**UFRJ**

# Fluid Mechanics Fundamentals and Applications

(Parte **1** de 9)

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McGRAW-HILL SERIES IN MECHANICAL ENGINEERING

Alciatore and 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 Barber:Intermediate Mechanics of Materials Beer/Johnston:Vector Mechanics for Engineers Beer/Johnston/DeWolf:Mechanics of Materials Borman and Ragland:Combustion Engineering Budynas:Advanced Strength and Applied Stress Analysis Çengel and Boles:Thermodynamics:An Engineering Approach Çengel and Cimbala:Fluid Mechanics:Fundamentals and Applications Çengel and Turner:Fundamentals of Thermal-Fluid Sciences Çengel:Heat Transfer:A Practical Approach Crespo da Silva:Intermediate Dynamics Dieter:Engineering Design:A Materials & Processing Approach Dieter: Mechanical Metallurgy Doebelin:Measurement Systems:Application & Design Dunn:Measurement & Data Analysis for Engineering & Science EDS,Inc.:I-DEAS Student Guide Hamrock/Jacobson/Schmid:Fundamentals of Machine Elements Henkel and Pense:Structure and Properties of Engineering Material Heywood:Internal Combustion Engine Fundamentals Holman:Experimental Methods for Engineers Holman: Heat Transfer Hsu:MEMS & Microsystems:Manufacture & Design Hutton:Fundamentals of Finite Element Analysis Kays/Crawford/Weigand:Convective Heat and Mass Transfer Kelly:Fundamentals of Mechanical Vibrations Kreider/Rabl/Curtiss:The Heating and Cooling of Buildings Mattingly:Elements of Gas Turbine Propulsion Meirovitch:Fundamentals of Vibrations Norton:Design of Machinery Palm: System Dynamics Reddy:An Introduction to Finite Element Method Ribando:Heat Transfer Tools Schaffer et al.:The Science and Design of Engineering Materials Schey:Introduction to Manufacturing Processes Schlichting: Boundary-Layer Theory Shames:Mechanics of Fluids Shigley/Mischke/Budynas: Mechanical Engineering Design Smith:Foundations of Materials Science and Engineering Stoecker:Design of Thermal Systems Suryanarayana and Arici:Design and Simulation of Thermal Systems Turns:An Introduction to Combustion:Concepts and Applications Ugural:Stresses in Plates and Shells Ugural:Mechanical Design:An Integrated Approach Ullman:The Mechanical Design Process Wark and Richards:Thermodynamics White: Fluid Mechanics White:Viscous Fluid Flow Zeid: Mastering CAD/CAM cen72367_fm.qxd 1/23/04 1:2 AM Page i

Department of Mechanical Engineering University of Nevada, Reno

Department of Mechanical and Nuclear Engineering The Pennsylvania State University cen72367_fm.qxd 1/23/04 1:2 AM Page i

Published by McGraw-Hill,a business unit of The McGraw-Hill Companies,Inc., 1221 Avenue of the Americas,New York,NY 10020. Copyright ©2006 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.

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This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOW/DOW 0 9 8 7 6 5 4 ISBN 0–07–247236–7

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Library of Congress Cataloging-in-Publication Data

Çengel,Yunus A.

Fluid mechanics :fundamentals and applications / Yunus A. Çengel,John M. Cimbala.—1st ed. p.cm.—(McGraw-Hill series in mechanical engineering) ISBN 0–07–247236–7 1. Fluid dynamics.I. Cimbala,John M.I. Title.II. Series.

TA357.C43 2006 620.1'06—dc22 2004058767 CIP w.mhhe.com cen72367_fm.qxd 1/23/04 1:2 AM Page iv

Dedication

To all students—In hopes of enhancing your desire and enthusiasm to explore the inner workings of our marvelous universe, of which fluid mechanics is a small but fascinating part; our hope is that this book enhances your love of learning, not only about fluid mechanics, but about life.

