Fluid Mechanics - White - 7th Edition PDF

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Summary

Conversion Factors from BG to SI Units To convert from To Multiply by Acceleration ft/s2 m/s2 0.3048 Area ft2 m 2 9.2903 E  2 mi2 m2 2.5900 E  6 acres m2 4.0469 E  3 Density slug/ft3 kg/m3 5.1538 E  2 lbm/ft3 kg/m3 1.6019 E  1 Energy ft-lbf J 1.3558 Btu J 1.0551 E  3 cal J 4.1868 Force lbf N ...

Description

Conversion Factors from BG to SI Units

Acceleration

To convert from

To

Multiply by

ft/s2

m/s2

0.3048

2

2

Area

ft mi2 acres

m m2 m2

9.2903 E  2 2.5900 E  6 4.0469 E  3

Density

slug/ft3 lbm/ft3

kg/m3 kg/m3

5.1538 E  2 1.6019 E  1

Energy

ft-lbf Btu cal

J J J

1.3558 1.0551 E  3 4.1868

Force

lbf kgf

N N

4.4482 9.8067

Length

ft in mi (statute) nmi (nautical)

m m m m

0.3048 2.5400 E  2 1.6093 E  3 1.8520 E  3

Mass

slug lbm

kg kg

1.4594 E  1 4.5359 E  1

Mass flow

slug/s lbm/s

kg/s kg/s

1.4594 E  1 4.5359 E  1

Power

ftlbf/s hp

W W

1.3558 7.4570 E  2

Conversion Factors from BG to SI Units (Continued) To convert from

To

Multiply by

Pressure

lbf/ft2 lbf/in2 atm mm Hg

Pa Pa Pa Pa

4.7880 6.8948 1.0133 1.3332

Specific weight

lbf/ft3

N/m3

1.5709 E  2

Specific heat

ft2/(s2R)

m2/(s2K)

1.6723 E  1

Surface tension

lbf/ft

N/m

1.4594 E  1

Temperature

F R

C K

tC  59(tF  32) 0.5556

Velocity

ft/s mi/h knot

m/s m/s m/s

0.3048 4.4704 E  1 5.1444 E  1

Viscosity

lbfs/ft2 g/(cms)

Ns/m2 Ns/m2

4.7880 E  1 0.1

Volume

ft3 L gal (U.S.) fluid ounce (U.S.)

m3 m3 m3 m3

2.8317 E  2 0.001 3.7854 E  3 2.9574 E  5

Volume flow

ft3/s gal/min

m3/s m3/s

2.8317 E  2 6.3090 E  5

E1 E3 E5 E2

EQUATION SHEET Ideal-gas law: p  RT, Rair  287 J/kg-K

1 Surface tension: p  Y(R1 1  R2 )

Hydrostatics, constant density:

Hydrostatic panel force: F  hCGA,

p2  p1  (z2 z1),   g

yCP Ixxsin /(hCG A), xCP Ixy sin /(hCG A) CV mass: d/dt( CV d )  g(AV)out

Buoyant force: FB  fluid(displaced volume) CV momentum: d/dt1 CV Vd 2

 g 3 (AV )V 4 out  g 3 (AV )V 4 in  g F Steady flow energy: (p/V 2/2gz)in 

 g (AV)in  0 CV angular momentum: d/dt( CV (r0 V)d )  g AV(r0V)out g AV(r0V)in g M 0 Acceleration: dV/dt  V/t

(p/V2/2gz)out  hfriction  hpump  hturbine

 u(V/x)  v(V/y) w(V/z)

Incompressible continuity:   V  0

Navier-Stokes: (dV/dt)gp  2V

Incompressible stream function (x,y):

Velocity potential (x, y, z):

u  /y;

v  /x

Bernoulli unsteady irrotational flow: /t  dp/  V 2/2 gz  Const Pipe head loss: hf  f(L /d)V 2/(2g) where f  Moody chart friction factor Laminar flat plate flow: /x  5.0/Re1/2 x , cf  0.664/Re1/2 x ,

CD  1.328/Re1/2 L

CD  Drag/1 12V 2A2; CL  Lift/1 12V2A2

Isentropic flow: T0 /T  1 5(k1)/26Ma2, 0/  (T0/T)1/(k1),

p0 /p  (T0/T)k(k1)

Prandtl-Meyer expansion: K  (k1)/(k1), K1/2tan1[(Ma21)/K]1/2tan1(Ma21)1/2 Gradually varied channel flow: dy/dx  (S0  S)/(1  Fr2), Fr  V/Vcrit

u  /x; v  /y; w  /z Turbulent friction factor: 1/ 1f 

2.0 log10 3 /(3.7d)  2.51/1Red 1f)4

Orifice, nozzle, venturi flow: QCdAthroat 3 2 p/5(14)6 4 1/2,   d/D Turbulent flat plate flow: /x  0.16/Re1/7 x , 1/7 cf  0.027/Re1/7 x , C D  0.031/Re L

