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# Viscous Fluid Flow - 3rd ed. - Frank M. White (2006)

(Parte **1** de 5)

McGraw-Hill Series in Mechanical Engineering

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VISCOUS FLUID FLOW Third Edition

Frank M. White University of Rhode Island

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VISCOUS FLUID FLOW, THIRD EDITION International Edition 2006

The McGraw·Hill Companies ,

Exclusive rights by McGraw-Hill Education (Asia), for manufacture and exporL This book cannot be re-exported from the country to which it is sold by McGraw-HilL The International Edition is not available in North America.

Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc. 1221 Avenue of the Americas, New York, NY 10020. Copyright© 2006, 1991, 1974 by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States.

10 09 08 07 06 05 04 03 02 01 20 09 08 07 06 05 CTF SLP

Library of Congress Control Number: 2004058182

When ordering this title, use ISBN 007-124493-X

Printed in Singapore w.mhhe.com

I Frankj M. White is Professor Emeritus of Mechanical and Ocean Engineering at the Utjiversity of Rhode Island. He is a native of Augusta, Georgia, and went to undergraduate school at Georgia Tech, receiving a B .M.E. degree in 1954. Then he attend~d the Massachusetts Institute of Technology for an S.M. degree in 1956, return~·l g to Georgia Tech to earn a Ph.D. degree in mechanical engineering in 1959. e began teaching aerospace engineering at Georgia Tech in 1957 and moved to the · niversity of Rhode Island in 1964. He retired in January 1998.

t the University of Rhode Island, Frank became interested in oceanographic and co~stal flow problems and in 1966 helped found the first Department of Ocean Engin~ering in the United States. His research interests have mainly been in viscous flow a' d convection heat transfer. Known primarily as a teacher and writer, he receiv d the ASEE Westinghouse Teaching Excellence Award in addition to seven Unive sity of Rhode Island teaching awards. His modest research accomplishments includ some 80 technical papers and reports, the ASME Lewis F. Moody Research Award in 1973, and the ASME Fluids Engineering Award in 1991. He is a Fellow of the ~SME and for 12 years served as editor-in-chief of the ASME Journal of Fluids JEngineering. He received a Distinguished Alumnus award from Georgia

Tech it 1990 and was elected to the Academy of Distinguished Georgia Tech Alumn· in 1994.

I addition to the present text, he has written three undergraduate textbooks:

Fluid echanics, Heat Transfer, and Heat and Mass Transfer. He continues to serve ~n the ASME Publications Committee and has been a consulting editor of the McGraJW-Hill Encyclopedia of Science and Technology since 1992. He lives with his wiff, Jeanne, in Narragansett, Rhode Island.

My wife, Jeanne Faucher White, is the key to this book.

Without her love and encouragement, I can't even get started.

