1. 1. F L U I D M E C H A N I C S FUNDAMENTALS AND APPLICATIONS cen72367_fm.qxd 11/23/04 11:22 AM Page i
2. 2. 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 engel and Boles: Thermodynamics: An Engineering Approach engel and Cimbala: Fluid Mechanics: Fundamentals and Applications engel and Turner: Fundamentals of Thermal-Fluid Sciences engel: 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 11/23/04 11:22 AM Page ii
3. 3. F L U I D M E C H A N I C S FUNDAMENTALS AND APPLICATIONS YUNUS A. ENGEL Department of Mechanical Engineering University of Nevada, Reno JOHN M. CIMBALA Department of Mechanical and Nuclear Engineering The Pennsylvania State University cen72367_fm.qxd 11/23/04 11:22 AM Page iii
4. 4. FLUID MECHANICS: FUNDAMENTALS AND APPLICATIONS 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. 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 DOW/DOW 0 9 8 7 6 5 4 ISBN 0072472367 Senior Sponsoring Editor: Suzanne Jeans Managing Developmental Editor: Debra D. Matteson Developmental Editor: Kate Scheinman Senior Marketing Manager: Mary K. Kittell Senior Project Manager: Sheila M. Frank Senior Production Supervisor: Sherry L. Kane Media Technology Producer: Eric A. Weber Senior Designer: David W. Hash (USE) Cover image: Getty/Eric Meola, Niagara Falls Senior Photo Research Coordinator: Lori Hancock Photo Research: Judy Ladendorf/The Permissions Group Supplemental Producer: Brenda A. Ernzen Compositor: Lachina Publishing Services Typeface: 10.5/12 Times Roman Printer: R. R. Donnelley Willard, OH Library of Congress Cataloging-in-Publication Data engel, Yunus A. Fluid mechanics : fundamentals and applications / Yunus A. engel, John M. Cimbala.1st ed. p. cm.(McGraw-Hill series in mechanical engineering) ISBN 0072472367 1. Fluid dynamics. I. Cimbala, John M. II. Title. III. Series. TA357.C43 2006 620.1'06dc22 2004058767 CIP www.mhhe.com cen72367_fm.qxd 11/23/04 11:22 AM Page iv
5. 5. D e d i c a t i o n To all studentsIn 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. cen72367_fm.qxd 11/23/04 11:22 AM Page v
6. 6. Yunus A. engel is Professor Emeritus of Mechanical Engineering at the University of Nevada, Reno. He received his B.S. in mechanical engineer- ing 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. engel is the coauthor of the widely adopted textbook Thermodynam- ics: 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. engel is the recipient of several outstanding teacher awards, and he has received the ASEE Meriam/Wiley Distinguished Author Award for excel- lence in authorship in 1992 and again in 2000. Dr. engel 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. Cimbala is Professor of Mechanical Engineering at The Penn- sylvania 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 com- putational fluid mechanics and heat transfer, turbulence, turbulence modeling, turbomachinery, indoor air quality, and air pollution control. During the aca- demic year 199394, Professor Cimbala took a sabbatical leave from the Uni- versity 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 Engineer- ing: 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 www.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 B O U T T H E A U T H O R S cen72367_fm.qxd 11/23/04 11:22 AM Page vi
7. 7. B R I E F C O N T E N T S C H A P T E R O N E INTRODUCTION AND BASIC CONCEPTS 1 C H A P T E R T W O PROPERTIES OF FLUIDS 35 C H A P T E R T H R E E PRESSURE AND FLUID STATICS 65 C H A P T E R F O U R FLUID KINEMATICS 121 C H A P T E R F I V E MASS, BERNOULLI, AND ENERGY EQUATIONS 171 C H A P T E R S I X MOMENTUM ANALYSIS OF FLOW SYSTEMS 227 C H A P T E R S E V E N DIMENSIONAL ANALYSIS AND MODELING 269 C H A P T E R E I G H T FLOW IN PIPES 321 C H A P T E R N I N E DIFFERENTIAL ANALYSIS OF FLUID FLOW 399 C H A P T E R T E N APPROXIMATE SOLUTIONS OF THE NAVIERSTOKES EQUATION 471 C H A P T E R E L E V E N FLOW OVER BODIES: DRAG AND LIFT 561 C H A P T E R T W E L V E COMPRESSIBLE FLOW 611 C H A P T E R T H I R T E E N OPEN-CHANNEL FLOW 679 C H A P T E R F O U R T E E N TURBOMACHINERY 735 C H A P T E R F I F T E E N INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS 817 cen72367_fm.qxd 11/23/04 11:22 AM Page vii
