An Introduction to Fluid Mechanics

Contents......Page 9
Preface......Page 15
Acknowledgments......Page 17
Part I Preparing to Study Flow......Page 19
1.1 Getting motivated......Page 21
1.2 Quick start: The mechanical energy balance......Page 26
1.2.1 MEB with no friction, no work: Macroscopic Bernoulli equation......Page 33
1.2.2 MEB with shaft work......Page 44
1.2.3 MEB with friction......Page 52
1.3 Connecting mathematics to fluid mechanics......Page 67
1.3.1.1 Derivatives......Page 68
1.3.1.2 Integrals......Page 72
1.3.2 Vector calculus......Page 76
1.3.2.1 Coordinate systems......Page 79
1.3.2.2 Tensors......Page 85
1.3.2.3 Differential operations......Page 88
1.3.2.4 Curvilinear coordinates......Page 92
1.3.3 Substantial derivative......Page 102
1.3.4 Practical advice......Page 109
1.4 Problems......Page 111
2.1 Viscosity......Page 124
2.2 Drag......Page 131
2.3 Boundary layers......Page 136
2.4 Laminar versus turbulent flow: Reynolds number......Page 145
2.5 Aerodynamics: Lift......Page 155
2.6 Supersonic flow......Page 161
2.7 Surface tension......Page 163
2.8 Flows with curved streamlines......Page 167
2.9 Magnetohydrodynamics......Page 171
2.10 Particulate flow......Page 172
2.11 Summary......Page 175
2.12 Problems......Page 176
Part II The Physics of Flow......Page 183
3.1 Motion of rigid bodies......Page 185
3.2 Motion of deformable media......Page 190
3.2.1 The continuum model......Page 193
3.2.1.1 Field Variables......Page 194
3.2.1.2 The Continuum Hypothesis......Page 199
3.2.1.3 Fluid Particles......Page 202
3.2.2 Control-volume approach......Page 205
3.2.2.1 Momentum Balance on a Control Volume......Page 208
3.2.2.2 The Convective Term......Page 212
3.2.3 Problem solving with control volumes......Page 224
3.2.3.1 Microscopic Control-Volume Problem......Page 225
3.2.3.2 Macroscopic Control-Volume Problem......Page 230
3.4 Problems......Page 236
4 Molecular Fluid Stresses......Page 246
4.1 Forces on a control volume......Page 247
4.2 Stationary fluids: Hydrostatics......Page 254
4.2.1 Gases......Page 255
4.2.2 Liquids......Page 259
4.2.3 Pascal\'s principle......Page 279
4.2.4.1 Manometers......Page 289
4.2.4.2 Hydraulic Lifts......Page 295
4.3 Fluids in motion......Page 301
4.3.1 Total molecular stress......Page 302
4.3.1.1 Stress Tensor......Page 304
4.3.1.2 Stress Sign Convention......Page 316
4.3.2 Isotropic and anisotropic stress......Page 320
4.4 Free-surface stress effects......Page 338
4.5 Problems......Page 351
5 Stress-Velocity Relationships......Page 364
5.1 Simple shear flow......Page 366
5.1.1 Velocity field......Page 368
5.1.2 Stress field......Page 369
5.1.3 Viscosity......Page 378
5.2 Newtonian fluids......Page 382
5.2.1 The constitutive equation......Page 387
5.2.2 Using the constitutive equation......Page 397
5.3 Non-Newtonian fluids......Page 411
5.3.1 Non-Newtonian viscosity......Page 412
5.3.2 Shear-induced normal stresses......Page 415
5.3.3 Inelastic constitutive equations......Page 420
5.3.4 Viscoelastic constitutive equations......Page 432
5.5 Problems......Page 436
Part III Flow Field Calculations......Page 445
6 Microscopic Balance Equations......Page 447
6.1 Deriving the microscopic balance equations......Page 448
6.1.1 Gauss-Ostrogradskii divergence theorem......Page 450
6.1.2 Mass balance......Page 451
6.1.3.1 General Fluids......Page 456