1-1 I-2

1-3 1-4

2-1 2-2

2-3 2-4

2-5 2-6 2-7 2-8 2-9 2-10 2-1 2-12 2-13

Jl>reface xiii ifjst of Symbols XVll I

~reliminary Concepts

rps tori cal Outline | 1 |

~ome Examples of Viscous-Flow Phenomena | 4 |

Plroperties of a Fluid | 15 |

~oundary Conditions for Viscous-Flow Problems | 45 |

I Siummary | 54 |

Problems | 5 |

Itundamental Equations of Compressible Viscous Flow 59 I

I1troduction | 59 |

qiassification of The Fundamental Equations | 59 |

Oonservation of Mass: The Equation of Continuity | 60 |

C!onservation of Momentum: The Navier-Stokes Equations | 62 |

T~e Energy Equation (First Law of Thermodynamics) | 69 |

Bpundary Conditions for Viscous Heat-Conducting Flow | 74 |

ojrthogonal Coordinate Systems | 75 |

Ntathematical Character of The Basic Equations | 7 |

Dpmensionless Parameters in Viscous Flow | 81 |

Vf rticity Considerations in Incompressible Viscous Flow | 84 |

Two-Dimensional Considerations: The Stream Function | 86 |

N~ninertial Coordinate S~stems | 8 |

Cpntrol-Volume Formulations | 89 |

~t:::~ i I

I ix x CONTENTS

3-1 Introduction and Classification of Solutions | 96 |

3-2 Couette Flows Due to Moving Surfaces | 98 |

3-3 Poiseuille Flow through Ducts | 106 |

3-4 Unsteady Duct Flows | 125 |

3-5 Unsteady Flows with Moving Boundaries | 129 |

3-6 Asymptotic Suction Flows | 135 |

3-7 Wind-Driven Flows: The Ekman Drift | 141 |

3-8 Similarity Solutions | 144 |

3-9 Low Reynolds Number: Linearized Creeping Motion | 165 |

3-10 Computational Fluid Dynamics | 183 |

Summary | 205 |

Problems | 205 |

3 Solutions of The Newtonian Viscous-Flow Equations 96

4-1 Introduction | 215 |

4-2 Laminar Boundary-Layer Equations | 225 |

4-3 Similarity Solutions for Steady Two-Dimensional Flow | 230 |

4-4 Free-Shear Flows | 251 |

4-5 Other Analytic Two-Dimensional Solutions | 257 |

4-6 Approximate Integral l'v1ethods | 261 |

4-7 Digital-Computer Solutions | 271 |

4-8 Thermal-Boundary-Layer Calculations | 278 |

4-9 Flow in the Inlet of Ducts | 287 |

4-10 Rotationally Symmetric Boundary Layers | 290 |

4-1 Asymptotic Expansions and Triple-Deck Theory | 300 |

4-12 Three-Dimensional Laminar Boundary Layers | 307 |

4-13 Unsteady Boundary Layers: Separation Anxiety | 318 |

4-14 Free-Convection Boundary Layers | 321 |

Summary | 328 |

Problems | 328 |

4 La1ninar Boundary Layers 215

5-1 Introduction: The Concept of Small-Disturbance Stability | 337 |

5-2 Linearized Stability of Parallel Viscous Flows | 344 |

5-3 Parametric Effects in the Linear Stability Theory | 357 |

5-4 Transition to Turbulence | 370 |

5-5 Engineering Prediction of Transition | 378 |

Summary | 394 |

5 The Stability of Laminar Flows 337 Problems ......................................................................................................................... 394

I CONTEJ1'ffS xi

6-1 6-2 6-3 6-4 6-5 6-6

6-7 6-8 6-9 6-10

7-1 7-2 7-3

7-4 7-5 7-6 7-7 7.8 7-9

~ncompressible Turbulent Mean Flow 398

Physical and Mathematical Description of Turbulence | 398 |

i I

rhe Reynolds Equations of Turbulent Motion | 406 |

1fhe Two-Dimensional Turbulent-Boundary-Layer Equations | 411 |

Velocity Profiles: The Inner, Outer, and Overlap Layers | 414 |

furbulent Flow in Pipes and Channels | 425 |

the Turbulent Boundary Layer on a Flat Plate | 433 |

turbulence Modeling | 440 |

,f\nalysis of Turbulent Boundary Layers with a Pressure Gradient | 454 |

free Turbulence: Jets, Wakes, and Mixing Layers | 473 |

rurbulent Convective Heat Transfer | 485 |

ummary | 498 |

froblems | 498 |

Compressible-Boundary-Layer Flow 505 I

fotroduction: The Compressible-Boundary-Layer Equations | 505 Solutio~s for Compressible Lamin.ar Flo~ ................................................... 511 |

~olut10ns for Lammar Flat-Plate and Stagnat1on-Pomt Flow | 514 |

¢ompressible Laminar Boundary Layers under Arbitrary Conditions | 525 |

$pecial Topics in Compressible Laminar Flow | 539 |

The Compressible-Turbulent-Boundary-Layer Equations | 544 |

'fvall and Wake Laws for Turbulent Compressible Flow | 547 |

¢ompressible Turbulent Flow Past a Flat Plate | 553 |

¢ompressible-Turbulent-Boundary-Layer Calculation with a Pressure Gradient | 561 |

~ummary | 566 |

Piroblems | 566 |

iransport Properties of Various Newtonian Fluids | 571 |

I • Jj\.ppend1ces 571

dylindrical and Spherical Polar Coordinates | 581 |

I A. Runge-Kutta Subroutine for N Simultaneous Differential Equations | 585 |

~quations of Motion of Incompressible Newtonian Fluids in

*ibliography | 590 |

Ibdex | x |

The thifd edition of this book continues the goal of serving as a senior or first-year gradua~e textbook on viscous flow with engineering applications. Students should be exp4cted to have knowledge of basic fluid mechanics, vector calculus, ordinary and pa*ial differential equations, and elementary numerical analysis. The material can be iselectively presented in a one-semester course or, with fuller coverage, in two qu~rters or even two semesters. At the author's institution, the text is used in a first-se~ester graduate course that has, as a prerequisite, a one-semester junior course fluid mechanics.

The evolution of viscous-flow prediction continues toward CFD instead of physic~] insight and mathematical analysis. However, this book still exists to intro- ' duce vi$cous-flow concepts, not software. Dozens of new books and monographs on

CFD a1e discussed and listed here for further specialized study. Since the second edition appeared in 1991, more than 10,0 new articles have been published on viscousl flows. Clearly, the present book is an introductory textbook, not a comprehensivel state-of-the-art treatment of the entire field. The goal is to make the book readable and informative and to introduce graduate students to the field.

New tJ this edition: I

• Ove~ 30 percent of the problems are new or revised.

