Understanding Fluid Flow

by Grae Worster

Overview

Understanding Fluid Flow takes a fresh approach to introducing fluid dynamics, with physical reasoning and mathematical developments inextricably intertwined. The ‘dry' fluid dynamics described by potential theory is set within the context of real viscous flows to give fundamental insight into how fluids behave. The book gives a flavor of theoretical, experimental and numerical approaches to analyzing fluid flow, and implicitly develops skills in applied mathematical modeling of physical systems. It is supplemented by movies that are freely downloadable.

Product Details

ISBN-13:	9780521132893
Publisher:	Cambridge University Press
Publication date:	12/14/2009
Series:	AIMS Library of Mathematical Sciences
Pages:	120
Product dimensions:	5.50(w) x 8.30(h) x 0.50(d)

About the Author

Grae Worster studied Mathematics at Cambridge University and gained a PhD in Geological Fluid Mechanics. He was an Instructor in Applied Mathematics at MIT, a Research Fellow at Trinity College, Cambridge and an Assistant Professor at Northwestern University before finally returning to Cambridge University in 1992, where he is Professor of Fluid Dynamics. Within the Institute of Theoretical Geophysics, his research encompasses the dynamics of buoyancy-driven flows associated with solidification and melting.

Table of Contents

Preface xi

1 Building intuition 1

Viscous fluids 1

Normal stress 3

The no-slip condition 3

A viscous gravity current 4

Dynamic viscosity 5

Tangential shear stress 6

Assignment 1 7

2 Parallel viscous flow 9

Momentum equation 9

Boundary conditions 10

Parallel flow in a channel 11

Poiseuille flow in a pipe 13

Film flow on a vertical surface 15

Couette versus Poiseuille 16

Unsteady parallel viscous flows 18

Kinematic viscosity 22

Viscous boundary layers 23

3 Viscous gravity currents 25

Scaling analysis 27

Velocity profile and volume flux 27

Conservation of mass 28

Similarity solution 29

Assignment 2 31

4 Equations of flow 37

The Navier-Stokes momentum equation 37

Hydrostatic and dynamic pressure 39

Mass conservation 40

Stream functions 42

Scaling the Navier-Stokes equations 45

Stagnation-point flow 49

Viscous boundary layer 50

Bernoulli's theorem 54

The momentum integral 57

5 Interactions between linear flows 63

Linear flow 63

Pure straining flow 64

Vorticity 65

The vorticity equation 65

Vortex stretching 66

Dissipation and generation of vorticity 68

6 Flows around rigid objects 71

Irrotational incompressible potential flow 71

Potential flow past a sphere 71

The force in potential flow 73

Flow separation and drag 74

The origin of separation 75

Circulation around a rigid body 77

Irrotational flow with circulation - causing lift 79

7 Waves and instability 83

Energy conservation in potential flow 83

Waves on deep water 84

Properties of deep-water waves 86

Ship wakes 88

Group velocity 90

Hydrodynamic instability 92

Turbulence 98

Epilogue 100

Bibliography 101

Index 103

Editorial Reviews

"The accounts collated in this book...is encouraging, not only for the survival of the great apes, but the many other organisms that share their habitat".
Peter Moore, Bulletin of the British Ecological Society

"Worster is commended for rigorously articulating complex phenomena in these short lectures while unraveling the salient features of fluid dynamics, including flow separation and shear layer roll up due to advection of vortices, to name some examples."
R.N. Laoulache, Choice Magazine

"I found the book a pleasant read, and I could imagine lecturers finding the exposition helpful in providing tips for class material or a different perspective. I enjoyed the tack taken by the author and his selection of topics. The book certainly gives an idea of the wide application of the methods of mathematics and physics to problems in areas ranging from geophysics to engineering."
Neil Balmforth, SIAM Review

From the Publisher