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Fluid Mechanics - Problem Solver - WILLIAMS, Angielskie techniczne
[ Pobierz całość w formacie PDF ]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
copyright owner. Inquiries should be addressed to 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
WV
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
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