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0123737354Fluidmechanics.Pdf Fluid Mechanics, Fourth Edition Founders of Modern Fluid Dynamics Ludwig Prandtl G. I. Taylor (1875–1953) (1886–1975) (Biographical sketches of Prandtl and Taylor are given in Appendix C.) Photograph of Ludwig Prandtl is reprinted with permission from the Annual Review of Fluid Mechanics, Vol. 19, Copyright 1987 by Annual Reviews www.AnnualReviews.org. Photograph of Geoffrey Ingram Taylor at age 69 in his laboratory reprinted with permission from the AIP Emilio Segre` Visual Archieves. Copyright, American Institute of Physics, 2000. Fluid Mechanics Fourth Edition Pijush K. Kundu Oceanographic Center Nova Southeastern University Dania, Florida Ira M. Cohen Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia, Pennsylvania with contributions by P. S. Ayyaswamy and H. H. Hu AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier Academic Press is an imprint of Elsevier 30 Corporate Drive, Suite 400 Burlington, MA 01803, USA Elsevier, The Boulevard, Langford Lane Kidlington, Oxford, OX5 1GB, UK © 2008 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data Kundu, Pijush K. Fluid mechanics / Pijush K. Kundu, Ira M. Cohen. – 4th ed. p. cm. Includes bibliographical references and index. ISBN 978-0-12-373735-9 (alk. paper) / 1. Fluid mechanics. I. Cohen, Ira M. II. Title. QA901.K86 2008 620.1’06–dc22 2007042765 Reprinted January 2010 – ISBN: 978-0-12-381399-2 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. For information on all Academic Press publications visit our Web site at www.elsevierdirect.com Printed in the United States 10 11 12 13 14 10 9 8 7 6 5 4 3 2 1 The fourth edition is dedicated to the memory of Pijush K. Kundu and also to my wife Linda and daughters Susan and Nancy who have greatly enriched my life. “Everything should be made as simple as possible, but not simpler.” —Albert Einstein “If nature were not beautiful, it would not be worth studying it. And life would not be worth living.” —Henry Poincare´ In memory of Pijush Kundu Pijush Kanti Kundu was born in Calcutta, India, on October 31, 1941. He received a B.S. degree in Mechanical Engineering in 1963 from Shibpur Engineering College of Calcutta University, earned an M.S. degree in Engineering from Roorkee University in 1965, and was a lecturer in Mechanical Engi- neering at the Indian Institute of Technology in Delhi from 1965 to 1968. Pijush came to the United States in 1968, as a doctoral stu- dent at Penn State University. With Dr. John L. Lumley as his advisor, he studied instabili- ties of viscoelastic fluids, receiving his doctor- ate in 1972. He began his lifelong interest in oceanography soon after his graduation, working as Research Associate in Oceano- graphy at Oregon State University from 1968 until 1972. After spending a year at the University de Oriente in Venezuela, he joined the faculty of the Oceanographic Center of Nova Southeastern University, where he remained until his death in 1994. During his career, Pijush contributed to a number of sub-disciplines in physical oceanography, most notably in the fields of coastal dynamics, mixed-layer physics, internal waves, and Indian-Ocean dynamics. He was a skilled data analyst, and, in this regard, one of his accomplishments was to introduce the “empirical orthogonal eigenfunction” statistical technique to the oceanographic community. I arrived at Nova Southeastern University shortly after Pijush, and he and I worked closely together thereafter. I was immediately impressed with the clarity of his scien- tific thinking and his thoroughness. His most impressive and obvious quality, though, was his love of science, which pervaded all his activities. Some time after we met, Pijush opened a drawer in a desk in his home office, showing me drafts of several chapters to a book he had always wanted to write. A decade later, this manuscript became the first edition of “Fluid Mechanics,” the culmination of his lifelong dream; which he dedicated to the memory of his mother, and to his wife Shikha, daughter Tonushree, and son Joydip. Julian P. McCreary, Jr., University of Hawaii Contents New in This Book ......................................... xvi Preface ................................................... xvii Preface to Third Edition.................................... xix Preface to Second Edition .................................. xxi Preface to First Edition .................................... xxiii Author’s Notes ............................................ xxvii Chapter 1 Introduction 1. Fluid Mechanics ................................................. 1 2. Units of Measurement ............................................ 2 3. Solids, Liquids, and Gases ........................................ 3 4. Continuum Hypothesis ........................................... 4 5. Transport Phenomena ............................................ 5 6. Surface Tension .................................................. 8 7. Fluid Statics ..................................................... 9 8. Classical Thermodynamics ........................................ 12 9. Perfect Gas ...................................................... 16 10. Static Equilibrium of a Compressible Medium ...................... 18 Exercises ........................................................ 22 Literature Cited .................................................. 24 Supplemental Reading ............................................ 24 Chapter 2 Cartesian Tensors 1. Scalars and Vectors............................................... 25 2. Rotation of Axes: Formal Definition of a Vector ..................... 26 3. Multiplication of Matrices ........................................ 29 4. Second-Order Tensor ............................................. 30 5. Contraction and Multiplication .................................... 32 vii viii Contents 6. Force on a Surface ............................................... 33 7. Kronecker Delta and Alternating Tensor ............................ 36 8. Dot Product ..................................................... 37 9. Cross Product.................................................... 38 10. Operator ∇: Gradient, Divergence, and Curl ........................ 38 11. Symmetric and Antisymmetric Tensors ............................. 40 12. Eigenvalues and Eigenvectors of a Symmetric Tensor ................ 41 13. Gauss’ Theorem ................................................. 44 14. Stokes’ Theorem ................................................. 47 15. Comma Notation ................................................. 49 16. Boldface vs Indicial Notation...................................... 49 Exercises ........................................................ 50 Literature Cited .................................................. 51 Supplemental Reading ............................................ 51 Chapter 3 Kinematics 1. Introduction ..................................................... 53 2. Lagrangian and Eulerian Specifications ............................. 54 3. Eulerian and Lagrangian Descriptions: The Particle Derivative ........ 55 4. Streamline, Path Line, and Streak Line ............................. 57 5. Reference Frame and Streamline Pattern............................ 59 6. Linear Strain Rate ................................................ 60 7. Shear Strain Rate ................................................ 61 8. Vorticity and Circulation .......................................... 62 9. Relative Motion near a Point: Principal Axes ........................ 64 10. Kinematic Considerations of Parallel Shear Flows ................... 67 11. Kinematic Considerations of Vortex Flows .......................... 68 12. One-, Two-, and Three-Dimensional Flows ......................... 71
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