Fluid mechanics

Cover Page......Page 1
Title Page......Page 4
Copyright Page......Page 5
Dedication Page......Page 6
CONTENTS......Page 8
Prefaces......Page 20
Acknowledgements......Page 29
List of Computer Programmes......Page 30
List of Symbols......Page 32
PART I  ELEMENTS OF FLUID MECHANICS......Page 35
1 Fluids and their
Properties......Page 37
1.2 Shear stress in a moving fluid......Page 39
1.3 Differences between solids and fluids......Page 40
1.4 Newtonian and non-Newtonian fluids......Page 41
1.6 Molecular structure of materials......Page 42
1.7 The continuum concept of a fluid......Page 44
1.8 Density......Page 45
1.9 Viscosity......Page 46
1.10 Causes of viscosity in gases......Page 47
1.11 Causes of viscosity in a liquid......Page 48
1.12 Surface tension......Page 49
1.13 Capillarity......Page 50
1.14 Vapour pressure......Page 51
1.16 Compressibility and the bulk modulus......Page 52
1.19 Specific heats of a gas......Page 54
1.20 Expansion of a gas......Page 55
Summary of important equations and concepts......Page 57
2 Pressure and Head......Page 59
2.1 Statics of fluid systems......Page 61
2.2 Pressure......Page 62
2.3 Pascal’s law for pressure at a point......Page 63
2.4 Variation of pressure vertically ina fluid under gravity......Page 64
2.5 Equality of pressure at the samelevel in a static fluid......Page 65
2.6 General equation for the variationof pressure due to gravity frompoint to point in a static fluid......Page 67
2.7 Variation of pressure with altitude in a fluid of constant density......Page 68
2.8 Variation of pressure with altitude in a gas at constant temperature......Page 69
2.9 Variation of pressure with altitude in a gas under adiabatic conditions......Page 70
2.10 Variation of pressure and density with altitude for a constant
temperature gradient......Page 73
2.11 Variation of temperature and pressure in the atmosphere......Page 74
2.12 Stability of the atmosphere......Page 76
2.13 Pressure and head......Page 78
2.14 The hydrostatic paradox......Page 79
2.15 Pressure measurement by manometer......Page 80
2.17 Pressure distribution in a liquid subject to horizontal acceleration......Page 86
2.19 General expression for the pressure in a fluid in relative equilibrium......Page 87
2.20 Forced vortex......Page 91
Problems......Page 92
3 Static Forces on Surfaces. Buoyancy......Page 95
3.2 Resultant force and centre of pressure on a plane surface under
uniform pressure......Page 97
3.3 Resultant force and centre of pressure on a plane surface immersed in
a liquid......Page 98
3.4 Pressure diagrams......Page 103
3.5 Force on a curved surface due to hydrostatic pressure......Page 106
3.6 Buoyancy......Page 108
3.8 Stability of a submerged body......Page 111
3.9 Stability of floating bodies......Page 112
3.11 Determination of the position of the metacentre relative to the centre of buoyancy......Page 113
3.12 Periodic time of oscillation......Page 116
3.13 Stability of a vessel carrying liquid in tanks with a free surface......Page 117
Problems......Page 120
PART II  CONCEPTS OF FLUID FLOW......Page 123
4 Motion of Fluid Particlesand Streams......Page 125
4.1 Fluid flow......Page 127
4.3 Frames of reference......Page 128
4.5 Compressible and incompressible flow......Page 129
4.6 One-, two- and three-dimensional flow......Page 130
4.8 Motion of a fluid particle......Page 131
4.9 Acceleration of a fluid particle......Page 133
4.10 Laminar and turbulent flow......Page 135
4.11 Discharge and mean velocity......Page 137
4.12 Continuity of flow......Page 139
4.13 Continuity equations for three-dimensional flow using
Cartesian coordinates......Page 142
Concluding remarks......Page 144
Problems......Page 145
5 The Momentum Equationand its Applications......Page 147
5.1 Momentum and fluid flow......Page 149
5.2 Momentum equation for two- and three-dimensional flow
along a streamline......Page 150
