L SECOND EDITION PIJUSH K. KUNDU 0 IRA M. COHEN Fluid Mechanics, Second Edition Founders of Modern Fluid Dynamics Ludwig Prandtl (1875-1953) G. I. Taylor (18861975) (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 See Visual Archieves. Copyright, American Institute of Physics, 2000. Fluid Mechanics Second Edition Rjucsh K. Kundu Oceanographic Center Nova Universily Dmiu. Florida Ira M. Cohen Departnient of Mechanicid En.gineering and Applied Meclurnics Universiry of Pennsylvania Philadelphici, Pennsylvania with a chapter on Computational Fluid Dynamics by Howard H. Hu ACADEMIC PRESS A HarcourL Sciencc and Technology Company San Diego San Francisco New York Boston London Sydney Tokyo Coverphoto: Karman vortex street behind a ckular cylindcr at R = 1 OS. Photograph by Sadatoshi Taneda Coverphoto: Karmnn vortex street behind a circular cylinder at R = 140. Photograph by Snd;ltoshi Taneda This book is printcd on acid-frcc paper. @ Copyright 02002,1990 by Elsevier Science (USA). All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocogy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department, Academic Pms, 6277 Sea Harbor Drive, Orlando, Florida 32887-6777 Academic press An imprint afElsevier Science 525 B Streek Suite 1900, San Diego, California 92101-4495, USA http://www.academicpress.com Academic Press 84 Theobalds Road, hdon WClX 8RR, UK http://www.academicpmss.com Library orcOngress Catalog Card Numbcr: 2001086884 International Standard RookNumber: 0-12-1782514 PRIMED m- THE =D STATES OF AMERICA 02 03 04 Hp 9 8 7 6 5 4 3 2 The second 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 “Ifnature were not beauhB1, it would not be worth studying it. And life would not be worth living ” -Henry Poincad 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 Oceanog- raphy 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 Preface xvii Preface to First Edition xix Author’s Notes xxiz ~~huplt?r 1 1.n troduction 1 2 1. Fluid Mechanics 2. Units of Measurement. 3. Solids, Liquids, and Gases. 3 4. Continuum Hypothesis 4 5. Transport Phmomena 6. Surfacc Tension 7. FluidStatics 9 8. Classical Thcrmodynamics 12 9. Perfcct: Gas 10. Static Equilibrium of a Compressible Medium 17 Exercises 22 Literature Cited 23 Supplemcntal Reading 23 5 8 16 Uiqter 2 (lartcsian X:nsors 1. ScalarsandVeclors 24 2. Rotation of Axes: Formal Dcfinition of a Vector 25 vi i [...]... between Infinitely Decp Fluids 16 Waves in a Finitc Layer Overlying an Infinitely Deep Fluid 17 Shallow Layer Overlying an Inhitcly Deep Fluid 18 Equations of Motion for a Continuously Stratified Fluid 19 Internal Wavcs in a Continuously Stratificd Fluid 20 Dispersion of Jntcrnal Wavcs in a Stratified Fluid 21 Encrgy Considerations of Internal Wavcs in a Stratified Fluid Exercises Litcrature... Litemium CiM 23 Supp/ernmLd R(!udirig 23 I lluid Mechanics Fluid mechanics deals with the flow of fluids Its study is important to physicists, whosc main interest is in understanding phcnomena They may, for example, be interested in learning what causcs the various typcs of wave phenomena in the atmosphere and in the ocean, why a layer of fluid hcated from below brcaks up into cellular patterns,... thc reader can follow up with specialized texts for a more comprehcnsive understanding An historical survey of fluid mcchanics from thc time of Archimedes (ca 250 B.C.E.) to approximately 1900 is provided in the Eleventh Edition of 7;he Encyclopmliu Britunnicu (1910) in Vol XIV (under “Hydromechanics,” pp 115-135) 1 am grateful to Professor Hcrrnan Gluck (Professor of Mathematics at the University of... computational fluid dynamics, graciously provided an cntircly new chapter, Chapter 1 1, thcrchy providing the student with an entree into this cxploding new field Both finite diffcrcncc and Gnite element methods arc introduced and a delailed worked-out cxamplc of each is provided 1 have becn a studcnt 01 fluid mechanics since 1954 when I entered college to study aeronauticalengineering I have been teaching fluid. .. from below brcaks up into cellular patterns, why a tcnnis ball hit with “top spin” dips rather sharply, how fish swim, and bow birds fly The study or fluid mechanics is just as important to engjneers, whose main interest is in the applications of fluid mechanics io solve industrial problems Aerospace engineers may be intcrcsted in designing airplanes that have low resistance and, at thc same time, high... interested in designing turbines, heat cxchangers, and fluid cou2l ings Chemical enginccrs may be intcrested in designing efficient devices to mix industrial chemicals The objectivcs of physicists and enginccrs, howevcr, are 1 not quite separable because the engineers need to understand and thc physicists need to be rnotivatcd through applications Fluid mechanics, like the study of any other branch of science,... withdrawn In contrast, a fluid de€orms Figme 11 Dclormtrlionof solid and fluid clcmcnts: (a) solid; and (b) tluid continuously under the action of a shear force, however small Thus, the clement of the fluid ABCD confined between parallel plates (Figure l.lb) deforms to shapes such as ABC’D’ and Al3C”D” as long as h e force F is maintained on the upper plate Therefore, wc say that a fluid flows The qualification... stress in the fluid, just as the drag cxperienced by the two trains results from the momentum exchangc through the transfer or coal particles Thc fluid above AB tends to push the fluid underneath forward, whereas the fluid below AB tends to drag tbe uppcr fluid backward Experiments show that the magnitude of the shear stress 7 along a surface such as AB is, io a good approximation,related to thc velocity... trcatcd and discusscd in this kxt This second cdition also contains additional material on slreamfunctions,boundary condilions, viscous flows, boundary layers, jets, and compressible flows Most important, there is an entirely ncw chapter on computationalfluid dynamicsthat introduces the student to the various tcchuiques for numerically integrating the cquations governing fluid motions HopcFully the introduction... forward to working with Yijush on the second edition after my term as department chainnan ended in mid-1997 For the next year and a half, howcvcr, scrious family health problems detoured any plans Discussions on this cdition resumed in July ol 1999 and wcrc concludcd in the Spring or 2000 when my work really started This hook remains thc principal work product of Pijush K Kundu, especially the lengthy chapters . L SECOND EDITION PIJUSH K. KUNDU 0 IRA M. COHEN Fluid Mechanics, Second Edition Founders of Modern Fluid Dynamics Ludwig. Copyright, American Institute of Physics, 2000. Fluid Mechanics Second Edition Rjucsh K. Kundu Oceanographic Center Nova Universily Dmiu.