Preface
Contents
1. Terminology; Velocity Fields, Particle Paths, Spatial and Material Coordinates
2. Some Examples of Fluid Motions
3. Some Preliminary Mathematics; An Algebraic Lemma and a Review of Vector Calculus
4. Flow of a Vector Field
5. The Transport Theorem
6. Conservation of Mass
7. Balance of Momentum; Cauchy's Stress Principle
8. Balance of Momentum; Equations of Motion
9. Perfect Fluids and Euler's Equations
10. Potential Flow
11. The Kutta-Joukowski Theorem and the paradox of lift
12. Energy of a Fluid and the Deformation Tensor
13. Momentum Transfer Equation and d'Alembert's Paradox
14. Kelvin's Circulation Theorem
15. The Helmholtz Theorem
16. Viscous Fluids and the Navier-Stokes Equation
17. The Reynolds Number Re
18. Stability, Bifurcation and Large Reynolds Numbers
19. A Brief Survey of Thermodynamics
20. Ideal Compressible Flow
21. Shock Waves
22. Boundary Layers
23. Remarks on Turbulence Theory
A. Some Vector Identities
B. Vector Calculus Formulae and the Navier-Stokes Equations in Cylindrical and Spherical Coordinates
C. The Stress Tensor for a Viscous Incompressible Fluid