5.3 Momentum correction factor......Page 151
5.4 Gradual acceleration of a fluid in a pipeline neglecting elasticity......Page 154
5.5 Force exerted by a jet striking a flat plate......Page 155
5.6 Force due to the deflection of a jet by a curved vane......Page 158
5.7 Force exerted when a jet is deflected by a moving curved vane......Page 159
5.8 Force exerted on pipe bends and closed conduits......Page 161
5.9 Reaction of a jet......Page 164
5.10 Drag exerted when a fluid flows over a flat plate......Page 171
5.11 Angular motion......Page 173
5.12 Euler’s equation of motion along a streamline......Page 176
5.13 Pressure waves and the velocity of sound in a fluid......Page 178
5.14 Velocity of propagation of a small surface wave......Page 181
5.15 Differential form of the continuity and momentum equations......Page 183
5.16 Computational treatment of the differential forms of the continuity and
momentum equations......Page 186
5.17 Comparison of CFD methodologies......Page 190
Summary of important equations and concepts......Page 197
Problems......Page 198
6 The Energy Equation
and its Applications......Page 201
6.1 Mechanical energy of a flowing fluid......Page 203
6.2 Steady flow energy equation......Page 207
6.3 Kinetic energy correction factor......Page 209
6.4 Applications of the steady flow energy equation......Page 210
6.5 Representation of energy changes in a fluid system......Page 213
6.6 The Pitot tube......Page 215
6.7 Determination of volumetric flow rate via Pitot tube......Page 216
6.9 Changes of pressure in a tapering pipe......Page 218
6.10 Principle of the venturi meter......Page 220
6.11 Pipe orifices......Page 222
6.13 Theory of small orifices discharging to atmosphere......Page 223
6.14 Theory of large orifices......Page 227
6.15 Elementary theory of notches and weirs......Page 228
6.16 The power of a stream of fluid......Page 232
6.17 Radial flow......Page 233
6.18 Flow in a curved path. Pressure gradient and change of total energy across
the streamlines......Page 234
6.19 Vortex motion......Page 237
Concluding remarks......Page 243
Problems......Page 244
7 Two-dimensional
Ideal Flow......Page 247
7.1 Rotational and irrotational flow......Page 249
7.2 Circulation and vorticity......Page 251
7.3 Streamlines and the stream function......Page 253
7.4 Velocity potential and potential flow......Page 255
7.5 Relationship between stream function and velocity potential. Flow nets......Page 259
7.6 Straight line flows and their combinations......Page 263
7.7 Combined source and sink flows. Doublet......Page 271
7.8 Flow past a cylinder......Page 276
7.9 Curved flows and their combinations......Page 279
7.10 Flow past a cylinder with circulation. Kutta–Joukowsky’s law......Page 284
7.11 Computer program ROTCYL......Page 287
Summary of important equations and concepts......Page 288
Problems......Page 289
PART III  DIMENSIONAL ANALYSIS AND SIMILARITY......Page 291
8 Dimensional Analysis......Page 293
8.3 Dimensional reasoning, homogeneity and dimensionless groups......Page 295
8.4 Fundamental and derived units and dimensions......Page 296
8.5 Additional fundamental dimensions......Page 298
8.6 Dimensions of derivatives and integrals......Page 300
8.8 Conversion between systems of units, including the treatment of dimensional
constants......Page 301
8.9 Dimensional analysis by the indicial method......Page 304
8.10 Dimensional analysis by the group method......Page 306
8.11 The significance of dimensionless groups......Page 314
Further reading......Page 315
Problems......Page 316
9 Similarity......Page 317
9.2 Dynamic similarity......Page 321
9.3 Model studies for flows without a free surface. Introduction to
approximate similitude at high Reynolds numbers......Page 326
9.4 Zone of dependence of Mach number......Page 328
9.5 Significance of the pressure coefficient......Page 329
9.6 Model studies in cases involving free surface flow......Page 330
