hydrostatic pressure 71
Buoyancy 73
Equilibrium of floating bodies 76
Stability of a submerged body 76
Stability of floating bodies 77
Determination of the metacentric height 78
Determination of the position of the metacentre relative to the centre
of buoyancy 78
Periodic time of oscillation 81
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 I I
Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
Motion of Fluid Particles and Streams 90
Fluid flow 92
Uniform flow and steady flow 93
Frames of reference 93
Real and ideal fluids 94
Compressible and incompressible flow 94
One-, two- and three-dimensional flow 95
Analysing fluid flow 96
Motion of a fluid particle 96
Acceleration of a fluid particle 98
Laminar and turbulent flow 100
Discharge and mean velocity 102
Continuity of flow 104
Continuity equations for three-dimensional flow using
Cartesian coordinates 107
Continuity equation for cylindrical coordinates 109
Concluding remarks 109
Summary of important equations and concepts 110
Problems 110
Chapter 5
5.1
5.2
CONCEPTS OF FLUID FLOW 88
The Momentum Equation and its Applications 112
Momentum and fluid flow 114
Momentum equation for two- and three-dimensional flow
along a streamline 115
Momentum correction factor 116
Gradual acceleration of a fluid in a pipeline neglecting elasticity 119
Force exerted by a jet striking a flat plate 120
Force due to the deflection of a jet by a curved vane 123
Force exerted when a jet is deflected by a moving curved vane 124
Force exerted on pipe bends and closed conduits 126
Reaction of a jet 129
Drag exerted when a fluid flows over a flat plate 136
Angular motion 138
Euler's equation of motion along a streamline 141
Pressure waves and the velocity of sound in a fluid 143
Velocity of propagation of a small surface wave 146
Free surface wave speed in unconfined fluid volumes 148
Differential form of the continuity and momentum equations 150
Computational treatment of the differential forms of the continuity and
momentum equations 153
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
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
6.17
6.18
6.19
Mechanical energy of a flowing fluid 170
Steady flow energy equation 174
Kinetic energy correction factor 176
Applications of the steady flow energy equation 177
Representation of energy changes in a fluid system 180
The Pitot tube 182
Determination of volumetric flow rate via Pitot tube 183
Computer program VOLFLO 185
Changes of pressure in a tapering pipe 185
Principle of the venturi meter 187
Pipe orifices 189
Limitation on the velocity of flow in a pipeline 190
Theory of small orifices discharging to the atmosphere 190
Theory of large orifices 194
Elementary theory of notches and weirs 195
The power of a stream of fluid 199
Radial flow 200
Flow in a curved path. Pressure gradient and change of total energy across
the streamlines 201
Vortex motion 204
Concluding remarks 210
Summary of important equations and concepts 211
Problems 211
Chapter 7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
The Energy Equation and its Applications 168
Two-dimensional Ideal Flow 214
Rotational and irrotational flow 216
Circulation and vorticity 218
Streamlines and the stream function 220
Velocity potential and potential flow 222
Relationship between stream function and velocity potential. Flow nets 226
Straight-line flows and their combinations 230
Combined source and sink flows. Doublet 238
Flow past a cylinder 243
Curved flows and their combinations 246
Flow past a cylinder with circulation. Kutta-Joukowsky's law 251
Computer program ROTCYL 254
Concluding remarks 255
Summary of important equations and concepts 255
Problems 256
PART I I I DIMENSIONAL ANALYSIS AND SIMILARITY 258
Chapter 8
8.1
8.2
Dimensional Analysis 260
Dimensional analysis 262
Dimensions and units 262
Contents
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
Dimensional reasoning, homogeneity and dimensionless groups 262
Fundamental and derived units and dimensions 263
Additional fundamental dimensions 265
Dimensions of derivatives and integrals 267
Units of derived quantities 268
Conversion between systems of units, including the treatment of dimensional
constants 268
Dimensional analysis by the indicial method 271
Dimensional analysis by the group method 273
The significance of dimensionless groups 281
Concluding remarks 282
Summary of important equations and concepts 282
Further reading 282
Problems 283
Chapter 9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
Similarity 284
Geometric similarity 288
Dynamic similarity 288
Model studies for flows without a free surface. Introduction to
approximate similitude at high Reynolds numbers 293
Zone of dependence of Mach number 295
Significance of the pressure coefficient 296
Model studies in cases involving free surface flow 297
Similarity applied to rotodynamic machines 299
River and harbour models 301
Groundwater and seepage models 307
Computer program GROUND, the simulation of groundwater
seepage 312
Pollution dispersion modelling, outfall effluent and stack plumes 313
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
10.2
10.3
xi
Incompressible, steady and uniform laminar flow between
parallel plates 328
Incompressible, steady and uniform laminar flow in circular
cross-section pipes 333
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
11.2
11.3
Qualitative description of the boundary layer 368
Dependence of pipe flow on boundary layer development at entry 370
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
12.1
12.2
12.3
12.4
12.5
12.6
12.7
Incompressible Flow around a Body 394
Regimes of external flow 396
Drag 397
Drag coefficient and similarity considerations 401
Resistance of ships 403
Flow past a cylinder 407
Flow past a sphere 411
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
13.1
13.2
13.3
13.4
13.5
Compressible Flow around a Body 438
Effects of compressibility 440
Shockwaves 445
Oblique shock waves 455
Supersonic expansion and compression 457
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
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
14.10
14.11
14.12
14.13
14.14
General approach 466
Incompressible flow through ducts and pipes 467
Computer program SIPHON 470
