Preface |
|
xi | |
|
|
1 | (18) |
|
|
2 | (4) |
|
1.2 The continuum approximation |
|
|
6 | (3) |
|
|
9 | (2) |
|
|
11 | (3) |
|
1.5 Cartesian coordinate systems |
|
|
14 | (1) |
|
|
15 | (4) |
|
|
19 | (76) |
|
|
21 | (20) |
|
|
21 | (3) |
|
|
24 | (3) |
|
|
27 | (2) |
|
|
29 | (4) |
|
|
33 | (1) |
|
2.6 Application: Earth's homentropic atmosphere |
|
|
34 | (4) |
|
2.7 Application; The Sun's convective envelope |
|
|
38 | (3) |
|
|
41 | (16) |
|
3.1 Archimedes' principle |
|
|
41 | (3) |
|
3.2 The gentle art of ballooning |
|
|
44 | (2) |
|
3.3 Stability of floating bodies |
|
|
46 | (2) |
|
|
48 | (9) |
|
|
57 | (12) |
|
4.1 Fluid interfaces in hydrostatic equilibrium |
|
|
57 | (1) |
|
4.2 The centrifugal force |
|
|
58 | (2) |
|
|
60 | (2) |
|
4.4 The Earth, the Moon, and the tides |
|
|
62 | (4) |
|
4.5 Application: The tides of Io |
|
|
66 | (3) |
|
|
69 | (26) |
|
5.1 Basic physics of surface tension |
|
|
69 | (4) |
|
|
73 | (3) |
|
5.3 Pressure discontinuity |
|
|
76 | (2) |
|
5.4 The Rayleigh-Plateau instability |
|
|
78 | (3) |
|
|
81 | (3) |
|
5.6 Meniscus at a flat wall |
|
|
84 | (2) |
|
5.7 Meniscus in a cylindrical tube |
|
|
86 | (2) |
|
5.8 Application: Sessile drops and captive bubbles |
|
|
88 | (2) |
|
5.9 Application: Pendant drops and tethered bubbles |
|
|
90 | (5) |
|
|
95 | (92) |
|
|
97 | (12) |
|
|
97 | (2) |
|
|
99 | (2) |
|
6.3 The nine components of stress |
|
|
101 | (3) |
|
6.4 Mechanical equilibrium |
|
|
104 | (2) |
|
6.5 Asymmetric stress tensors |
|
|
106 | (3) |
|
|
109 | (16) |
|
|
109 | (3) |
|
7.2 The displacement field |
|
|
112 | (4) |
|
7.3 Geometrical meaning of the strain tensor |
|
|
116 | (3) |
|
|
119 | (1) |
|
|
120 | (5) |
|
|
125 | (14) |
|
8.1 Young's modulus and Poisson's ratio |
|
|
125 | (3) |
|
8.2 Hooke's law in isotropic matter |
|
|
128 | (4) |
|
8.3 Static uniform deformation |
|
|
132 | (2) |
|
|
134 | (5) |
|
|
139 | (24) |
|
9.1 Equations of elastostatics |
|
|
139 | (3) |
|
9.2 Standing up to gravity |
|
|
142 | (4) |
|
|
146 | |
|
|
130 | (23) |
|
9.5 Application: Radial deformation of a spherical body |
|
|
153 | (3) |
|
9.6 Application: Radial deformation of a cylindrical body |
|
|
156 | (7) |
|
|
163 | (14) |
|
10.1 Small deflections without torsion |
|
|
163 | (3) |
|
10.2 Buckling instability |
|
|
166 | (3) |
|
10.3 Large deflections without torsion |
|
|
169 | (2) |
|
10.4 Mixed bending and twisting |
|
|
171 | (2) |
|
10.5 Application: The helical spring |
|
|
173 | (4) |
|
11 Computational elastostatics |
|
|
177 | (10) |
|
11.1 Theory of the numeric method |
|
|
177 | (3) |
|
11.2 Discretization of space |
|
|
180 | (2) |
|
11.3 Application: Gravitational settling in two dimensions |
|
|
182 | (5) |
|
|
187 | (150) |
|
|
189 | (18) |
|
|
189 | (3) |
|
|
192 | (2) |
|
|
194 | (4) |
|
12.4 Equations of continuum dynamics |
|
|
198 | (2) |
|
12.5 Application: Big Bang |
|
|
200 | (1) |
|
12.6 Application: Newtonian cosmology |
|
|
201 | (6) |
|
|
207 | (22) |
|