9.7 Similarity applied to rotodynamic machines......Page 332
9.8 River and harbour models......Page 334
9.9 Groundwater and seepage models......Page 340
9.10 Computer program GROUND, the simulation of groundwater
seepage......Page 345
9.11 Pollution dispersion modelling, outfall effluent and stack plumes......Page 346
9.12 Pollutant dispersion in one-dimensional steady uniform flow......Page 349
Summary of important equations and concepts......Page 354
References......Page 355
Problems......Page 356
PART IV  BEHAVIOUR OF REAL FLUIDS......Page 357
10 Laminar and Turbulent Flows in
Bounded Systems......Page 359
10.1 Incompressible, steady and uniform laminar flow between
parallel plates......Page 361
10.2 Incompressible, steady and uniform laminar flow in circular
cross-section pipes......Page 366
10.3 Incompressible, steady and uniform turbulent flow in
bounded conduits......Page 370
10.4 Incompressible, steady and uniform turbulent flow in circular
cross-section pipes......Page 373
10.5 Steady and uniform turbulent flow in open channels......Page 377
10.6 Velocity distribution in turbulent, fully developed pipe flow......Page 378
10.8 Separation losses in pipe flow......Page 387
10.9 Significance of the Colebrook–White equation in pipe and
duct design......Page 394
Concluding remarks......Page 397
Further reading......Page 398
Problems......Page 399
11 Boundary Layer......Page 401
11.1 Qualitative description of the boundary layer......Page 403
11.2 Dependence of pipe flow on boundary layer development at entry......Page 405
11.3 Factors affecting transition from laminar to turbulent
flow regimes......Page 406
11.4 Discussion of flow patterns and regions within the turbulent
boundary layer......Page 407
11.5 Prandtl mixing length theory......Page 409
11.6 Definitions of boundary layer thicknesses......Page 412
11.7 Application of the momentum equation to a general section of
boundary layer......Page 413
11.8 Properties of the laminar boundary layer formed over a flat plate in
the absence of a pressure gradient in the flow direction......Page 414
11.9 Properties of the turbulent boundary layer over a flat plate in the
absence of a pressure gradient in the flow direction......Page 419
11.11 Effect of pressure gradient on boundary layer development......Page 423
Summary of important equations and concepts......Page 426
Problems......Page 427
12 Incompressible Flow around a Body......Page 429
12.1 Regimes of external flow......Page 431
12.2 Drag......Page 432
12.3 Drag coefficient and similarity considerations......Page 436
12.4 Resistance of ships......Page 438
12.5 Flow past a cylinder......Page 442
12.6 Flow past a sphere......Page 446
12.7 Flow past an infinitely long aerofoil......Page 453
12.8 Flow past an aerofoil of finite length......Page 461
12.9 Wakes and drag......Page 465
12.10 Computer program WAKE......Page 470
Problems......Page 471
13 Compressible Flow around a Body......Page 473
13.1 Effects of compressibility......Page 475
13.2 Shock waves......Page 480
13.3 Oblique shock waves......Page 490
13.4 Supersonic expansion and compression......Page 492
Concluding remarks......Page 494
Problems......Page 495
PART V  STEADY FLOW IN PIPES, DUCTS AND OPEN CHANNELS......Page 497
14 Steady Incompressible Flow in Pipe and
Duct Systems......Page 499
14.1 General approach......Page 501
14.2 Incompressible flow through ducts and pipes......Page 502
14.3 Computer program SIPHON......Page 505
14.4 Incompressible flow through pipes in series......Page 506
14.5 Incompressible flow through pipes in parallel......Page 508
14.6 Incompressible flow through branching pipes. The three-reservoir
problem......Page 510
14.7 Incompressible steady flow in duct networks......Page 513
14.8 Resistance coefficients for pipelines in series and in parallel......Page 521
14.10 Incompressible flow through a pipe network......Page 525
