Introduction to theoretical aerodynamics and hydrodynamics

220 Pages·2011·2.02 MB·English

by  Sears W.M.

Introduction to Theoretical Aerodynamics and
Hydrodynamics
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Introduction to Theoretical
Aerodynamics and
Hydrodynamics
William R. Sears
Edited by Demetri P. Telionis
Virginia Polytechnic Institute and State University
EducAtIon SErIES
Joseph A. Schetz
Editor-in-Chief
Virginia Polytechnic Institute and State University
Blacksburg, Virginia
Published by
AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS, INC.
1801 ALEXANDER BELL DRIVE, RESTON, VA 20191-4344
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American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
1 2 3 4 5
Library of Congress Cataloging-in-Publication Data
Sears, William Rees, 1913-2002.
Introduction to theoretical aerodynamics and hydrodynamics /
William R.Sears.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-60086-773-6
1. Aerodynamics. 2. Hydrodynamics. I. Title.
TL570.S38 2011
533′.62—dc22
2010052541
Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All
rights reserved. Printed in the United States of America. No part of this publication
may be reproduced, distributed, or transmitted, in any form or by any means, or
stored in a database or retrieval system, without the prior written permission of the
publisher.
Data and information appearing in this book are for informational purposes only.
AIAA is not responsible for any injury or damage resulting from use or reliance, nor
does AIAA warrant that use or reliance will be free from privately owned rights.
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AIAA EducAtIon SErIES
Editor-In-Chief
Joseph A. Schetz
Virginia Polytechnic Institute and State University
Editorial Board
Takahira Aoki Brian Landrum
University of Tokyo University of Alabama in Huntsville

João Luiz F. Azevedo Timothy C. Lieuwen
Comando-Geral De Tecnologia Georgia Institute of Technology
Aeroespacial
Michael Mohaghegh
Karen D. Barker The Boeing Company
Robert H. Bishop Conrad F. Newberry
University of Texas at Austin
Brett Newman
Richard Colgren Old Dominion University
University of Kansas
Joseph N. Pelton
James R. DeBonis George Washington University
NASA Glenn Research Center
Mark A. Price
Kajal K. Gupta Queen’s University Belfast
NASA Dryden Flight Research Center
David M. Van Wie
Rikard B. Heslehurst Johns Hopkins University
University of New South Wales
Rakesh K. Kapania
Virginia Polytechnic Institute and
State University
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ConTenTs
Preface xi
Preface (1970) xiii
Chapter 1 Kinematics of Fluid Flows 1
1.1 Introduction 1
1.2 Functional Representation of Fluid Motion 2
1.3 Eulerian Equations 3
1.4 Continuity 3
1.5 Plane Flow 6
1.6 Axisymmetric Flow 6
1.7 Stream Function for Plane Flow 7
1.8 Stream Function for Axisymmetric Flow 9
1.9 Vorticity 10
1.10 Circulation 12
1.11 Velocity Potential 13
1.12 Kinematic Properties of Rotational Flows 17
1.13 Velocity Field of a Vortex in
Incompressible Flow 18
1.14 Velocity Induced by a Vortex Filament 20
Reference 22
Problems 22
Chapter 2 Dynamics of Frictionless Fluids 25
2.1 Frictionless Fluids 25
2.2 Pressure 26
2.3 Eulerian Equations of Motion 26
2.4 Other Forms of the Equations of Motion 28
2.5 Integration of the Dynamical Equations in S pecial Cases 29
2.6 Some Dynamical Properties of Rotational Flow 32
2.7 Irrotational and Incompressible Flow 35
2.8 Physical Interpretation of Velocity Potential 35
2.9 Equations in a Moving Coordinate System 37
Reference 39
Problems 39
vii
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viii Introduction to Theoretical Aerodynamics and Hydrodynamics
Chapter 3 Irrotational Motion of an Incompressible Fluid:
Laplace’s Equation 41
3.1 Introduction 41
3.2 Laplace’s Equation 42
3.3 Membrane Analogy 44
3.4 Plane Irrotational Incompressible Flow 45
3.5 Elementary Plane Flows 49
3.6 Other Elementary Plane Flows 53
3.7 Elementary Axisymmetric Flows 59
3.8 Other Elementary Axisymmetric Flows 61
Problems 64
Chapter 4 M otion of Bodies in an Incompressible
Frictionless Fluid 67
4.1 Introduction 67
4.2 Flow Past a Blunt-Ended Rod 70
4.3 Flow Past a Sphere 71
4.4 Flow Around a Circular Cylinder 72
4.5 M ultiply-Connected Regions and Cyclic C onstants 75
4.6 Dirichlet’s Theorem 79
4.7 Barriers 81
4.8 Distribution of Singularities: Plane Case 83
4.9 Distributions of Sources: Axisymmetric Case 90
4.10 Method of Images 93
4.11 Nonsteady Flows 97
4.12 Impulse and Momentum 102
4.13 P roof of Kelvin’s Result: Force Equals Rate of
Change of Impulse 105
4.14 I mpulse Components in Terms of Kinetic Energy 107
4.15 Case of Pure Translation: Apparent Mass 109
4.16 Steady Translation: D’Alembert’s P aradox 112
4.17 Approximate Calculation of Airship Force D istribution 114
4.18 Extension to Cyclic Flows 115
References 116
Problems 116
Chapter 5 P lane Irrotational Incompressible Flow:
Complex Variables 121
5.1 Introduction 121
5.2 Regular Functions 123
5.3 Complex Potential Is a Regular Function 128
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Contents ix
5.4 Complex Velocity 130
5.5 Complex Potentials of Simple Flows 132
5.6 Conformal Mapping 137
5.7 Singularities of a Transformation 139
5.8 Conformal Mapping in Hydrodynamics 140
5.9 Some Examples of Conformal Transformations 141
5.10 Example of the Use of Conformal Mapping 151
5.11 General Expressions for the Force on a Cylinder 154
5.12 Cauchy’s Theorems Regarding Contour Integrals 156
5.13 Blasius’s Formulas 157
5.14 Laurent’s Expansion 158
5.15 Residues 159
5.16 Poles and Essential Singularities 160
5.17 Force on a Body in a Parallel Stream 163
5.18 Calculation of Force and Moment in a
Transformed Plane 165
References 167
Problems 167
Appendix Vector Analysis 171
A.1 Introduction 171
A.2 Methods of Representing Vectors in Symbols 172
A.3 Transformation of Vectors 173
A.4 Multiplication of Vectors 176
A.5 Derivatives Involving Vectors 180
A.6 Expansion Formulas 187
A.7 Volume and Surface Integrals—Gauss’s Theorem 188
A.8 Stokes’s Theorem 189
A.9 Vector Operators in General Curvilinear
Orthogonal Coordinates 190
A.10 Dyadic Products and Second-Order Tensors 196
A.11 Rotating Coordinate Systems 197
Reference 198
Problems 199
Index 201
Supporting Materials 205
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