Fundamentals of Fluid Dynamics

Preface v

Chapter 1. Vector Calculus 1
1.1. Review / 2
1.2. The Del (∇)Operator / 3
1.3. Indicial Notation / 4
1.4. The ε–δ Theorem / 7
1.5. Vector Calculus / 8
1.6. Curvilinear Coordinate System / 10
1.7. Integral Theorems / 15
Exercise Problems for Chapter 1 / 20
Solved Problems for Chapter 1 / 22

Chapter 2. Thermodynamic Properties of Fluids 35
2.1. Equation of State / 36
2.2. The First Law of Thermodynamics / 37
2.3. Isentropic Processes / 43
2.4. Compressibility / 48
Exercise Problems for Chapter 2 / 49
Solved Problems for Chapter 2 / 51

Chapter 3. Fluid Statics 63
3.1. Pressure / 64
3.2. Equation of Fluid Statics / 65
3.3. Examples of Hydrostatics / 67
3.4. Hypsometric Equation / 70
3.5. Stability of the Atmospheric Column / 73
Exercise Problems for Chapter 3 / 78
Solved Problems for Chapter 3 / 81

Chapter 4. Fluid Kinematics 97
4.1. Pictorial Method of Description / 98
4.2. Eulerian Representation / 98
4.3. Particle Derivative of the Velocity Vector / 103
4.4. Physical Meaning of Gradient, Divergence and Curl / 106
4.5. Linear and Shear Strain Rates / 110
Exercise Problems for Chapter 4 / 113
Solved Problems for Chapter 4 / 116

Chapter 5. Conservation Laws 131
5.1. Equation of Continuity / 132
5.2. Mass Conservation for Material Volume / 134
5.3. Conservation of Momentum / 135
5.4. Conservation of Vorticity / 137
Exercise Problems for Chapter 5 / 139
Solved Problems for Chapter 5 / 142

Chapter 6. Frictionless Flow 151
6.1. Force / 152
6.2. Equation of Motion / 153
6.3. Euler’s Equation / 155
6.4. Bernoulli Equation / 158
6.5. Equation of Motion in Cylindrical Coordinates / 162
Exercise Problems for Chapter 6 / 166
Solved Problems for Chapter 6 / 169

Chapter 7. Motion with Rotation 181
7.1. Vorticity / 182
7.2. Vortex Motions / 182
7.3. Circulation Theorem / 185
7.4. Vorticity Equation / 187
7.5. Vorticity Equation in Cylindrical Coordinates / 190
Exercise Problems for Chapter 7 / 194
Solved Problems for Chapter 7 / 197

Chapter 8. Velocity Potential and Stream Function 215
8.1. Velocity Potential / 216
8.2. Stream Function / 219
8.3. Vortex Filament and Vortex Tube / 224
8.4. Superposition of Flows / 226
8.5. Complex Potential / 231
Exercise Problems for Chapter 8 / 236
Solved Problems for Chapter 8 / 239

Chapter 9. Viscous Flow 253
9.1. Physical Meaning of Viscous Stress / 254
9.2. Symmetry of Viscous Stress / 255
9.3. Constitutive Equation for a Newtonian Fluid / 257
9.4. Navier-Stokes Equation / 261
9.5. Simple Examples of Viscous Flow / 262
9.6. The Reynolds Number / 269
Exercise Problems for Chapter 9 / 271
Solved Problems for Chapter 9 / 274

Chapter 10. The Effect of the Earth’s Rotation 295
10.1. Motion in a Rotating Frame of Reference / 296
10.2. Fictitious Acceleration in a Rotating Frame / 297
10.3. Equation of Motion in a Rotating Frame / 299
10.4. Vorticity Equation in a Rotating Frame / 300
10.5. The Geostrophic Equation / 304
10.6. Vorticity Conservation on the β-Plane / 306
10.7. The Rossby Number / 309
10.8. The Ekman Number / 310
Exercise Problems for Chapter 10 / 312
Solved Problems for Chapter 10 / 316

Chapter 11. Energy Conservation Principles 333
11.1. Conservation of Mechanical Energy / 334
11.2. Conservation of Internal Energy / 336
11.3. General Relations among Physical Properties / 338
11.4. Entropy Equation and the Second Law / 339
Exercise Problems for Chapter 11 / 342
Solved Problems for Chapter 11 / 345

Appendix 355
A.1. Useful Constants and Parameters / 356
A.2. MKS Units of Physical Quantities / 358
A.3. Equation of Motion in Spherical Coordinates / 359
A.4. Vorticity Equation in Spherical Coordinates / 360

Index 363