8. 8. Preface xv C H A P T E R O N E INTRODUCTION AND BASIC CONCEPTS 1 11 Introduction 2 What Is a Fluid? 2 Application Areas of Fluid Mechanics 4 12 The No-Slip Condition 6 13 A Brief History of Fluid Mechanics 7 14 Classification of Fluid Flows 9 Viscous versus Inviscid Regions of Flow 9 Internal versus External Flow 10 Compressible versus Incompressible Flow 10 Laminar versus Turbulent Flow 11 Natural (or Unforced) versus Forced Flow 11 Steady versus Unsteady Flow 11 One-, Two-, and Three-Dimensional Flows 12 15 System and Control Volume 14 16 Importance of Dimensions and Units 15 Some SI and English Units 16 Dimensional Homogeneity 18 Unity Conversion Ratios 20 17 Mathematical Modeling of Engineering Problems 21 Modeling in Engineering 21 18 Problem-Solving Technique 22 Step 1: Problem Statement 22 Step 2: Schematic 23 Step 3: Assumptions and Approximations 23 Step 4: Physical Laws 23 Step 5: Properties 23 Step 6: Calculations 23 Step 7: Reasoning, Verification, and Discussion 23 19 Engineering Software Packages 24 Engineering Equation Solver (EES) 25 FLUENT 26 110 Accuracy, Precision, and Significant Digits 26 Application Spotlight: What Nuclear Blasts and Raindrops Have in Common 31 Summary 30 References and Suggested Reading 30 Problems 32 C H A P T E R T W O PROPERTIES OF FLUIDS 35 21 Introduction 36 Continuum 36 22 Density and Specific Gravity 37 Density of Ideal Gases 38 23 Vapor Pressure and Cavitation 39 24 Energy and Specific Heats 41 25 Coefficient of Compressibility 42 Coefficient of Volume Expansion 44 26 Viscosity 46 27 Surface Tension and Capillary Effect 51 Capillary Effect 53 Summary 55 References and Suggested Reading 56 Application Spotlight: Cavitation 57 Problems 58 C H A P T E R T H R E E PRESSURE AND FLUID STATICS 65 31 Pressure 66 Pressure at a Point 67 Variation of Pressure with Depth 68 32 The Manometer 71 Other Pressure Measurement Devices 74 33 The Barometer and Atmospheric Pressure 75 34 Introduction to Fluid Statics 78 C O N T E N T S cen72367_fm.qxd 11/23/04 11:22 AM Page viii
9. 9. CONTENTS ix 35 Hydrostatic Forces on Submerged Plane Surfaces 79 Special Case: Submerged Rectangular Plate 82 36 Hydrostatic Forces on Submerged Curved Surfaces 85 37 Buoyancy and Stability 89 Stability of Immersed and Floating Bodies 92 38 Fluids in Rigid-Body Motion 95 Special Case 1: Fluids at Rest 96 Special Case 2: Free Fall of a Fluid Body 97 Acceleration on a Straight Path 97 Rotation in a Cylindrical Container 99 Summary 102 References and Suggested Reading 103 Problems 103 C H A P T E R F O U R FLUID KINEMATICS 121 41 Lagrangian and Eulerian Descriptions 122 Acceleration Field 124 Material Derivative 127 42 Fundamentals of Flow Visualization 129 Streamlines and Streamtubes 129 Pathlines 130 Streaklines 132 Timelines 134 Refractive Flow Visualization Techniques 135 Surface Flow Visualization Techniques 136 43 Plots of Fluid Flow Data 136 Profile Plots 137 Vector Plots 137 Contour Plots 138 44 Other Kinematic Descriptions 139 Types of Motion or Deformation of Fluid Elements 139 Vorticity and Rotationality 144 Comparison of Two Circular Flows 147 45 The Reynolds Transport Theorem 148 Alternate Derivation of the Reynolds Transport Theorem 153 Relationship between Material Derivative and RTT 155 Application Spotlight: Fluidic Actuators 157 Summary 156 References and Suggested Reading 158 Problems 158 C H A P T E R F I V E MASS, BERNOULLI, AND ENERGY EQUATIONS 171 51 Introduction 172 