14.11 Head balance method for pipe networks......Page 526
14.12 Computer program HARDYC......Page 527
14.13 The quantity balance method for pipe networks......Page 529
14.14 Quasi-steady flow......Page 532
Summary of important equations and concepts......Page 538
Problems......Page 539
15 Uniform Flow in Open Channels......Page 543
15.1 Flow with a free surface in pipes and open channels......Page 545
15.2 Resistance formulae for steady uniform flow in open channels......Page 547
15.3 Optimum shape of cross-section for uniform flow in open
channels......Page 552
15.4 Optimum depth for flow with a free surface in covered channels......Page 556
Concluding remarks......Page 559
Further reading......Page 560
Problems......Page 561
16 Non-uniform Flow in Open Channels......Page 563
16.1 Specific energy and alternative depths of flow......Page 565
16.2 Critical depth in non-rectangular channels......Page 567
16.3 Computer program CRITNOR......Page 569
16.4 Non-dimensional specific energy curves......Page 570
16.5 Occurrence of critical flow conditions......Page 571
16.6 Flow over a broad-crested weir......Page 572
16.7 Effect of lateral contraction of a channel......Page 573
16.8 Non-uniform steady flow in channels......Page 576
16.9 Equations for gradually varied flow......Page 577
16.10 Classification of water surface profiles......Page 579
16.11 The hydraulic jump......Page 582
16.12 Location of a hydraulic jump......Page 584
16.13 Computer program CHANNEL......Page 585
Untitled......Page 586
Summary of important equations and concepts......Page 591
Further reading......Page 592
Problems......Page 593
17 Compressible Flow in Pipes......Page 595
17.1 Compressible flow. The basic equations......Page 597
17.2 Steady isentropic flow in non-parallel-sided ducts neglecting
friction......Page 598
17.3 Mass flow through a venturi meter......Page 599
17.4 Mass flow from a reservoir through an orifice or
convergent–divergent nozzle......Page 602
17.5 Conditions for maximum discharge from a reservoir through
a convergent–divergent duct or orifice......Page 603
17.6 The Laval nozzle......Page 604
17.7 Normal shock wave in a diffuser......Page 608
17.8 Compressible flow in a duct with friction under adiabatic conditions.
Fanno flow......Page 613
17.9 Isothermal flow of a compressible fluid in a pipeline......Page 617
Concluding remarks......Page 620
Problems......Page 621
PART VI  FLUID MECHANICS FOR ENVIRONMENTAL CHANGE......Page 623
18 Environmental Change and Renewable
Energy Technologies......Page 625
18.1 Environmental change......Page 627
18.2 The application of wind turbines to electrical power generation......Page 637
18.3 Wave energy conversion for electrical power generation......Page 651
18.4 Tidal power......Page 666
Concluding remarks......Page 667
Summary of important concepts......Page 668
Further reading......Page 669
References......Page 670
19 Environmental Change and Rainfall Runoff Flow Modelling......Page 671
19.1 Gradually varied unsteady free surface flow......Page 673
19.2 Computer program UNSCHAN......Page 681
19.3 Implicit four-point scheme......Page 683
19.4 Flood routeing......Page 685
19.5 The prediction of flood behaviour......Page 687
19.6 Time-dependent urban stormwater routeing......Page 692
19.7 Combined free surface and pressure surge analysis. Siphonic rainwater
systems......Page 695
Summary of important equations amd concepts......Page 704
References......Page 705
PART VII  UNSTEADY FLOW IN BOUNDED SYSTEMS......Page 707
20 Pressure Transient Theory and Surge Control......Page 709
20.1 Wave propagation velocity and its dependence on pipe and
fluid parameters and free gas......Page 717
20.2 Computer program WAVESPD......Page 723
20.4 Application of the simplified equations to explain pressure
transient oscillations......Page 725
20.5 Surge control......Page 730
