# Theoretical Fluid Mechanics

- Richard Fitzpatrick

- December 2017

### Description

*Theoretical Fluid Mechanics* has been written to aid physics students who wish to pursue a course of self-study in fluid mechanics. It is a comprehensive, completely self-contained text with equations of fluid mechanics derived from first principles, and any required advanced mathematics is either fully explained in the text, or in an appendix. It is accompanied by about 180 exercises with completely worked out solutions. It also includes extensive sections on the application of fluid mechanics to topics of importance in astrophysics and geophysics. These topics include the equilibrium of rotating, self-gravitating, fluid masses; tidal bores; terrestrial ocean tides; and the Eddington solar model.

### About Editors

Richard Fitzpatrick is a professor of physics at the University of Texas at Austin, where he has been a faculty member since 1994. He is a member of the Royal Astronomical Society, a fellow of the American Physical Society, and the author of *Maxwell's Equations and the Principles of Electromagnetism* (2008), *An Introduction to Celestial Mechanics* (2012), *Oscillations and Waves: An Introduction* (2013), *Plasma Physics: An Introduction* (2014), and *Quantum Mechanics* (2015). He earned a master's degree in physics from the University of Cambridge and a DPhil in astronomy from the University of Sussex.

### Table of Contents

1 - Mathematical Models of Fluid Motion

2 - Hydrostatics

3 - Surface Tension

4 - Incompressible Inviscid Flow

5 - Two-Dimensional Incompressible Inviscid Flow

6 - Two-Dimensional Potential Flow

7 - Axisymmetric Incompressible Inviscid Flow

8 - Incompressible Boundary Layers

9 - Incompressible Aerodynamics

10 - Incompressible Viscous Flow

11 - Waves in Incompressible Fluids

12 - Terrestrial Ocean Tides

13 - Equilibrium of Compressible Fluids

14 - One-Dimensional Compressible Inviscid Flow

15 - Two-Dimensional Compressible Inviscid Flow

Appendix A - Vectors and Vector Fields

Appendix B - Cartesian Tensors

Appendix C - Non-Cartesian Coordinates

Appendix D - Ellipsoidal Potential Theory

Appendix E - Calculus of Variations

Appendix F - Solutions to Exercises in Chapter 1

Appendix G - Solutions to Exercises in Chapter 2

Appendix H - Solutions to Exercises in Chapter 3

Appendix I - Solutions to Exercises in Chapter 4

Appendix J - Solutions to Exercises in Chapter 5

Appendix K - Solutions to Exercises in Chapter 6

Appendix L - Solutions to Exercises in Chapter 7

Appendix M - Solutions to Exercises in Chapter 8

Appendix N - Solutions to Exercises in Chapter 9

Appendix O - Solutions to Exercises in Chapter 10

Appendix P - Solutions to Exercises in Chapter 11

Appendix Q - Solutions to Exercises in Chapter 12

Appendix R - Solutions to Exercises in Chapter 13

Appendix S - Solutions to Exercises in Chapter 14

Appendix T - Solutions to Exercises in Chapter 15

Appendix U - Solutions to Exercises in Appendix A

Appendix V - Solutions to Exercises in Appendix B

Appendix W - Solutions to Exercises in Appendix C

Appendix X - Solutions to Exercises in Appendix D

Appendix Y - Solutions to Exercises in Appendix E

### Bibliographic

Hardback ISBN: 9780750315524

Ebook ISBN: 9780750315548

DOI: 10.1088/978-0-7503-1554-8

Publisher: Institute of Physics Publishing