2-D potential flow: 2  2  0 One-dimensional isentropic area change: A/A*(1/Ma)[1{(k1)/2}Ma2](1/2)(k1)/(k1) Uniform flow, Manning’s n, SI units: V0(m/s)  (1.0/n) 3 Rh(m) 4 2/3S1/2 0 Euler turbine formula: Power  Q(u2Vt2  u1Vt1), u  r

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Fluid Mechanics

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McGraw-Hill Series in Mechanical Engineering Alciatore/Histand Introduction to Mechatronics and Measurement Systems Anderson Computational Fluid Dynamics: The Basics with Applications Anderson Fundamentals of Aerodynamics Anderson Introduction to Flight Anderson Modern Compressible Flow Beer/Johnston Vector Mechanics for Engineers: Statics and Dynamics Beer/Johnston Mechanics of Materials Budynas Advanced Strength and Applied Stress Analysis Budynas/Nisbett Shigley’s Mechanical Engineering Design Çengel Heat and Mass Transfer: A Practical Approach Çengel Introduction to Thermodynamics & Heat Transfer Çengel/Boles Thermodynamics: An Engineering Approach Çengel/Cimbala Fluid Mechanics: Fundamentals and Applications Çengel/Turner Fundamentals of Thermal-Fluid Sciences Dieter Engineering Design: A Materials & Processing Approach Dieter Mechanical Metallurgy Dorf/Byers Technology Ventures: From Idea to Enterprise Finnemore/Franzini Fluid Mechanics with Engineering Applications

Hamrock/Schmid/Jacobson Fundamentals of Machine Elements Heywood Internal Combustion Engine Fundamentals Holman Experimental Methods for Engineers Holman Heat Transfer Kays/Crawford/Weigand Convective Heat and Mass Transfer Meirovitch Fundamentals of Vibrations Norton Design of Machinery Palm System Dynamics Reddy An Introduction to Finite Element Method Schey Introduction to Manufacturing Processes Smith/Hashemi Foundations of Materials Science and Engineering Turns An Introduction to Combustion: Concepts and Applications Ugural Mechanical Design: An Integrated Approach Ullman The Mechanical Design Process White Fluid Mechanics White Viscous Fluid Flow

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Fluid Mechanics Seventh Edition

Frank M. White University of Rhode Island

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FLUID MECHANICS, SEVENTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions © 2008, 2003, and 1999. 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. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOC/DOC 1 0 9 8 7 6 5 4 3 2 1 0 ISBN 978-0-07-352934-9 MHID 0-07-352934-6 Vice President & Editor-in-Chief: Marty Lange Vice President, EDP/Central Publishing Services: Kimberly Meriwether-David Global Publisher: Raghothaman Srinivasan Senior Sponsoring Editor: Bill Stenquist Director of Development: Kristine Tibbetts Developmental Editor: Lora Neyens Senior Marketing Manager: Curt Reynolds Senior Project Manager: Lisa A. Bruflodt Production Supervisor: Nicole Baumgartner Design Coordinator: Brenda A. Rolwes Cover Designer: Studio Montage, St. Louis, Missouri (USE) Cover Image: Copyright SkySails Senior Photo Research Coordinator: John C. Leland Photo Research: Emily Tietz/Editorial Image, LLC Compositor: Aptara, Inc. Typeface: 10/12 Times Roman Printer: R. R. Donnelley All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. Library of Congress Cataloging-in-Publication Data White, Frank M. Fluid mechanics / Frank M. White. —7th ed. p. cm. — (Mcgraw-Hill series in mechanical engineering) Includes bibliographical references and index. ISBN 978–0–07–352934–9 (alk. paper) 1. Fluid mechanics. I. Title. TA357.W48 2009 620.1’06—dc22 2009047498 www.mhhe.com

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About the Author

Frank M. White is Professor Emeritus of Mechanical and Ocean Engineering at the University of Rhode Island. He studied at Georgia Tech and M.I.T. In 1966 he helped found, at URI, the first department of ocean engineering in the country. Known primarily as a teacher and writer, he has received eight teaching awards and has written four textbooks on fluid mechanics and heat transfer. From 1979 to 1990 he was editor-in-chief of the ASME Journal of Fluids Engineering and then served from 1991 to 1997 as chairman of the ASME Board of Editors and of the Publications Committee. He is a Fellow of ASME and in 1991 received the ASME Fluids Engineering Award. He lives with his wife, Jeanne, in Narragansett, Rhode Island.