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Yunus A. Çengelis Professor Emeritus of Mechanical Engineering at the University of Nevada,Reno. He received his B.S. in mechanical engineering from Istanbul Technical University and his M.S. and Ph.D. in mechanical engineering from North Carolina State University. His research areas are renewable energy,desalination,exergy analysis,heat transfer enhancement, radiation heat transfer,and energy conservation. He served as the director of the Industrial Assessment Center (IAC) at the University of Nevada,Reno, from 1996 to 2000. He has led teams of engineering students to numerous manufacturing facilities in Northern Nevada and California to do industrial assessments,and has prepared energy conservation,waste minimization,and productivity enhancement reports for them.

Dr. Çengel is the coauthor of the widely adopted textbook Thermodynamics:An Engineering Approach,4th edition(2002),published by McGraw-Hill. He is also the author of the textbook Heat Transfer:A Practical Approach,2nd edition (2003),and the coauthor of the textbook Fundamentals of Thermal- Fluid Sciences,2nd edition (2005),both published by McGraw-Hill. Some of his textbooks have been translated to Chinese,Japanese,Korean,Spanish, Turkish,Italian,and Greek.

Dr. Çengel is the recipient of several outstanding teacher awards,and he has received the ASEE Meriam/Wiley Distinguished Author Award for excellence in authorship in 1992 and again in 2000.

Dr. Çengel is a registered Professional Engineer in the State of Nevada,and is a member of the American Society of Mechanical Engineers (ASME) and the American Society for Engineering Education (ASEE).

John M. Cimbalais Professor of Mechanical Engineering at The Pennsylvania State Univesity,University Park. He received his B.S. in Aerospace Engineering from Penn State and his M.S. in Aeronautics from the California Institute of Technology (CalTech). He received his Ph.D. in Aeronautics from CalTech in 1984 under the supervision of Professor Anatol Roshko,to whom he will be forever grateful. His research areas include experimental and computational fluid mechanics and heat transfer,turbulence,turbulence modeling, turbomachinery,indoor air quality,and air pollution control. During the academic year 1993–94,Professor Cimbala took a sabbatical leave from the University and worked at NASA Langley Research Center,where he advanced his knowledge of computational fluid dynamics (CFD) and turbulence modeling.

Dr. Cimbala is the coauthor of the textbook Indoor Air Quality Engineering:Environmental Health and Control of Indoor Pollutants(2003),published by Marcel-Dekker,Inc. He has also contributed to parts of other books,and is the author or co-author of dozens of journal and conference papers. More information can be found at w.mne.psu.edu/cimbala.

Professor Cimbala is the recipient of several outstanding teaching awards and views his book writing as an extension of his love of teaching. He is a member of the American Institute of Aeronautics and Astronautics (AIAA),the American Society of Mechanical Engineers (ASME),the American Society for Engineering Education (ASEE),and the American Physical Society (APS).

A BOUT THE AUTHORS cen72367_fm.qxd 1/23/04 1:2 AM Page vi

CHAPTER ONE INTRODUCTION AND BASIC CONCEPTS1

CHAPTER TW O PROPERTIES OF FLUIDS35

CHAPTER THREE PRESSURE AND FLUID STATICS65

CHAPTER FOUR FLUID KINEMATICS121

CHAPTER FIVE MASS, BERNOULLI, AND ENERGY EQUATIONS171

CHAPTER SIX MOMENTUM ANALYSIS OF FLOW SYSTEMS227

CHAPTER SEVEN DIMENSIONAL ANALYSIS AND MODELING269

CHAPTER EIGHT FLOW IN PIPES321

CHAPTER NINE DIFFERENTIAL ANALYSIS OF FLUID FLOW399

CHAPTER TEN APPROXIMATE SOLUTIONS OF THE NAVIER–STOKES EQUATION471

CHAPTER ELEVEN FLOW OVER BODIES: DRAG AND LIFT561

CHAPTER TWEL VE COMPRESSIBLE FLOW 611

CHAPTER THIR TEEN OPEN-CHANNEL FLOW 679

CHAPTER FOUR TEEN TURBOMACHINER Y 735

CHAPTER FIFTEEN INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS817 cen72367_fm.qxd 1/23/04 1:2 AM Page vii