Conservation of Mass 172 Conservation of Momentum 172 Conservation of Energy 172 52 Conservation of Mass 173 Mass and Volume Flow Rates 173 Conservation of Mass Principle 175 Moving or Deforming Control Volumes 177 Mass Balance for Steady-Flow Processes 177 Special Case: Incompressible Flow 178 53 Mechanical Energy and Efficiency 180 54 The Bernoulli Equation 185 Acceleration of a Fluid Particle 186 Derivation of the Bernoulli Equation 186 Force Balance across Streamlines 188 Unsteady, Compressible Flow 189 Static, Dynamic, and Stagnation Pressures 189 Limitations on the Use of the Bernoulli Equation 190 Hydraulic Grade Line (HGL) and Energy Grade Line (EGL) 192 55 Applications of the Bernoulli Equation 194 56 General Energy Equation 201 Energy Transfer by Heat, Q 202 Energy Transfer by Work, W 202 57 Energy Analysis of Steady Flows 206 Special Case: Incompressible Flow with No Mechanical Work Devices and Negligible Friction 208 Kinetic Energy Correction Factor, a 208 Summary 215 References and Suggested Reading 216 Problems 216 C H A P T E R S I X MOMENTUM ANALYSIS OF FLOW SYSTEMS 227 61 Newtons Laws and Conservation of Momentum 228 62 Choosing a Control Volume 229 63 Forces Acting on a Control Volume 230 cen72367_fm.qxd 11/23/04 11:22 AM Page ix
10. 10. 64 The Linear Momentum Equation 233 Special Cases 235 Momentum-Flux Correction Factor, b 235 Steady Flow 238 Steady Flow with One Inlet and One Outlet 238 Flow with No External Forces 238 65 Review of Rotational Motion and Angular Momentum 248 66 The Angular Momentum Equation 250 Special Cases 252 Flow with No External Moments 253 Radial-Flow Devices 254 Summary 259 References and Suggested Reading 259 Problems 260 C H A P T E R S E V E N DIMENSIONAL ANALYSIS AND MODELING 269 71 Dimensions and Units 270 72 Dimensional Homogeneity 271 Nondimensionalization of Equations 272 73 Dimensional Analysis and Similarity 277 74 The Method of Repeating Variables and the Buckingham Pi Theorem 281 Historical Spotlight: Persons Honored by Nondimensional Parameters 289 75 Experimental Testing and Incomplete Similarity 297 Setup of an Experiment and Correlation of Experimental Data 297 Incomplete Similarity 298 Wind Tunnel Testing 298 Flows with Free Surfaces 301 Application Spotlight: How a Fly Flies 304 Summary 305 References and Suggested Reading 305 Problems 305 C H A P T E R E I G H T FLOW IN PIPES 321 81 Introduction 322 82 Laminar and Turbulent Flows 323 Reynolds Number 324 83 The Entrance Region 325 Entry Lengths 326 84 Laminar Flow in Pipes 327 Pressure Drop and Head Loss 329 Inclined Pipes 331 Laminar Flow in Noncircular Pipes 332 85 Turbulent Flow in Pipes 335 Turbulent Shear Stress 336 Turbulent Velocity Profile 338 The Moody Chart 340 Types of Fluid Flow Problems 343 86 Minor Losses 347 87 Piping Networks and Pump Selection 354 Piping Systems with Pumps and Turbines 356 88 Flow Rate and Velocity Measurement 364 Pitot and Pitot-Static Probes 365 Obstruction Flowmeters: Orifice, Venturi, and Nozzle Meters 366 Positive Displacement Flowmeters 369 Turbine Flowmeters 370 Variable-Area Flowmeters (Rotameters) 372 Ultrasonic Flowmeters 373 Electromagnetic Flowmeters 375 Vortex Flowmeters 376 Thermal (Hot-Wire and Hot-Film) Anemometers 377 Laser Doppler Velocimetry 378 Particle Image Velocimetry 380 Application Spotlight: How Orifice Plate Flowmeters Work, or Do Not Work 383 Summary 384 References and Suggested Reading 385 Problems 386 C H A P T E R N I N E DIFFERENTIAL ANALYSIS OF FLUID FLOW 399 91 Introduction 400 92 Conservation of MassThe Continuity Equation 400 Derivation Using the Divergence Theorem 401 Derivation Using an Infinitesimal Control Volume 402 Alternative Form of the Continuity Equation 405 Continuity Equation in Cylindrical Coordinates 406 Special Cases of the Continuity Equation 406 93 The Stream Function 412 The Stream Function in Cartesian Coordinates 412 The Stream Function in Cylindrical Coordinates 419 The Compressible Stream Function 420 x FLUID MECHANICS cen72367_fm.qxd 11/23/04 12:13 PM Page x
