LSECOND EDITION PIJUSH K. KUNDU 0 IRA COHEN pot

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 [...]... scs 661 665 667 671 676 6 80 685 6 90 694 696 700 702 704 xvi Ctrnteith Literature Cited Supplemental R a i g edn +pen& 705 706 A Some Properties of Common Fluids A1 A2 A3 A4 Useful Conversion Factors Properties of Pure Water at Atmospheric Pressure Properties of Dry Air at Atmospheric Pressure Properties of Standard Atmosphere 707 708 708 709 Appendix B Curvilinear Coordi.nates... Shect Excrcises 76 77 79 81 82 84 86 88 92 94 97 99 104 108 109 1 10 114 117 121 122 124 14 2 125 126 126 1 30 134 136 141 144 145 Literature Cited SupplementalReading 146 147 Ctuqter 6 1rrotati.onalFlow 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1.7 18 19 20 21 22 Relevance of IrrotationalFlow Theory Velocity Potential: Laplace Equation Application of Complex Variables ... Stokes’ Solution and Oseen’s Improvement 14 Hele-Shaw Flow ia 15 F n l Remarks Exercises Literature Cited SupplementalReading 4 274 277 279 282 289 2 90 292 295 297 302 306 308 309 311 311 (Xapter 10 Boundary Layers and Related Topics 2 Introduction Boundary Layer Approximation 3 Different Measures of Boundary Layer Thickness 4 Boundary Layer on a Flat plate with... mcchanics from thc time of Archimedes (ca 2 50 B.C.E.) to approximately 1 900 is provided in the Eleventh Edition of 7;he Encyclopmliu Britunnicu (19 10) in Vol XIV (under “Hydromechanics,” pp 115-135) 1 am grateful to Professor Hcrrnan Gluck (Professor of Mathematics at the University of Pennsylvania) for scnding me this article Hydrostatics and classical (constant density) potential flows arc reviewed in considerable... 9 Tnviscid Stability of Parallel Flows 10 Some Results of Parallel Viscous Flows 11 Experimental Verification of Boundary Layer Instability 12 Comments on Nonlinear Effects ‘I3 Transition 14 Deterministic Chaos Exercises Literature Cited TI 378 3 80 385 393 406 424 427 428 4 30 431 432 444 448 453 461 467 471 475 4 80 482 483 485 493 495 Uurpler 13 ‘li.xhmlcncc ‘1... 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 Cited 1 Tntroduction 209 213 216 218 221 225 227 2 30 232 234 238 2 40 242 245 24a 2 50 254 255 NondimensionalParameters Determined from Differential Equations Dimensional... to hear that Pijush had died suddenly and unexpectedly It saddened me gcatly bccause I M been looking 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 200 0 when my work... Since this edition was completed,I found that thcrc is even more new and original material I would like to add But, alas, that will have to wait for the next edition The new figures and modifications of old figures were donc by Maryeileen Ranford with occasional assistance from the school’s software expert, Paul W Shaffer I greatly appreciate their job well done Ira M Cohen Preface to First Edition This... Streamfunctionand Velocity Potential for hisymmetric Flow Simple Examples of Axisymmetric Flows Flow around a Streamlined Body of Revolution Flow around an Arbitrary Body of Revolution Concluding Remarks Exercises Literam Cited Supplemental Reading 148 1 50 152 154 156 157 157 159 1 60 163 166 1 70 171 173 175 176 181 184 185 187 188 I89 1 90 192 192 chi!pter 7 Gravity Waves... 2 70 2 70 2 70 I Introduction 2 Analogy between Heat and Vorticity Diffusion 3 Pressure Change Due to Dynamic Effects 271 273 273 2 3 4 5 6 7 xii CMtml8 Steady Flow between Parallel Plates lw 5 Steady F o in a Pipe Steady Flow between Concentric Cylinders 6 7 Impulsively Started Plate: Similarity Solutions 8 Diffusion of a Vortex Sheet 9 Decay of a Line Vortex 10 . Supplemental Reading Index 705 706 707 708 708 709 7 10 712 712 715 716 717 718 Preface My involvemcnt with Pijush Kundu s FluidMechunics first. concludcd in the Spring or 200 0 when my work really started. This hook remains thc principal work product of Pijush K. Kundu, especially the lengthy