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 [...]... more comprehcnsive understanding An historical survey of fluid 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... 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 B 1 Cylindrical Polar Coordinates B2 Plane Polar Coordinates B3 Spherical Polar Coordinates +per& 7 10 712 712 C Founders of Modern... Operdtion of Nozzlcs at Dimerent Back Pressures Effects of Friction and Heating in Constant-Area Ducts Mach Cone IO Oblique Shock Wave 1 1 Expansion and Compression in Supersonic Flow 12 Thin Airfoil Thcory in Supersonic Flow Exerci 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... Diffusion of a Vortex Sheet 9 Decay of a Line Vortex 10 Flow Due to an Oscillating Plate 11 High and Low Reynolds Number Flows 12 Creeping Flow around a Sphere 13 Nonuniformityof 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 ... Orr-Sommerfeld Equation 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... July ol 1999 and wcrc 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 chapters on Gravity Waves, Instability, and Geophysical Fluid Dynamics, his areas or expertise I have addcd ncw material to all of the other chapters, often providing an alternative point of view Specifically, vcctor field derivativeshave... Prolessor Wallace D Hayes (1918- 200 1), who expressed xvii xviii PrcJacw fluid mechanicsin the clearest way I have ever seen, and Professor Martin D Kruskal, whose use of mathematics to solve difficult physical problcms was developed to a high art form and reminds me of a Vivaldi trumpet concerto His codificationof rules of applied limit processes into the principles of “Asymptotology” remajns with me... 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 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... thinks of 20 possible moves; he analyzes all of them and picks the one that he likes A great chess player, on the othcr hand, analyzes only two o thrcc possible moves; r his unusual intuition (part of which must have grown from expcrience) allows him immediately to rule out a large number of moves without going through an apparent logical analysis Ludwig Prandtl, onc of the founders of modem fluid mechanics,. .. used most of the timc The basic uniis I TAl3LE 1.1 STUnits ~~ _ Quantity Namc of unit Lcnpth Mass Tim Tcmpcralure Frcqucnq Force Pressurc bcw Power mew kilogram second kelvin hertz ncwton pascal joule Symbol Equivalent _ rn ks Y K H Z S-' N Pa kgms Nm -2 Nm Js ' J W wall TABLE 1.2 Common Refixcs Prclix Symbol Multiplc M k 106 10 ' d c 10- 2 _ Mcgii Kilo Dcci Ccnti Milli Micro IO ' rn P 10- 6 of t h i . L SECOND EDITION PIJUSH K. KUNDU 0 IRA M. COHEN Fluid Mechanics, Second Edition Founders of Modern Fluid Dynamics Ludwig Prandtl (1875-1953) G UK http://www.academicpmss.com Library orcOngress Catalog Card Numbcr: 200 108 6884 International Standard RookNumber: 0- 12-1782514 PRIMED m- THE =D STATES OF AMERICA 02 03 04 . Dimensional Matrix 4 . Buckingham's Pi Theorem 5 . 6 . 7 . Nondimensional Parameters and Dynamic Similarity Commcnls on Model Testing Significance of Common Nondimensional