11. 11. 94 Conservation of Linear MomentumCauchys Equation 421 Derivation Using the Divergence Theorem 421 Derivation Using an Infinitesimal Control Volume 422 Alternative Form of Cauchys Equation 425 Derivation Using Newtons Second Law 425 95 The NavierStokes Equation 426 Introduction 426 Newtonian versus Non-Newtonian Fluids 427 Derivation of the NavierStokes Equation for Incompressible, Isothermal Flow 428 Continuity and NavierStokes Equations in Cartesian Coordinates 430 Continuity and NavierStokes Equations in Cylindrical Coordinates 431 96 Differential Analysis of Fluid Flow Problems 432 Calculation of the Pressure Field for a Known Velocity Field 432 Exact Solutions of the Continuity and NavierStokes Equations 437 Summary 455 References and Suggested Reading 456 Problems 456 C H A P T E R T E N APPROXIMATE SOLUTIONS OF THE NAVIERSTOKES EQUATION 471 101 Introduction 472 102 Nondimensionalized Equations of Motion 473 103 The Creeping Flow Approximation 476 Drag on a Sphere in Creeping Flow 479 104 Approximation for Inviscid Regions of Flow 481 Derivation of the Bernoulli Equation in Inviscid Regions of Flow 482 105 The Irrotational Flow Approximation 485 Continuity Equation 485 Momentum Equation 487 Derivation of the Bernoulli Equation in Irrotational Regions of Flow 487 Two-Dimensional Irrotational Regions of Flow 490 Superposition in Irrotational Regions of Flow 494 Elementary Planar Irrotational Flows 494 Irrotational Flows Formed by Superposition 501 CONTENTS xi 106 The Boundary Layer Approximation 510 The Boundary Layer Equations 515 The Boundary Layer Procedure 520 Displacement Thickness 524 Momentum Thickness 527 Turbulent Flat Plate Boundary Layer 528 Boundary Layers with Pressure Gradients 534 The Momentum Integral Technique for Boundary Layers 539 Application Spotlight: Droplet Formation 549 Summary 547 References and Suggested Reading 548 Problems 550 C H A P T E R E L E V E N FLOW OVER BODIES: DRAG AND LIFT 561 111 Introduction 562 112 Drag and Lift 563 113 Friction and Pressure Drag 567 Reducing Drag by Streamlining 568 Flow Separation 569 114 Drag Coefficients of Common Geometries 571 Biological Systems and Drag 572 Drag Coefficients of Vehicles 574 Superposition 577 115 Parallel Flow over Flat Plates 579 Friction Coefficient 580 116 Flow over Cylinders and Spheres 583 Effect of Surface Roughness 586 117 Lift 587 End Effects of Wing Tips 591 Lift Generated by Spinning 594 Application Spotlight: Drag Reduction 600 Summary 598 References and Suggested Reading 599 Problems 601 C H A P T E R T W E L V E COMPRESSIBLE FLOW 611 121 Stagnation Properties 612 122 Speed of Sound and Mach Number 615 123 One-Dimensional Isentropic Flow 617 Variation of Fluid Velocity with Flow Area 620 Property Relations for Isentropic Flow of Ideal Gases 622 cen72367_fm.qxd 11/23/04 12:13 PM Page xi
12. 12. 124 Isentropic Flow through Nozzles 624 Converging Nozzles 625 ConvergingDiverging Nozzles 629 125 Shock Waves and Expansion Waves 633 Normal Shocks 633 Oblique Shocks 640 PrandtlMeyer Expansion Waves 644 126 Duct Flow with Heat Transfer and Negligible Friction (Rayleigh Flow) 648 Property Relations for Rayleigh Flow 654 Choked Rayleigh Flow 655 127 Adiabatic Duct Flow with Friction (Fanno Flow) 657 Property Relations for Fanno Flow 660 Choked Fanno Flow 663 Application Spotlight: Shock-Wave/ Boundary-Layer Interactions 667 Summary 668 References and Suggested Reading 669 Problems 669 C H A P T E R T H I R T E E N OPEN-CHANNEL FLOW 679 131 Classification of Open-Channel Flows 680 Uniform and Varied Flows 680 Laminar and Turbulent Flows in Channels 681 132 Froude Number and