Preface xv

CHAPTER ONE INTRODUCTION AND BASIC CONCEPTS1

What Is a Fluid?2 Application Areas of Fluid Mechanics4

Viscous versus Inviscid Regions of Flow9 Internal versus External Flow10 Compressible versus Incompressible Flow10 Laminar versus Turbulent Flow11 Natural (or Unforced) versus Forced Flow11 Steady versus Unsteady Flow11 One-, Two-, and Three-Dimensional Flows12

Some SI and English Units16 Dimensional Homogeneity 18 Unity Conversion Ratios20

1–7Mathematical Modeling of Engineering Problems 21

Modeling in Engineering21 1–8 Problem-Solving Technique 2

Step 1: Problem Statement22 Step 2: Schematic23 Step 3: Assumptions and Approximations23 Step 4: Physical Laws23 Step 5: Properties23 Step 6: Calculations23 Step 7: Reasoning, Verification, and Discussion23

1–9Engineering Software Packages24

Engineering Equation Solver (EES)25 FLUENT 26

1–10 Accuracy, Precision, and Significant Digits 26

Application Spotlight:What Nuclear Blasts and Raindrops Have in Common31

Summary 30 References and Suggested Reading30 Problems 32

CHAPTER TW O PROPERTIES OF FLUIDS35

Continuum 36 2–2Density and Specific Gravity37

Coefficient of Volume Expansion44 2–6 Viscosity 46 2–7Surface Tension and Capillary Effect51

Capillary Effect53

Summary 5 References and Suggested Reading56

Application Spotlight: Cavitation 57 Problems 58

CHAPTER THREE PRESSURE AND FLUID STATICS65

C ONTENTS cen72367_fm.qxd 1/23/04 1:2 AM Page viii

CONTENTS ix

3–5Hydrostatic Forces on Submerged Plane Surfaces 79

Special Case: Submerged Rectangular Plate82

3–6Hydrostatic Forces on Submerged Curved Surfaces 85

3–7Buoyancy and Stability89

Special Case 1: Fluids at Rest96 Special Case 2: Free Fall of a Fluid Body97 Acceleration on a Straight Path97 Rotation in a Cylindrical Container99

Summary 102 References and Suggested Reading103 Problems 103

CHAPTER FOUR FLUID KINEMATICS121

Acceleration Field 124 Material Derivative 127

4–2Fundamentals of Flow Visualization129

Streamlines and Streamtubes129 Pathlines 130 Streaklines 132 Timelines 134 Refractive Flow Visualization Techniques135 Surface Flow Visualization Techniques136

4–3Plots of Fluid Flow Data136

4–5The Reynolds Transport Theorem148

Alternate Derivation of the Reynolds Transport

Theorem 153 Relationship between Material Derivative and RTT155

Application Spotlight: Fluidic Actuators 157

Summary 156 References and Suggested Reading158 Problems 158

MASS, BERNOULLI, AND ENERGY EQUATIONS 171

Conservation of Mass172 Conservation of Momentum172 Conservation of Energy172

5–2Conservation of Mass173

Mass and Volume Flow Rates173 Conservation of Mass Principle175 Moving or Deforming Control Volumes177 Mass Balance for Steady-Flow Processes177 Special Case: Incompressible Flow178

Acceleration of a Fluid Particle186 Derivation of the Bernoulli Equation186 Force Balance across Streamlines188 Unsteady, Compressible Flow189 Static, Dynamic, and Stagnation Pressures189 Limitations on the Use of the Bernoulli Equation190 Hydraulic Grade Line (HGL) and Energy Grade Line (EGL)192

