KUNDU Fluid Mechanics 2 Episode 1 ppt

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 [...]... 7 Intcraction ol Vortices 8 Vortcx Shect Excrcises 76 77 79 81 82 84 86 88 92 94 97 99 10 4 10 8 10 9 11 0 11 4 11 7 12 1 12 2 12 4 14 2 12 5 12 6 12 6 13 0 13 4 13 6 14 1 14 4 14 5 Literature Cited SupplementalReading 14 6 14 7 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... Exercises Literam Cited Supplemental Reading 14 8 15 0 1 52 15 4 15 6 15 7 15 7 15 9 16 0 16 3 16 6 17 0 17 1 17 3 17 5 17 6 18 1 18 4 18 5 18 7 18 8 I89 19 0 1 92 1 92 chi!pter 7 Gravity Waves 1 2 3 4 5 Introduction TheWaveEquation WavcParameters SurfaceGravity Waves Some Features of Surface Gravity Waves 19 4 19 4 19 6 19 9 20 3 6 Approximalions for Deep and Shallow Water 7 Tnfluence... 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 20 9 21 3 21 6 21 8 22 1 22 5 22 7 23 0 23 2 23 4 23 8 24 0 24 2 24 5 24 a 25 0 25 4 25 5 NondimensionalParameters Determined from... 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 27 4 27 7 27 9 28 2 28 9 29 0 29 2 29 5 29 7 3 02 306 308 309 311 311 (Xapter 10 Boundary Layers... Theory of nrbulent Dispersion Exercises Literature Ciled SupplementalReading 5 12 514 517 524 522 528 536 539 540 546 5 52 553 554 Chapter I4 Geophysical Fluid Dynamks 1 Introduction 2 Vertical Variation of Density in Atmosphere and Ocean 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Equations of Motion Approximate Equations for a T i Layer on a Rotating Sphere hn Geostrophic... 11 Dynamics of Sports Balls 12 Two-DimensionalJets 13 Secondary Flows 14 Perturbation Techniques 15 An Example of a Regular Perturbation Problem 16 An Example of a Singular Perturbation Problem 17 Decay of a Laminar Shear Layer Exercises Literature Cited Supplemental Reading 1 3 12 313 318 3 21 323 3 32 335 336 339 346 347 350 358 359 364 366 3 71 374... and Three-DimensionalFlows 13 The Stxamfunction 14 Polar Coordinates Exercises Supplemental Reading 50 51 52 53 56 56 58 58 60 63 65 68 69 72 73 75 1 Tntmduction 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 I7 18 19 Timc Derivatives of Volume lntegrals Conservationof M s as Streamfunctions:Revisited and Generalized Origin of Forces in Fluid Stress at a Point... Curvilinear Coordi.nates B 1 Cylindrical Polar Coordinates B2 Plane Polar Coordinates B3 Spherical Polar Coordinates +per& 710 7 12 7 12 C Founders of Modern Fluid Dynamics Ludwig Prandtl(l875 -19 53) Geofli-ey Ingram Taylor (18 86 -19 75) Supplemental Reading Index 715 716 717 718 Preface My involvemcnt with Pijush Kundu s FluidMechunics first began in April 19 91 with a letter from him... Significance of Common Nondimensional Parametcrs Exerciscs Litcrature Cited Supplemcnlal Reading 25 6 25 7 26 1 26 2 26 4 26 6 26 8 27 0 27 0 27 0 I Introduction 2 Analogy between Heat and Vorticity Diffusion 3 Pressure Change Due to Dynamic Effects 27 1 27 3 27 3 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... I:.quationsof State 13 S1w:c:ific:I l r ~ t s 13 Stttmd IAW of l‘tierrri(xiynomics 14 TdS R e l u h f i sIm(i 15 15 Tlitmml Expansion Cot:ftitit:rit 15 9 l+&l C h I6 IO Skilie Equilihhm ( f a (,~ompn?ssil)kc Mxliwn 17 Poierihl ‘liimpcratiircarid Thsity 1 9 %de lkigh d thr 4trnouphcnt 21 EX(!triS(%S 22 Litemium CiM 23 Supp/ernmLd R(!udirig 23 I lluid Mechanics Fluid mechanics deals . 79 81 82 84 86 88 92 94 97 99 10 4 10 8 10 9 11 0 11 4 11 7 12 1 12 2 12 4 12 4 12 5 12 6 12 6 13 0 13 4 13 6 14 1 14 4 14 5 Literature Cited 14 6 Supplemental Reading 14 7 Ctuqter. Mapping 14 8 15 0 1 52 15 4 15 6 15 7 15 7 15 9 16 0 16 3 16 6 17 0 17 1 17 3 17 5 17 6 18 1 18 4 18 5 18 7 18 8 .I 89 19 0 1 92 1 92 chi!pter 7 Gravity Waves 1 . Introduction 19 4 2 2 . Analogy between Heat and Vorticity Diffusion 3 . Pressure Change Due to Dynamic Effects 20 9 21 3 21 6 21 8 22 1 22 5 22 7 23 0 23 2 23 4 23 8 24 0 24 2 24 5 24 a 25 0 25 4 25 5