6.1.3.2 Newtonian Fluids......Page 459
6.1.4 Energy balance......Page 460
6.2 Using microscopic-balance equations......Page 463
6.2.1 Solution methodology......Page 464
6.2.1.1 The Equations......Page 465
6.2.1.2 Applying the Equations......Page 470
6.2.2 Boundary conditions......Page 482
6.2.3.1 Total Force on a Wall......Page 490
6.2.3.2 Torque......Page 496
6.2.3.3 Flow Rate and Average Velocity......Page 499
6.2.3.4 Velocity and Stress Extrema......Page 501
6.3 Summary......Page 503
6.4 Problems......Page 504
7.1 Circular pipes......Page 512
7.1.1 Laminar flow in pipes......Page 515
7.1.2 Turbulent flow in pipes......Page 529
7.1.2.1 Momentum balance in turbulent flow......Page 535
7.1.2.2 Dimensional analysis......Page 536
7.1.2.3 Data correlations......Page 547
7.2 Noncircular conduits......Page 558
7.2.1.1 Poisson equation......Page 559
7.2.1.2 Poiseuille number and hydraulic diameter......Page 572
7.2.2 Turbulent flow in noncircular ducts......Page 588
7.3 More complex internal flows......Page 590
7.3.1 Unsteady-state solutions......Page 591
7.3.2 Quasi-steady-state solutions......Page 595
7.3.3 Geometrically complex flows (including lubrication approximation, converging flows, and entry flows)......Page 598
7.4 Problems......Page 603
8 External Flows......Page 618
8.1 Flow around a sphere......Page 619
8.1.1 Creeping flow around a sphere......Page 622
8.1.2 Noncreeping flow around a sphere......Page 640
8.1.2.1 Dimensional Analysis of Noncreeping Flow......Page 646
8.1.2.2 Flow Patterns......Page 665
8.1.2.3 Potential flow......Page 668
8.2 Boundary layers......Page 691
8.2.1 Laminar boundary layers......Page 696
8.2.2 Turbulent boundary layers......Page 714
8.2.3 Flow past blunt objects......Page 723
8.3.1 Vorticity......Page 736
8.3.2 Dimensional analysis redux......Page 744
8.4 Problems......Page 751
Part IV Advanced Flow Calculations......Page 757
9.1 Deriving the macroscopic balance equations......Page 759
9.1.1 Macroscopic mass-balance equation......Page 760
9.1.2 Macroscopic momentum-balance equation......Page 763
9.1.3 Energy balance......Page 768
9.1.3.1 Closed systems......Page 769
9.1.3.2 Open systems......Page 771
9.1.3.3 Mechanical energy balance......Page 777
9.2 Using the macroscopic balance equations......Page 784
9.2.1 Pressure-measurement devices......Page 787
9.2.2 Flow-rate-measurement devices......Page 790
9.2.3 Valves and fittings......Page 797
9.2.4 Pumps......Page 818
9.2.4.1 Pump Sizing......Page 819
9.2.4.2 Net Positive Suction Head......Page 832
9.2.5 Open-channel flow......Page 841
9.3 Problems......Page 848
10.1 Viscosity, drag, and boundary layers......Page 856
10.2.1 Strategy......Page 858
10.2.2 Software packages......Page 860
10.2.3 Accuracy......Page 861
10.3 Laminar flow, turbulent flow......Page 863
10.3.1 Statistical modeling of turbulence......Page 864
10.3.2 Flow instability......Page 869
10.4 Lift, circulation......Page 871
10.5 Flows with curved streamlines......Page 879
10.6 Compressible flow and supersonic flow......Page 885
10.8 Problems......Page 892
Part V Appendices......Page 897
 Appendix A: Glossary......Page 899
B.1 Differential operations on vectors and tensors......Page 910
B.2 Differential operations in rectangular and curvilinear coordinates......Page 916
Bibliography......Page 925
Index......Page 935