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To Jeanne

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Contents

Preface

xi

Chapter 1 Introduction 3 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14

Preliminary Remarks 3 History and Scope of Fluid Mechanics 4 Problem-Solving Techniques 6 The Concept of a Fluid 6 The Fluid as a Continuum 8 Dimensions and Units 9 Properties of the Velocity Field 17 Thermodynamic Properties of a Fluid 18 Viscosity and Other Secondary Properties 25 Basic Flow Analysis Techniques 40 Flow Patterns: Streamlines, Streaklines, and Pathlines 41 The Engineering Equation Solver 46 Uncertainty in Experimental Data 46 The Fundamentals of Engineering (FE) Examination 48 Problems 49 Fundamentals of Engineering Exam Problems 57 Comprehensive Problems 58 References 61

Chapter 2 Pressure Distribution in a Fluid 65 2.1 2.2 2.3 2.4

Pressure and Pressure Gradient 65 Equilibrium of a Fluid Element 67 Hydrostatic Pressure Distributions 68 Application to Manometry 75

2.5 2.6 2.7 2.8 2.9 2.10

Hydrostatic Forces on Plane Surfaces 78 Hydrostatic Forces on Curved Surfaces 86 Hydrostatic Forces in Layered Fluids 89 Buoyancy and Stability 91 Pressure Distribution in Rigid-Body Motion 97 Pressure Measurement 105 Summary 109 Problems 109 Word Problems 132 Fundamentals of Engineering Exam Problems 133 Comprehensive Problems 134 Design Projects 135 References 136

Chapter 3 Integral Relations for a Control Volume 139 3.1 3.2 3.3 3.4 3.5 3.6 3.7

Basic Physical Laws of Fluid Mechanics 139 The Reynolds Transport Theorem 143 Conservation of Mass 150 The Linear Momentum Equation 155 Frictionless Flow: The Bernoulli Equation 169 The Angular Momentum Theorem 178 The Energy Equation 184 Summary 195 Problems 195 Word Problems 224 Fundamentals of Engineering Exam Problems 224 Comprehensive Problems 226 Design Project 227 References 227 vii

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Contents

Chapter 4 Differential Relations for Fluid Flow 229 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10

The Acceleration Field of a Fluid 230 The Differential Equation of Mass Conservation 232 The Differential Equation of Linear Momentum 238 The Differential Equation of Angular Momentum 244 The Differential Equation of Energy 246 Boundary Conditions for the Basic Equations 249 The Stream Function 253 Vorticity and Irrotationality 261 Frictionless Irrotational Flows 263 Some Illustrative Incompressible Viscous Flows 268 Summary 276 Problems 277 Word Problems 288 Fundamentals of Engineering Exam Problems 288 Comprehensive Problems 289 References 290

Chapter 5 Dimensional Analysis and Similarity 5.1 5.2 5.3 5.4 5.5

Introduction 298 The Principle of Dimensional Homogeneity 296 The Pi Theorem 302 Nondimensionalization of the Basic Equations 312 Modeling and Its Pitfalls 321 Summary 333 Problems 333 Word Problems 342 Fundamentals of Engineering Exam Problems 342 Comprehensive Problems 343 Design Projects 344 References 344

Chapter 6 Viscous Flow in Ducts 6.1 6.2 6.3 6.4 6.5

293

347

Reynolds Number Regimes 347 Internal versus External Viscous Flow 352 Head Loss—The Friction Factor 355 Laminar Fully Developed Pipe Flow 357 Turbulence Modeling 359

6.6 6.7 6.8 6.9 6.10 6.11 6.12

Turbulent Pipe Flow 365 Four Types of Pipe Flow Problems 373 Flow in Noncircular Ducts 379 Minor or Local Losses in Pipe Systems 388 Multiple-Pipe Systems 397 Experimental Duct Flows: Diffuser Performance 403 Fluid Meters 408 Summary 429 Problems 430 Word Problems 448 Fundamentals of Engineering Exam Problems 449 Comprehensive Problems 450 Design Projects 452 References 453

Chapter 7 Flow Past Immersed Bodies 457 7.1 7.2 7.3 7.4 7.5 7.6

Reynolds Number and Geometry Effects 457 Momentum Integral Estimates 461 The Boundary Layer Equations 464 The Flat-Plate Boundary Layer 467 Boundary Layers with Pressure Gradient 476 Experimental External Flows 482 Summary 509 Problems 510 Word Problems 523 Fundamentals of Engineering Exam Problems 524 Comprehensive Problems 524 Design Project 525 References 526

Chapter 8 Potential Flow and Computational Fluid Dynamics 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9