20.6 Control of surge following valve closure, with pump running and
surge tank applications......Page 732
20.7 Computer program SHAFT......Page 739
20.8 Control of surge following pump shutdown......Page 741
Summary of important equations and concepts......Page 746
Further reading......Page 748
Problems......Page 749
21 Simulation of Unsteady Flow Phenomena in Pipe,
Channel and Duct Systems......Page 751
21.1 Development of the St Venant equations of continuity and motion......Page 753
21.2 The method of characteristics......Page 759
21.3 Network simulation......Page 772
21.4 Computer program FM5SURG. The simulation of waterhammer......Page 774
21.5 Computer programs FM5WAVE and FM5GUTT. The simulation
of open-channel free surface and partially filled pipe flow, with
and without lateral inflow......Page 784
21.6 Simulation of low-amplitude air pressure transient propagation......Page 790
21.7 Computer program FM5AIR. The simulation of unsteady air flow in
pipe and duct networks......Page 791
Untitled......Page 795
Concluding remarks......Page 798
Further reading......Page 799
References......Page 800
PART VIII  FLUID MACHINERY. THEORY, PERFORMANCE AND APPLICATION......Page 801
22 Theory of Rotodynamic Machines......Page 803
22.1 Introduction......Page 805
22.2 One-dimensional theory......Page 807
22.3 Isolated blade and cascade considerations......Page 815
22.4 Departures from Euler’s theory and losses......Page 823
22.5 Compressible flow through rotodynamic machines......Page 829
Further reading......Page 833
Problems......Page 834
23 Performance of Rotodynamic Machines......Page 835
23.1 The concept of performance characteristics......Page 837
23.2 Losses and efficiencies......Page 838
23.3 Dimensionless coefficients and similarity laws......Page 844
23.4 Computer program SIMPUMP......Page 850
23.5 Scale effects......Page 851
23.6 Type number......Page 852
23.7 Centrifugal pumps and fans......Page 855
23.8 Axial flow pumps and fans......Page 857
23.9 Mixed flow pumps and fans......Page 860
23.10 Water turbines......Page 861
23.11 The Pelton wheel......Page 862
23.12 Francis turbines......Page 866
23.13 Axial flow turbines......Page 871
23.14 Hydraulic transmissions......Page 874
Concluding remarks......Page 881
Summary of important equations and concepts......Page 882
Problems......Page 883
24 Positive Displacement Machines......Page 885
24.1 Reciprocating pumps......Page 887
24.2 Rotary pumps......Page 898
24.3 Rotary gear pumps......Page 899
24.4 Rotary vane pumps......Page 900
24.5 Rotary piston pumps......Page 901
Concluding remarks......Page 903
Summary of important equations and concepts......Page 904
Problems......Page 905
25 Machine–Network Interactions......Page 907
25.1 Fans, pumps and fluid networks......Page 909
25.2 Parallel and series pump operation......Page 916
25.3 Fans in series and parallel......Page 918
25.4 Fan and system matching. An application of the steady flow
energy equation......Page 923
25.5 Change in the pump speed and the system......Page 927
25.6 Change in the pump size and the system......Page 930
25.7 Changes in fan speed, diameter and air density......Page 932
25.8 Jet fans......Page 935
25.9 Computer program MATCH......Page 943
25.10 Cavitation in pumps and turbines......Page 944
25.11 Fan and pump selection......Page 949
25.12 Fan suitability......Page 953
25.13 Ventilation and airborne contamination as a criterion for fan
selection......Page 956
Untitled......Page 964
Concluding remarks......Page 966
Summary of important equations and concepts......Page 967
Problems......Page 968
A1.1 Variation of some properties of water with temperature......Page 973
A1.4 Some properties of common liquids......Page 974
A1.6 International Standard Atmosphere......Page 975
A1.8 Absolute viscosity of some common fluids......Page 976
Appendix 2 Values of Drag Coefficient
C
D
for Various
Body Shapes......Page 977
INDEX......Page 978