13.1 Euler equation For incompressible ideal flow |
|
|
207 | (2) |
|
13.2 Application: Collapse of a spherical cavity |
|
|
209 | (2) |
|
13.3 Steady incompressible ideal flow |
|
|
211 | (5) |
|
|
216 | (3) |
|
|
219 | (1) |
|
|
220 | (2) |
|
13.7 Application: Cylinder in uniform crosswind |
|
|
222 | (3) |
|
13.8 Application: Sphere in a uniform stream |
|
|
225 | (1) |
|
13.9 d'Alembert's paradox |
|
|
226 | (3) |
|
|
229 | (14) |
|
14.1 Small-amplitude sound waves |
|
|
229 | (4) |
|
14.2 Steady compressible flow |
|
|
233 | (4) |
|
14.3 Application: The Laval nozzle |
|
|
237 | (6) |
|
|
243 | (18) |
|
|
243 | (3) |
|
15.2 Velocity-driven planar flow |
|
|
246 | (4) |
|
15.3 Dynamics of incompressible Newtonian fluids |
|
|
250 | (3) |
|
15.4 Classification of flows |
|
|
253 | (2) |
|
15.5 Dynamics of compressible Newtonian fluids |
|
|
255 | (2) |
|
15.6 Application: Viscous attenuation of sound |
|
|
257 | (4) |
|
|
261 | (26) |
|
16.1 Steady, incompressible, viscous flow |
|
|
261 | (1) |
|
16.2 Pressure-driven channel flow |
|
|
262 | (3) |
|
16.3 Gravity-driven planar flow |
|
|
265 | (3) |
|
|
268 | (6) |
|
16.5 Phenomenology of turbulent pipe flow |
|
|
274 | (3) |
|
16.6 Laminar cylindric flow |
|
|
277 | (4) |
|
16.7 Secondary flow and Taylor vortices |
|
|
281 | (6) |
|
|
287 | (22) |
|
|
287 | (2) |
|
17.2 Creeping flow around a solid ball |
|
|
289 | (5) |
|
|
294 | (4) |
|
|
298 | (6) |
|
17.5 Application: Loaded journal bearing |
|
|
304 | (5) |
|
|
309 | (14) |
|
|
309 | (3) |
|
18.2 Steady flow in a rotating system |
|
|
312 | (3) |
|
|
315 | (3) |
|
18.4 Application: Steady bathtub vortex |
|
|
318 | (2) |
|
18.5 Debunking an urban legend |
|
|
320 | (3) |
|
19 Computational fluid dynamics |
|
|
323 | (14) |
|
19.1 Unsteady, incompressible flow |
|
|
323 | (2) |
|
19.2 Temporal discretization |
|
|
325 | (1) |
|
19.3 Spatial discretization |
|
|
326 | (4) |
|
19.4 Application: Laminar channel entry flow |
|
|
330 | (7) |
|
IV Balance and conservation |
|
|
337 | (64) |
|
|
339 | (16) |
|
20.1 Quantities and sources |
|
|
339 | (3) |
|
|
342 | (1) |
|
|
343 | (3) |
|
20.4 Angular momentum balance |
|
|
346 | (2) |
|
20.5 Kinetic energy balance |
|
|
348 | (3) |
|
20.6 Mechanical energy balauce |
|
|
351 | (4) |
|
|
355 | (16) |
|
|
355 | (4) |
|
|
359 | (7) |
|
21.3 Application: The Francis turbine |
|
|
366 | (5) |
|
|
371 | (22) |
|
22.1 First Law of Thermodynamics |
|
|
371 | (4) |
|
22.2 Incompressible fluid at rest |
|
|
375 | (5) |
|
22.3 Incompressible fluid in motion |
|
|
380 | (4) |
|
22.4 General homogeneous isotropic fluids |
|
|
384 | (9) |
|
|
393 | (8) |
|
23.1 Entropy in classical thermodynamics |
|
|
393 | (2) |
|
|
395 | (3) |
|
|
398 | (3) |
|
|
401 | (186) |
|
|
403 | (16) |
|
|
403 | (3) |
|
|
406 | (3) |
|
24.3 Refraction and reflection |
|
|
409 | (5) |
|
|
414 | (5) |
|
|
419 | (24) |
|
|
419 | (3) |
|
25.2 Harmonic surface waves |
|
|
422 | (2) |
|
25.3 Open surface gravity waves |
|
|
424 | (5) |
|
|
429 | (2) |
