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First Course in Fluid Dynamics

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ISBN-10: 0521274249

ISBN-13: 9780521274241

Edition: 1983

Authors: A. R. Paterson

List price: $89.99
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Description:

How can the drag coefficient of a car be reduced? What factors govern the variation in the shape of the Earth's magnetosphere? What is the basis of weather prediction? These are examples of problems that can only be tackled with a sound knowledge of the principles and methods of fluid dynamics. This important discipline has applications which range from the study of the large-scale properties of the galaxies to the design of high precision engineering components. This book introduces the subject of fluid dynamics from the first principles. The first eleven chapters cover all the basic ideas of fluid mechanics, explaining carefully the modelling and mathematics needed. The last six chapters…    
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Book details

List price: $89.99
Copyright year: 1983
Publisher: Cambridge University Press
Publication date: 11/10/1983
Binding: Paperback
Pages: 540
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.584
Language: English

Preface
Introduction
Fluid dynamics
Structure of the text
Method of working
Reference
Mathematical preliminaries
Background knowledge
Polar coordinate systems
The vector derivative, [down triangle, open]
Cartesian tensor methods
Integration formulae
Formulae in polar coordinates
Exercises
References
Physical preliminaries
Background knowledge
Mathematical modelling
Properties of fluids
Dimensional reasoning
Exercise
Observational preliminaries
The continuum model
Fluid velocity and particle paths
Definitions
Streamlines and streaklines
Exercises
References
Mass conservation and stream functions
The continuity equation
The convective derivative
The stream function for two-dimensional flows
Some basic stream functions
Some flow models and the method of images
The (Stokes) stream function for axisymmetric flows
Models using the Stokes stream function
Exercises
References
Vorticity
Analysis of the motion near a point
Simple model flows
Models for vortices
Definitions and theorems for vorticity
Examples of vortex lines and motions
Exercises
References
Hydrostatics
Body forces
The stress tensor
The form of the stress tensor
Hydrostatic pressure and forces
Exercises
References
Thermodynamics
Basic ideas and equations of state
Energy and entropy
The perfect gas model
The atmosphere
Exercises
References
The equation of motion
The fundamental form
Stress and rate of strain
The Navier-Stokes equation
Discussion of the Navier-Stokes equation
Exercises
References
Solutions of the Navier-Stokes equations
Flows with only one coordinate
Some flows with two variables
A boundary layer flow
Flow at high Reynolds number
Exercises
References
Inviscid flow
Euler's equation
The vorticity equation
Kelvin's theorem
Bernoulli's equation
Examples using Bernoulli's equation
A model for the force on a sphere in a stream
Exercises
References
Potential theory
The velocity potential and Laplace's equation
General properties of Laplace's equation
Simple irrotational flows
Solutions by separation of variables
Separation of variables for an axisymmetric flow: Legendre polynomials
Two unsteady flows
Bernoulli's equation for unsteady irrotational flow
The force on an accelerating cylinder
D'Alembert's paradox
Exercises
References
Sound waves in fluids
Background
The linear equations for sound in air
Plane sound waves
Plane waves in musical instruments
Plane waves interacting with boundaries
Energy and energy flow in sound waves
Sound waves in three dimensions
Exercises
References
Water waves
Background
The linear equations
Plane waves on deep water
Energy flow and group velocity
Waves at an interface
Waves on shallower water
Oscillations in a container
Bessel functions
Exercises
References
High speed flow of air
Subsonic and supersonic flows
The use of characteristics
The formation of discontinuities
Plane shock waves
Exercises
References
Steady surface waves in channels
One-dimensional approximation
Hydraulic jumps or bores
Changes across a hydraulic jump
Solitary waves
Exercises
References
The complex potential
Simple complex potentials
More complicated potentials
Potentials for systems of vortices
Image theorems
Calculation of forces
Exercises
References
Conformal mappings and aerofoils
An example
Mappings in general
Particular mappings
A sequence of mappings
The Joukowski transformation of an ellipse
The cambered aerofoil
Further details on aerofoils
Exercises
References
Hints for exercises
Answers for exercises
Books for reference
Index