Preface to the ninth edition ................................... ix
1 Fundamental concepts ......................................... 1
1.1 The characteristics of fluids ........................... 1
1.2 Notation, dimensions, units and related matters ......... 4
1.3 Properties of fluids ................................... 12
1.4 The perfect gas: equation of state ..................... 17
1.5 Compressibility ........................................ 20
1.6 Viscosity .............................................. 21
1.7 Surface tension ........................................ 28
1.8 Basic characteristics of fluids in motion .............. 30
1.9 Classification and description of fluid flow ........... 33
1.10 The roles of experimentation and theory in fluid
mechanics .............................................. 38
1.11 Summary ................................................ 41
Problems .................................................... 41
2 Fluid statics ............................................... 43
2.1 Introduction ........................................... 43
2.2 Variation of pressure with position in a fluid ......... 43
2.3 The measurement of pressure ............................ 48
2.4 First and second moments of area ....................... 57
2.5 Hydrostatic thrusts on submerged surfaces .............. 59
2.6 Buoyancy ............................................... 69
2.7 The stability of bodies in fluids ...................... 71
2.8 Equilibrium of moving fluids ........................... 80
Problems .................................................... 84
3 The principles governing fluids in motion ................... 89
3.1 Introduction ........................................... 89
3.2 Acceleration of a fluid particle ....................... 89
3.3 The continuity equation ................................ 90
3.4 Bernoulli's equation ................................... 92
3.5 General energy equation for steady flow of any fluid ... 96
3.6 Pressure variation perpendicular to streamlines ....... 107
3.7 Simple applications of Bernoulli's equation ........... 109
Problems ................................................... 131
4 The momentum equation ...................................... 134
4.1 Introduction .......................................... 134
4.2 The momentum equation for steady flow ................. 134
4.3 Applications of the momentum equation ................. 138
Problems ................................................... 156
5 Physical similarity and dimensional analysis ............... 159
5.1 Introduction .......................................... 159
5.2 Types of physical similarity .......................... 160
5.3 Ratios of forces arising in dynamic similarity ........ 162
5.4 The principal dimensionless groups of fluid dynamics .. 167
5.5 Other dimensionless groups ............................ 167
5.6 Dimensional analysis .................................. 170
5.7 The application of dynamic similarity ................. 179
5.8 Ship resistance ....................................... 182
Problems ................................................... 188
6 Laminar flow between solid boundaries ...................... 191
6.1 Introduction .......................................... 191
6.2 Steady laminar flow in circular pipes: the Hagen-
Poiseuille law ........................................ 191
6.3 Steady laminar flow through an annulus ................ 198
6.4 Steady laminar flow between parallel planes ........... 199
6.5 Steady laminar flow between parallel planes, one of
which is moving ....................................... 204
6.6 The measurement of viscosity .......................... 210
6.7 Fundamentals of the theory of hydrodynamic
lubrication ........................................... 220
6.8 Laminar flow through porous media ..................... 239
Problems ................................................... 242
7 Flow and losses in pipes and fittings ...................... 245
7.1 Introduction .......................................... 245
7.2 Flow in pipes of circular cross-section ............... 245
7.3 Variation of friction factor .......................... 249
7.4 Distribution of shear stress in a circular pipe ....... 257
7.5 Friction in non-circular conduits ..................... 259
7.6 Other losses in pipes ................................. 260
7.7 Total head and pressure lines ......................... 271
7.8 Pipes in combination .................................. 277
7.9 Conditions near the pipe entry ........................ 283
7.10 Quasi-steady flow in pipes ............................ 284
7.11 Flow measurement ...................................... 287
Problems ................................................... 292
8 Boundary layers, wakes and other shear layers .............. 298
8.1 Introduction .......................................... 298
8.2 Description of the boundary layer ..................... 299
8.3 The thickness of the boundary layer ................... 301
8.4 The momentum equation applied to the boundary layer ... 303
8.5 The laminar boundary layer on a flat plate with zero
pressure gradient ..................................... 306
8.6 The turbulent boundary layer on a smooth flat plate
with zero pressure gradient ........................... 313
8.7 Friction drag for laminar and turbulent boundary
layers together ....................................... 317
8.8 Effect of pressure gradient ........................... 320