|
|
431 | (3) |
|
25.6 Global wave properties |
|
|
434 | (5) |
|
25.7 Statistics of wind-generated ocean waves |
|
|
439 | (4) |
|
|
443 | (18) |
|
|
443 | (5) |
|
|
448 | (2) |
|
26.3 Stationary shocks in uniformly moving fluids |
|
|
450 | (4) |
|
26.4 Application: Atmospheric blast wave |
|
|
454 | (7) |
|
|
461 | (20) |
|
27.1 Free cylindrical vortices |
|
|
461 | (3) |
|
|
464 | (2) |
|
|
466 | (5) |
|
27.4 Advective vortex spin-up |
|
|
471 | (1) |
|
27.5 Steady vortex sustained by secondary flow |
|
|
472 | (3) |
|
27.6 Application: The bathtub vortex |
|
|
475 | (6) |
|
|
481 | (32) |
|
28.1 Basic physics of boundary layers |
|
|
481 | (4) |
|
28.2 Boundary layer theory |
|
|
485 | (2) |
|
|
487 | (5) |
|
28.4 Turbulence in the Blasius layer |
|
|
492 | (4) |
|
28.5 Planar stagnation flow |
|
|
496 | (2) |
|
28.6 Self-similar boundary layers |
|
|
498 | (3) |
|
28.7 Laminar boundary layer separation |
|
|
501 | (1) |
|
|
502 | (3) |
|
28.9 Wall derivative plus momentum balance |
|
|
505 | (1) |
|
28.10 Momentum plus energy balance |
|
|
506 | (2) |
|
28.11 Integral approximation to separation |
|
|
508 | (5) |
|
|
513 | (34) |
|
|
513 | (3) |
|
29.2 Aerodynamic forces and moments |
|
|
516 | (1) |
|
|
517 | (3) |
|
|
520 | (7) |
|
|
527 | (5) |
|
29.6 Lift, drag, and the trailing wake |
|
|
532 | (5) |
|
29.7 Two-dimensional airfoil theory |
|
|
537 | (4) |
|
29.8 The distant laminar wake |
|
|
541 | (6) |
|
|
547 | (18) |
|
30.1 Heat-driven convection |
|
|
547 | (5) |
|
30.2 Convective instability |
|
|
552 | (3) |
|
30.3 Linear stability analysis of convection |
|
|
555 | (2) |
|
30.4 Application: Rayleigh-Benard convection |
|
|
557 | (8) |
|
|
565 | (22) |
|
31.1 Scaling in fully developed turbulence |
|
|
565 | (6) |
|
31.2 Mean flow and fluctuations |
|
|
571 | (3) |
|
31.3 Universal inner layer near a smooth wall |
|
|
574 | (5) |
|
|
579 | (2) |
|
31.5 Application: Turbulent channel flow |
|
|
581 | (1) |
|
31.6 Application: Turbulent pipe flow |
|
|
582 | (2) |
|
|
584 | (3) |
|
|
587 | (44) |
|
|
589 | (6) |
|
|
589 | (1) |
|
|
590 | (1) |
|
A.3 Moment of force and angular momentum |
|
|
591 | (1) |
|
A.4 Power and kinetic energy |
|
|
592 | (1) |
|
A.5 Internal and external forces |
|
|
593 | (1) |
|
A.6 Hierarchies of particle interactions |
|
|
594 | (1) |
|
|
595 | (16) |
|
|
595 | (1) |
|
|
596 | (2) |
|
|
598 | (1) |
|
|
599 | (2) |
|
B.5 Cartesian coordinate transformations |
|
|
601 | (3) |
|
B.6 Scalars, vectors, and tensors |
|
|
604 | (7) |
|
|
611 | (8) |
|
|
611 | (2) |
|
|
613 | (1) |
|
C.3 Fundamental integral theorems |
|
|
614 | (1) |
|
C.4 Proofs of the fundamental integral theorems |
|
|
615 | (1) |
|
C.5 Field transformations |
|
|
616 | (3) |
|
D Curvilinear coordinates |
|
|
619 | (8) |
|
D.1 Cylindrical coordinates |
|
|
619 | (4) |
|
D.2 Spherical coordinates |
|
|
623 | (4) |
|
|
627 | (4) |
|
|
627 | (2) |
|
|
629 | (2) |
Answers to problems |
|
631 | (34) |
References |
|
665 | (8) |
Index |
|
673 | |