• Newt.lmaterial has been added to Chapters 1, 3, and 4 on microftows, slip in liquids, gas sip flow in tubes and channels, and a novel micropump.

• Secf on 2-9 on Dimensional Analysis is completely rewritten. Material has been! added on Euler's equation and inviscid flow analysis and their relation to viscqus flow.

I xiii xiv PREFACE

• Chapter 5 begins with the classic Kelvin-Helmholtz wind-wave instability.

• Turbulence modeling in Chapter 6 is completely rewritten, expanded, and updated

• Chapter 7 includes a detailed discussion of isentropic flow analysis to increase its relation to the understanding of viscous effects.

• References are completely updated. • An Instructor and Student Resource Web Site is available to users of the text.

The seven-chapter format of the book remains the same. Chapter 1 covers the basic properties of fluids and introductory concepts. New material has been added on microflows, slip in liquids, and an improved discussion of boundary conditions for flow. Chapter 2 covers the basic equations of flow, with a bit of condensing of Secs.

2-8, 9 and 2-1, 12. Section 2-9 on Dimensional Analysis has been completely rewritten. Material has been added on Euler's equation and inviscid flow analysis and their relation to viscous flow.

Chapter 3 treats a variety of laminar-flow solutions, both analytical and numerical, of the Navier-Stokes equation. A number of new exact solutions are discussed and the Stokes paradox is illuminated a bit more. The creeping-flow discussion is updated. Two new interesting engineering CFD applications are given for liquid spheres and a novel micropump. Chapter 4 has some obsolete material deleted, such as the Stratford separation criterion. A new section has been added on unsteady boundary layers, including acoustic streaming and the Goldstein/MRS separation criteria. Numerical solutions are covered, but the traditional integral methods remain.

Chapter 5 has dropped the beam-buckling instability analogy and now begins with the classic Kelvin-Helmholtz wind-wave instability. A great wind-shear photo by Brooks Martner has been added. The concept of pseudoresonance has been added. Section 5-4 on transition processes has been completely rewritten. New results of DNS transition prediction are now discussed.

Chapter 6 has been updated with many new references, but the basic outline of turbulent mean-flow prediction remains. Section 6-7 on modeling has been completely rewritten. The power-law overlap layer controversy is now included. DNS predictions are augmented.

Chapter 7 has two new photos of supersonic boundary-layer flow. Isentropic flow analysis is added to increase our understanding of viscous effects. There is a new discussion of Morkovin's hypothesis. Section 7-7 on compressible wall-wake laws has been rewritten.

The three Appendices are pretty much the same. More fluid property data have been added to App. A. Appendix C, a Runge-Kutta subroutine, is still useful and clarifies numerical integration. However, more and more readers are changing to spreadsheet calculations.

I PREFAqE xv

I SUPlfLEMENTS

The 1ew Instructor and Student Resource Web Site, http://www.mhhe.com/ whitele, will house general text information, the solutions to end-of-chapter problems qunder password-protection), additional problems (with password-protected solutiqns), and helpful Web links.

I ACKlNOWLEDGMENTS

There ]are many people to thank. Much appreciated comments, suggestions, photos, charts~ corrections, and encouragement were received from Leon van Dommelen of Florid~ State University; Gary Settles of Penn State University; Steven Schneider of Purdu¢ University; Kyle Squires of Arizona State University; Chihyung Wen of Da- Yeh Upiversity, Taiwan; Brooks Martner of the NOAA Environmental Technology Labonhory; Jay Khodadadi of Auburn University; Philipp Epple of Friedrich- ' Alexa1der-Universitat; Jurgen Thoenes of the University of Alabama at Huntsville; Luca cjl' Agostino of Universita Degli Studi di Pisa; Raul Machado of the Royal Institute of Technology (KTH), Sweden; Gordon Holloway of the University of New Brunsi.rick; Abdulaziz Almukbel of George Washington University; Dale Hart of Louisi~na Tech University; Debendra K. Das of the University of Alaska Fairbanks; Alexa~der Smits of Princeton University; Hans Fernholz of Technische Unive*itaet Berlin; Peter Bernard of the University of Maryland; John Borg of Marqu~tte University; Philip Drazin of the University of Bristol, UK; Ashok Rao of Rant;ho Santa Margarita, CA; Deborah Pence of Oregon State University; Joseph I

Katz of Johns Hopkins University; Pierre Dogan of the Colorado School of Mines;

Philip I Burgers of San Diego, CA; Beth Darchi of the American Society of Mech~nical Engineers; and Norma Brennan of the American Institute of Aeron4utics and Astronautics.

