Fluid Mechanics - Problem Solver - WILLIAMS.pdf - Angielskie techniczne - mrseba

The aim of this series is to provide an inexpensive source of fully solved

problems in a wide range of mathematical topics. Initial volumes cater

mainly for the needs of first-year and some second-year undergraduates

(and other comparable students) in mathematics, engineering and the

physical sciences, but later ones deal also with more advanced material. To

allow the optimum amount of space to be devoted to problem solving,

explanatory text and theory is generally kept to a minimum, and the scope

of each book is carefully limited to permit adequate coverage. The books are

devised to be used in conjunction with standard lecture courses in place of,

or alongside, conventional texts. They will be especially useful to the student

as an aid to solving exercises set in lecture courses. Normally, further problems

with answers are included as exercises for the reader.

This book provides the beginning student in theoretical Fluid Mechanics

with all the salient results together with solutions to problems which he is

likely to meet in his examinations. Whilst the essentials of basic theory are

either explained, discussed or fully developed according to importance, the

accent of the work is an explanation by illustration through the medium of

worked examples.

The coverage is essentially first- or second-year level and the book will be

valuable to all students reading for a degree or diploma in pure or applied

science where fluid mechanics is part of the course.

mechanics

J. WILLIAMS

PRICE NET

f 1.50

IN U.K. ONLY

ISBN 0 04 519015 1

fluid

Problem Solvers

Edited by L. Marder

Senior Lecturer in Mathematics, University of Southampton

No. 15

Fluid Mechanics

Problem Solvers

Fluid Mechanics

1 ORDINARY DIFFERENTIAL EQUATIONS - J. Heading

2 CALCULUS OF SEVERAL VARIABLES - L. Marder

3 VECTOR ALGEBRA - L. Marder

4 ANALYTICAL MECHANICS - D. F. Lawden

5 CALCULUS OF ONE VARIABLE - K. Hirst

6 COMPLEX NUMBERS - J. Williams

7 VECTOR FIELDS - L. Marder

8 MATRICES AND VECTOR SPACES - F. Brickell

9 CALCULUS OF VARIATIONS - J. W. Craggs

10 LAPLACE TRANSFORMS - J. Williams

11 STATISTICS I - A. K. Shahani and P. K. Nandi

12 FOURIER SERIES AND BOUNDARY VALUE PROBLEMS -

W. E. Williams

13 ELECTROMAGNETISM - D. F. Lawden

14 GROUPS -D. A. R. Wallace

J. WILLIAMS

Senior Lecturer in Appl~edMathemat2

Universzty of Exeter -

* 15 FLUID MECHANICS - J. Williams

16 STOCHASTIC PROCESSES - R. Coleman

LONDON . GEORGE ALLEN & UNWIN LTD

RUSKIN HOUSE MUSEUM STREET

First publishedw/

Contents

This book is copyriiht under the Berne Convention.

All rights are reserved. Apart from any fair dealing for the

purpose of private study, research, criticism or review, as

permitted under the Copyright Act 1956, no part of this

publication may be reproduced, stored in a retrieval system,

or transmitted, in any form or by any means, electronic,

electrical, chemical, mechanical, optical, photocopying

recording or otherwise, without the prior permission of the

publishers.

Q George Allen & Unwin Ltd, 1974

I ntro uction

1.2 The mobile operator DIDt

1.3 Flux through a surface

1.4 Equation of continuity

(1 5' ate of change of momentum

a Wej emE

1.7 F'EGZeequation

1.8 one-dimeisional gas dynamics

1.9 Channel flow

1.10 Impulsive motion

1.11 Kinetic energy

1.12 The boundary condition

1.13 Expanding bubbles

ISBN 0 04 519014 3 hardback

0 04 519015 1 paperback

Elementary complex potential

-- _/-----

2.6 Boundary condition on a moving cylinder

2.7 Kinetic energy

2.8 Rotating cylinders

2.9 Conformal mapving

2.10 Joukowski transformation

2.11 Kutta condition

2.12 The ~chwarz-~hristoffel

transformation

Printed in Great Britain

by Page Bros (Nonvich) Ltd., Norwich

in 10 on 12 pt Times Mathematics Series 569

4.2 Spherical polar coordinates

4.3 Elementary results

4.4 Butler's sphere theorem

4.5 Impulsive motion

4.6 Miscellaneous examples

TABLE 1 List of the main symbols used

TABLE 2 Some useful results in vector calculus

INDEX

2.13 Impulsive motion

Two-DlpyNsIoaAr uvsrEAor PLOW*

3.1. Fundamentals

3.2 -Pressure a& forces in unsteady flow ,

3.3 ,Paths of liquides

3.4 Surface waves

Chapter 1

General Flow

1.1 Introduction Fluid mechanics is concerned with the behaviour

of fluids (liquids or gases) in motion. One method, due to Lagrange, traces

the progress of the individual fluid particles in their movement. Each

particle in the continuum is labelled by its initial position vector (say)

a relative to a fixed origin 0 at time t = 0. At any subsequent time t > 0

this position vector becomes r = r(a, t) from which the particle's locus or

pathline is determined. In general, this pathline will vary with each fluid

particle. Thus every point P of the continuum will be traversed by an

infinite number of particles each with its own pathline. In Figure 1.1 let

A,, A,, A, be three such particles labelled by their position vectors

a, ,a,;a,. respectively, at time t = 0. Travelling along their separate

Figure I. I

pathlines, these fluid particles will arrive at P at different times and

continue to move to occupy the points A;, A;, A;, respectively, at some

time t = T. These points, together with P, lie on a curve called the streak-

line associated with the point P. If a dye is introduced at P a thin strand of

colour will appear along this streakline PA; A; Aj at time t = T. It is

obvious that this streakline emanating from P will change its shape with

time. A fourth fluid particle A, which at time t = 0 lies on the pathline

A,P will, in general, have a different pathline A, A: which may never pass

through P. The situation created by the 1,agrangian approach is com-

plicated and tells us more than we normally need to know about the fluid

Fluid Mechanics - Problem Solver - WILLIAMS.pdf

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