Incompressible flow through pipes in series 471
Incompressible flow through pipes in parallel 473
Incompressible flow through branching pipes. The three-reservoir
problem 475
Incompressible steady flow in duct networks 478
Resistance coefficients for pipelines in series and in parallel 486
Incompressible flow in a pipeline with uniform draw-off 489
Incompressible flow through a pipe network 489
Head balance method for pipe networks 490
Computer program HARDYC 491
The quantity balance method for pipe networks 493
Quasi-steady flow 495
Concluding remarks 501
Summary of important equations and concepts 502
Further reading 502
Problems 502
Chapter 15
15.1
15.2
Uniform Flow in Open Channels 506
Flow with a free surface in pipes and open channels 508
Resistance formulae for steady uniform flow in open channels 510
15.3
15.4
Optimum shape of cross-section for uniform flow in open
channels 515
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
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
16.10
16.11
16.12
16.13
16.14
Specific energy and alternative depths of flow 526
Critical depth in non-rectangular channels 528
Computer program CRITNOR 530
Non-dimensional specific energy curves 531
Occurrence of critical flow conditions 532
Flow over a broad-crested weir 533
Effect of lateral contraction of a channel 534
Non-uniform steady flow in channels 537
Equations for gradually varied flow 538
Classification of water surface profiles 540
The hydraulic jump 543
Location of a hydraulic jump 545
Computer program CHANNEL 546
Annular water flow considerations 547
Concluding remarks 550
Summary of important equations and concepts 551
Further reading 551
Problems 551
Chapter 17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
Non-uniform Flow in Open Channels 524
Compressible Flow in Pipes 554
Compressible flow. The basic equations 556
Steady isentropic flow in non-parallel-sided ducts neglecting
friction 557
Mass flow through a venturi meter 558
Mass flow from a reservoir through an orifice or
convergent-divergent nozzle 561
Conditions for maximum discharge from a reservoir through
a convergent-divergent duct or orifice 562
The Laval nozzle 563
Normal shock wave in a diffuser 567
Compressible flow in a duct with friction under adiabatic conditions.
Fanno flow 572
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
18.2
18.3
18.4
Environmental change 586
The application of wind turbines to electrical power generation 603
Wave energy conversion for electrical power generation 616
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
19.2
19.3
19.4
19.5
19.6
19.7
19.8
Gradually varied unsteady free surface flow 638
Computer program UNSCHAN 646
Implicit four-point scheme 648
Flood routeing 650
The prediction of flood behaviour 652
Time-dependent urban stormwater routeing 657
Rainwater and grey water reuse 662
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
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
Pressure Transient Theory and Surge Control 684
Wave propagation velocity and its dependence on pipe and
fluid parameters and free gas 692
Computer program WAVESPD 698
Simplification of the basic pressure transient equations 700
Application of the simplified equations to explain pressure
transient oscillations 700
Surge control 705
Control of surge following valve closure, with pump running and
surge tank applications 706
Computer program SHAFT 714
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
21.2
21.3
21.4
21.5
21.6
21.7
21.8
Development of the St Venant equations of continuity and motion 728
The method of characteristics 734
Network simulation 747
Computer program FM5SURG. The simulation of waterhammer 749
Computer programs FM5WAVE and FM5GUTT. The simulation
of open-channel free surface and partially filled pipe flow, with
and without lateral inflow 759
Simulation of low-amplitude air pressure transient propagation 765
Computer program FM5AIR. The simulation of unsteady airflowin
pipe and duct networks 766
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
22.1
22.2
22.3
22.4
22.5
Introduction 794
One-dimensional theory 796
Isolated blade and cascade considerations 804
Departures from Euler's theory and losses 812
Compressible flow through rotodynamic machines 818
Concluding remarks 822
Summary of important equations and concepts 822
Further reading 822
Problems 823
Chapter 23
23.1
23.2
23.3
23.4
23.5
23.6
23.7
Theory of Rotodynamic Machines 792
Performance of Rotodynamic Machines 824
The concept of performance characteristics 826
Losses and efficiencies 827
Dimensionless coefficients and similarity laws 833
Computer program SIM PUMP 839
Scale effects 840
Type number 841
Centrifugal pumps and fans 844
Contents
23.8
23.9
23.10
23.11
23.12
23.13
23.14
Axial flow pumps and fans 846
Mixed flow pumps and fans 849
Water turbines 850
The Pelton wheel 851
Francis turbines 855
Axial flow turbines 860
Hydraulic transmissions 863
Concluding remarks 870
Summary of important equations and concepts 870
Problems 871
Chapter 24
24.1
24.2
24.3
24.4
24.5
24.6
Reciprocating pumps 876
Rotary pumps 887
Rotary gear pumps 888
Rotary vane pumps 889
Rotary piston pumps 890
Hydraulic motors 892
Concluding remarks 892
Summary of important equations and concepts 893
Problems 893
Chapter 25
25.1
25.2
25.3
25.4
25.5
25.6
25.7
25.8
25.9
25.10
25.11
25.12
25.13
25.14
25.15
25.16
Positive Displacement Machines 874
Machine-Network Interactions 896
Fans, pumps and fluid networks 898
Parallel and series pump operation 905
Fans in series and parallel 907
Fan and system matching. An application of the steady flow
energy equation 912
Change in the pump speed and the system 916
Change in the pump size and the system 919
Changes in fan speed, diameter and air density 921
Jet fans 923
Computer program MATCH 931
Cavitation in pumps and turbines 932
Fan and pump selection 937
Fan suitability 941
Modelling and simulation of network air flow distribution 944
Ventilation and airborne contamination as a criterion for fan
selection 959
Computer program CONTAM 966
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
xvii
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 CD for Various
Body Shapes 988
Index 989
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