I I have tried to incorporate almost all of the reviewer comments, criticisms, correcdions, and improvements. The third edition has greatly benefited from the review~rs of the second edition text, as well as the reviewers of the third edition i • manus<pnpt:

i Malcoljm J. Andrews, Texas A&M University

Mehdi tsheghi, Carnegie Mellon University Rober~LBreidenthal, University of Washington H. A. tjlassan, North Carolina State University Herma~ Krier, University of Illinois, Urbana-Champaign Daniel \Maynes, Brigham Young University SureshiMenon, Georgia Institute of Technology Mered*h Metzger, University of Utah Kamra* Mohseni, University of Colorado

Ugo Pipmelli, University of Maryland Steven r· Schneider, Purdue University xvi

Kendra Sharp, Pennsylvania State University Marc K. Smith, Georgia Institute of Technology Leon van Dommelen, FAMU-FSU Steve Wereley, Purdue University

The editors and staff at McGraw-Hill Higher Education, Amanda Green,

Jonathan Plant, Peggy Lucas, Rory Stein, Mark Neitlich, and Linda Avenarius, were constantly helpful and informative. The University of Rhode Island continues to humor me, even in retirement.

Frank M. White whitef@egr.uri.edu j I

Englis | Symbols |

a A b B

C, Ci, Cr cP, cv c

Ci D

Dh

Du e, E er f, F f, F, g g

G(Pr) h h, ho H speed of sound; acceleration (Chap. 2), body radius (Chap. 4) area; amplitude, Eq. (5-40); damping parameter, Eq. (6-90) jet or wake width, Fig. 6-35 stagnation-point velocity gradient (Sec. 3-8.1); turbulent wall-law intercept constant, Eq. (6-38a) wall-law shift due to roughness, Eq. (6-60) wave phase speeds (Chap. 5) specific heats, Eq. (1-69) Chapman-Rubesin parameter, Eq. (7-20) species concentrations (Chap. 1) diameter; drag force (Chap. 4); diffusion coefficient (Chap. 1) duct hydraulic diameter, Eq. (3-5) turbulent transport or diffusion, Eq. ( 6-1) internal energy internal plus kinetic plus potential energy, Eq. (2-113) force similarity variables acceleration of gravity heat-transfer parameter, Eqs. (3-172) and ( 4-78) enthalpy; duct width; heat-transfer coefficient metric coefficients, Eqs. (2-58) and (4-229) stagnation enthalpy, h + V2 /2 shape factor, B* /8; stagnation enthalpy, Eq. (7-3) alternate shape factor, (o -8*)/8 jet momentum, Eqs. (4-97), (4-206), and (6-144) thermal conductivity; roughness height (Chaps. 5 and 6) xvii xviii K e L

Lslip m in M n p p

Q r r, e, z r, e, ,\ ro R s s t T T*

Uo, Ur' U:::. u,v,w !1u

U,W v* vf3 v w x,y,z z bulk modulus, Eq. (1-84); duct pressure-drop parameter, Eq. ( 4-17 6); turbulence kinetic energy, Eq. (6-16); stagnation-point velocity gradient, Fig. 7-6 mean-free path (Chap. l); mixing length, Eq. (6-8) characteristic length slip length of a liquid, Eq. ( 1-89) mass; wedge-velocity exponent, Eq. (4-69) mass rate of flow molecular weight; moment, Eq. (3-190) normal to the wall; power-law exponent, Eq. (1-35) pressure effective pressure, p + pgz pressure gradient parameter, Eq. (3-42); duct perimeter heat-transfer rate per unit area; turbulence level, Eq. (5-43) heat; volume flow rate, Eq. (3-35) radial coordinate; recovery factor, Eq. (7-16) cylindrical polar coordinates, Eq. (2-63) spherical polar coordinates, Eq. (2-65) cylinder surface radius, Fig. 4-34 gas constant; body radius entropy Sutherland constant, Eq. (1-36); laminar shear parameter, Eq. (4-134); van Driest parameter, Eq. (7 -130) time temperature; percent turbulence, Eq. (5-43) wall heat-flux temperature, qw/(pcPv*); compressible-flow reference temperature, Eq. (7-42) surface tension coefficient Cartesian velocity components cylindrical polar velocity components turbulent velocity fluctuations wake velocity defect, Fig. 6-35c and Eq. (6-155) freestream velocity components wall-friction velocity, ( T ..,j p}-\,,)112 wake velocity, Eq. (6-137) velocity; also UjU0, Eq. (6-133) volume (Chap. 2) rate of work done on an element, Eq. (2-36) Cartesian coordinates gas compressibility factor, p/(pRT) boundary-layer shear stress stress tensor hypersonic interaction parameter, Eq. (7-86) dimensionless pressure gradient, Eq. (6-36); similarity variable, Eq. (7-19) vorticity; angular velocity; frequency molecular potential functions, Chap. 1 angular velocity heat-transfer coefficient, Eq. (3-14); ratio oT/o, Eq. (4-24)

(Parte **1** de 5)