# Fluid Dynamics: Part 1: Classical Fluid Dynamics

## Anatoly I. Ruban and Jitesh S. B. Gajjar

### Abstract

This book, the first of a four-part series on fluid dynamics, consists of four chapters on classical theory suitable for an introductory undergraduate course. Chapter 1 discusses the continuum hypothesis and introduces macroscopic functions. The forces acting inside a fluid are analysed, and the Navier–Stokes equations are derived for incompressible and compressible fluids. Chapter 2 studies the properties of flows represented by exact solutions of the Navier–Stokes equations, including Couette flow between two parallel plates, Hagen–Poiseuille flow through a pipe, and Kármán flow above an inf ... More

This book, the first of a four-part series on fluid dynamics, consists of four chapters on classical theory suitable for an introductory undergraduate course. Chapter 1 discusses the continuum hypothesis and introduces macroscopic functions. The forces acting inside a fluid are analysed, and the Navier–Stokes equations are derived for incompressible and compressible fluids. Chapter 2 studies the properties of flows represented by exact solutions of the Navier–Stokes equations, including Couette flow between two parallel plates, Hagen–Poiseuille flow through a pipe, and Kármán flow above an infinite rotating disk. Chapter 3 deals with inviscid incompressible flows, starting with a discussion of integrals of the Euler equations, the Bernoulli integral, and the Cauchy–Lagrange integral. Kelvin’s Circulation Theorem is proved, and used to identify physical situations where a flow can be treated as potential. Attention is principally directed at two-dimensional potential flows. These can be described in terms of a complex potential, allowing the full power of the theory of functions of a complex variable to be used. The method of conformal mapping is introduced and used to study various flows, including flow past Joukovskii aerofoils. Chapter 4 introduces the elements of gasdynamics, describing compressible flows of a perfect gas, including supersonic flows. Particular attention is paid to the theory of characteristics, which is used, for example, to analyse Prandtl–Meyer flow over a body surface bend and a corner. Shock waves are discussed and the chapter concludes with analysis of unsteady flows, including the theory of blast waves.

*Keywords: *
fluid dynamics,
Navier–Stokes equations,
Euler equations,
gasdynamics,
supersonic flows

### Bibliographic Information

Print publication date: 2014 |
Print ISBN-13: 9780199681730 |

Published to Oxford Scholarship Online: August 2014 |
DOI:10.1093/acprof:oso/9780199681730.001.0001 |

### Authors

#### Affiliations are at time of print publication.

Anatoly I. Ruban, *author*

Professor, Department of Mathematics, Imperial College London

Jitesh S. B. Gajjar, *author*

Professor of Applied Mathematics, School of Mathematics, University of Manchester

More
Less