8.9 Boundary-layer control ................................ 338
8.10 Effect of compressibility on drag ..................... 340
8.11 Eddy viscosity and the mixing-length hypothesis ....... 341
8.12 Velocity distribution in turbulent flow ............... 344
8.13 Free turbulence ....................................... 352
8.14 Computational fluid dynamics .......................... 353
Problems ................................................... 358
9 The flow of an inviscid fluid .............................. 361
9.1 Introduction .......................................... 361
9.2 The stream function ................................... 362
9.3 Circulation and vorticity ............................. 364
9.4 Velocity potential .................................... 367
9.5 Flow nets ............................................. 370
9.6 Basic patterns of flow ................................ 373
9.7 Combining flow patterns ............................... 383
9.8 Combinations of basic flow patterns ................... 384
9.9 Functions of a complex variable ....................... 399
9.10 An introduction to elementary aerofoil theory ......... 403
Problems ................................................... 410
10 Flow with a free surface ................................... 414
10.1 Introduction .......................................... 414
10.2 Types of flow in open channels ........................ 415
10.3 The steady-flow energy equation for open channels ..... 416
10.4 Steady uniform flow: the Chezy equation ............... 419
10.5 The boundary layer in open channels ................... 423
10.6 Optimum shape of cross-section ........................ 425
10.7 Flow in closed conduits only partly full .............. 426
10.8 Simple waves and surges in open channels .............. 427
10.9 Specific energy and alternative depths of flow ........ 431
10.10 The hydraulic jump ................................... 438
10.11 The occurrence of critical conditions ................ 443
10.12 Gradually varied flow ................................ 456
10.13 Oscillatory waves .................................... 464
10.14 Tsunamis ............................................. 480
10.15 Conclusion ........................................... 482
Problems ................................................... 483
11 Compressible flow of gases ................................. 487
11.1 Introduction .......................................... 487
11.2 Thermodynamic concepts ................................ 487
11.3 Energy equation with variable density: static and
stagnation temperature ................................ 491
11.4 The speed of sound .................................... 493
11.5 Shockwaves ............................................ 499
11.6 Supersonic flow round a corner ........................ 512
11.7 The Pitot tube in compressible flow ................... 517
11.8 Some general relations for one-dimensional flows ...... 520
11.9 One-dimensional flow through nozzles .................. 522
11.10 Compressible flow in pipes of constant
cross-section ........................................ 530
11.11 High-speed flow past an aerofoil ..................... 544
11.12 Analogy between compressible flow and flow with a
free surface ......................................... 546
11.13 Flow visualization ................................... 548
Problems ................................................... 550
12 Unsteady flow .............................................. 554
12.1 Introduction .......................................... 554
12.2 Inertia pressure ...................................... 555
12.3 Pressure transients ................................... 558
12.4 Surge tanks ........................................... 583
Problems ................................................... 588
13 Fluid machines ............................................. 591
13.1 Introduction .......................................... 591
13.2 Reciprocating pumps ................................... 592
13.3 Turbines .............................................. 596
13.4 Rotodynamic pumps ..................................... 625
13.5 Hydrodynamic transmissions ............................ 651
13.6 The effect of size on the efficiency of fluid
machines .............................................. 656
Problems ................................................... 657
14 Fluid mechanics in a changing world ........................ 663
14.1 Introduction .......................................... 663
14.2 Energy generation in a changing world ................. 663
14.3 Wind energy and wind farms ............................ 664
14.4 Wave and tidal energy ................................. 665
14.5 A comparison of different energy generation
technologies .......................................... 666
14.6 Rising sea levels ..................................... 669
14.7 Fresh water; its management and distribution .......... 670
14.8 Conclusion ............................................ 671
Appendix 1 Units and conversion factors ....................... 672
Appendix 2 Physical constants and properties of fluids ........ 676
Appendix 3 Tables of gas flow functions ....................... 681
Appendix 4 Algebraic symbols .................................. 688
Answers to problems ........................................... 694
Index ......................................................... 698
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