529

Introduction and Review 529 Elementary Plane Flow Solutions 532 Superposition of Plane Flow Solutions 539 Plane Flow Past Closed-Body Shapes 545 Other Plane Potential Flows 555 Images 559 Airfoil Theory 562 Axisymmetric Potential Flow 574 Numerical Analysis 579

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Contents ix Summary 593 Problems 594 Word Problems 604 Comprehensive Problems 605 Design Projects 606 References 606

Chapter 9 Compressible Flow 609 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10

Introduction: Review of Thermodynamics 609 The Speed of Sound 614 Adiabatic and Isentropic Steady Flow 616 Isentropic Flow with Area Changes 622 The Normal Shock Wave 629 Operation of Converging and Diverging Nozzles 637 Compressible Duct Flow with Friction 642 Frictionless Duct Flow with Heat Transfer 654 Two-Dimensional Supersonic Flow 659 Prandtl-Meyer Expansion Waves 669 Summary 681 Problems 682 Word Problems 695 Fundamentals of Engineering Exam Problems 696 Comprehensive Problems 696 Design Projects 698 References 698

Chapter 10 Open-Channel Flow 701 10.1 10.2 10.3 10.4 10.5 10.6

Introduction 701 Uniform Flow: The Chézy Formula 707 Efficient Uniform-Flow Channels 712 Specific Energy: Critical Depth 714 The Hydraulic Jump 722 Gradually Varied Flow 726

10.7

Flow Measurement and Control by Weirs 734 Summary 741 Problems 741 Word Problems 754 Fundamentals of Engineering Exam Problems 754 Comprehensive Problems 754 Design Projects 756 References 756

Chapter 11 Turbomachinery 11.1 11.2 11.3 11.4 11.5 11.6

759

Introduction and Classification 759 The Centrifugal Pump 762 Pump Performance Curves and Similarity Rules 768 Mixed- and Axial-Flow Pumps: The Specific Speed 778 Matching Pumps to System Characteristics 785 Turbines 793 Summary 807 Problems 807 Word Problems 820 Comprehensive Problems 820 Design Project 822 References 822

Appendix A Physical Properties of Fluids Appendix B Compressible Flow Tables Appendix C Conversion Factors

824 829

836

Appendix D Equations of Motion in Cylindrical Coordinates Answers to Selected Problems 840 Index 847

838

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Preface

General Approach

The seventh edition of Fluid Mechanics sees some additions and deletions but no philosophical change. The basic outline of eleven chapters, plus appendices, remains the same. The triad of integral, differential, and experimental approaches is retained. Many problem exercises, and some fully worked examples, have been changed. The informal, student-oriented style is retained. A number of new photographs and figures have been added. Many new references have been added, for a total of 435. The writer is a firm believer in “further reading,” especially in the postgraduate years.

Learning Tools

The total number of problem exercises continues to increase, from 1089 in the first edition, to 1675 in this seventh edition. There are approximately 20 new problems added to each chapter. Most of these are basic end-of-chapter problems, classified according to topic. There are also Word Problems, multiple-choice Fundamentals of Engineering Problems, Comprehensive Problems, and Design Projects. The appendix lists approximately 700 Answers to Selected Problems. The example problems are structured in the text to follow the sequence of recommended steps outlined in Sect. 1.3, Problem-Solving Techniques. The Engineering Equation Solver (EES) is available with the text and continues its role as an attractive tool for fluid mechanics and, indeed, other engineering problems. Not only is it an excellent solver, but it also contains thermophysical properties, publication-quality plotting, units checking, and many mathematical functions, including numerical integration. The author is indebted to Sanford Klein and William Beckman, of the University of Wisconsin, for invaluable and continuous help in preparing and updating EES for use in this text. For newcomers to EES, a brief guide to its use is found on this book’s website.

Content Changes

There are some revisions in each chapter. Chapter 1 has added material on the history of late 20th century fluid mechanics, notably the development of Computational Fluid Dynamics. A very brief introduction to the acceleration field has been added. Boundary conditions for slip flow have been added. There is more discussion of the speed of sound in liquids. The treatment of thermal conductivity has been moved to Chapter 4. xi

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Preface

Chapter 2 introduces a photo, discussion, and new problems for the deep ocean submersible vehicle, ALVIN. The density distribution in the troposphere is now given explicitly. There are brief remarks on the great Greek mathematician, Archimedes. Chapter 3 has been substantially revised. Reviewers wanted Bernoulli’s equation moved ahead of angular velocity and energy, to follow linear momentum. I did this and followed their specific improvements, but truly extensive renumbering and rearranging was necessary. Pressure and velocity conditions at a tank surface have an improved discussion. A brie...