Energy Transfer by Heat, Q202 Energy Transfer by Work, W202

5–7Energy Analysis of Steady Flows206

Special Case: Incompressible Flow with No Mechanical Work

Devices and Negligible Friction208 Kinetic Energy Correction Factor, a208

Summary 215 References and Suggested Reading216 Problems 216

MOMENTUM ANALYSIS OF FLOW SYSTEMS 227

6–1Newton’s Laws and Conservation of Momentum228 cen72367_fm.qxd 1/23/04 1:2 AM Page ix

Special Cases235 Momentum-Flux Correction Factor, b235 Steady Flow238 Steady Flow with One Inlet and One Outlet238 Flow with No External Forces238

6–5Review of Rotational Motion and Angular Momentum 248

6–6The Angular Momentum Equation250

Special Cases252 Flow with No External Moments253 Radial-Flow Devices 254

Summary 259 References and Suggested Reading259 Problems 260

CHAPTER SEVEN DIMENSIONAL ANALYSIS AND MODELING269

Nondimensionalization of Equations 272 7–3Dimensional Analysis and Similarity277

7–4The Method of Repeating Variables and the Buckingham Pi Theorem281

Historical Spotlight:Persons Honored by Nondimensional Parameters 289

7–5Experimental Testing and Incomplete Similarity 297

Setup of an Experiment and Correlation of Experimental

Data 297

Incomplete Similarity 298 Wind Tunnel Testing298 Flows with Free Surfaces301

Application Spotlight:How a Fly Flies304

Summary 305 References and Suggested Reading305 Problems 305

CHAPTER EIGHT FLOW IN PIPES321

8–1 Introduction 322 8–2Laminar and Turbulent Flows323 Reynolds Number324

8–3The Entrance Region325

Entry Lengths326 8–4Laminar Flow in Pipes327

Pressure Drop and Head Loss329 Inclined Pipes331 Laminar Flow in Noncircular Pipes332

8–5Turbulent Flow in Pipes335

Piping Systems with Pumps and Turbines356 8–8Flow Rate and Velocity Measurement364

Pitot and Pitot-Static Probes365 Obstruction Flowmeters: Orifice, Venturi, and Nozzle

Meters 366

Application Spotlight:How Orifice Plate Flowmeters Work,or Do Not Work383

Summary 384 References and Suggested Reading385 Problems 386

CHAPTER NINE DIFFERENTIAL ANALYSIS OF FLUID FLOW399

9–2Conservation of Mass—The Continuity Equation 400

Derivation Using the Divergence Theorem401 Derivation Using an Infinitesimal Control Volume402 Alternative Form of the Continuity Equation405 Continuity Equation in Cylindrical Coordinates406 Special Cases of the Continuity Equation406

The Stream Function in Cartesian Coordinates412 The Stream Function in Cylindrical Coordinates419 The Compressible Stream Function420 x FLUID MECHANICS cen72367_fm.qxd 1/23/04 12:13 PM Page x

9–4Conservation of Linear Momentum—Cauchy’s Equation 421

Derivation Using the Divergence Theorem421 Derivation Using an Infinitesimal Control Volume422 Alternative Form of Cauchy’s Equation425 Derivation Using Newton’s Second Law425

9–5The Navier–Stokes Equation426

Introduction 426 Newtonian versus Non-Newtonian Fluids427 Derivation of the Navier–Stokes Equation for Incompressible,

Isothermal Flow428

Continuity and Navier–Stokes Equations in Cartesian

Coordinates 430

Continuity and Navier–Stokes Equations in Cylindrical Coordinates 431

9–6Differential Analysis of Fluid Flow Problems 432

Calculation of the Pressure Field for a Known Velocity

Field 432

Exact Solutions of the Continuity and Navier–Stokes Equations 437

Summary 455 References and Suggested Reading456 Problems 456

APPROXIMATE SOLUTIONS OF THE NAVIER–STOKES EQUATION 471

10–2Nondimensionalized Equations of Motion473

10–3The Creeping Flow Approximation476

Drag on a Sphere in Creeping Flow479

10–4Approximation for Inviscid Regions of Flow481

(Parte **1** de 9)