Wave Speed 683 Speed of Surface Waves 685 133 Specific Energy 687 134 Continuity and Energy Equations 690 135 Uniform Flow in Channels 691 Critical Uniform Flow 693 Superposition Method for Nonuniform Perimeters 693 136 Best Hydraulic Cross Sections 697 Rectangular Channels 699 Trapezoidal Channels 699 137 Gradually Varied Flow 701 Liquid Surface Profiles in Open Channels, y(x) 703 Some Representative Surface Profiles 706 Numerical Solution of Surface Profile 708 138 Rapidly Varied Flow and Hydraulic Jump 709 139 Flow Control and Measurement 714 Underflow Gates 714 Overflow Gates 716 Summary 723 References and Suggested Reading 724 Problems 725 C H A P T E R F O U R T E E N TURBOMACHINERY 735 141 Classifications and Terminology 736 142 Pumps 738 Pump Performance Curves and Matching a Pump to a Piping System 739 Pump Cavitation and Net Positive Suction Head 745 Pumps in Series and Parallel 748 Positive-Displacement Pumps 751 Dynamic Pumps 754 Centrifugal Pumps 754 Axial Pumps 764 143 Pump Scaling Laws 773 Dimensional Analysis 773 Pump Specific Speed 775 Affinity Laws 777 144 Turbines 781 Positive-Displacement Turbines 782 Dynamic Turbines 782 Impulse Turbines 783 Reaction Turbines 785 145 Turbine Scaling Laws 795 Dimensionless Turbine Parameters 795 Turbine Specific Speed 797 Gas and Steam Turbines 800 Application Spotlight: Rotary Fuel Atomizers 802 Summary 803 References and Suggested Reading 803 Problems 804 C H A P T E R F I F T E E N INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS 817 151 Introduction and Fundamentals 818 Motivation 818 Equations of Motion 818 Solution Procedure 819 Additional Equations of Motion 821 Grid Generation and Grid Independence 821 Boundary Conditions 826 Practice Makes Perfect 830 xii FLUID MECHANICS cen72367_fm.qxd 11/23/04 12:13 PM Page xii
13. 13. 152 Laminar CFD Calculations 831 Pipe Flow Entrance Region at Re 500 831 Flow around a Circular Cylinder at Re 150 833 153 Turbulent CFD Calculations 840 Flow around a Circular Cylinder at Re 10,000 843 Flow around a Circular Cylinder at Re 107 844 Design of the Stator for a Vane-Axial Flow Fan 845 154 CFD with Heat Transfer 853 Temperature Rise through a Cross-Flow Heat Exchanger 853 Cooling of an Array of Integrated Circuit Chips 855 155 Compressible Flow CFD Calculations 860 Compressible Flow through a ConvergingDiverging Nozzle 861 Oblique Shocks over a Wedge 865 156 Open-Channel Flow CFD Calculations 866 Flow over a Bump on the Bottom of a Channel 867 Flow through a Sluice Gate (Hydraulic Jump) 868 Application Spotlight: A Virtual Stomach 869 Summary 870 References and Suggested Reading 870 Problems 871 A P P E N D I X 1 PROPERTY TABLES AND CHARTS (SI UNITS) 885 TABLE A1 Molar Mass, Gas Constant, and Ideal-Gas Specfic Heats of Some Substances 886 TABLE A2 Boiling and Freezing Point Properties 887 TABLE A3 Properties of Saturated Water 888 TABLE A4 Properties of Saturated Refrigerant-134a 889 TABLE A5 Properties of Saturated Ammonia 890 TABLE A6 Properties of Saturated Propane 891 TABLE A7 Properties of Liquids 892 TABLE A8 Properties of Liquid Metals 893 TABLE A9 Properties of Air at 1 atm Pressure 894 TABLE A10 Properties of Gases at 1 atm Pressure 895 CONTENTS xiii TABLE A11 Properties of the Atmosphere at High Altitude 897 FIGURE A12 The Moody Chart for the Friction Factor for Fully Developed Flow in Circular Pipes 898 TABLE A13 One-dimensional isentropic compressible flow functions for an ideal gas with k 1.4 899 TABLE A14 One-dimensional normal shock functions for an ideal gas with k 1.4 900 TABLE A15 Rayleigh flow functions for an ideal gas with k 1.4 901 TABLE A16 Fanno flow functions for an ideal gas with k 1.4 902 A P P E N D I X 2 PROPERTY TABLES AND CHARTS (ENGLISH UNITS) 903 TABLE A1E Molar Mass, Gas Constant, and Ideal-Gas Specific Heats of Some Substances 904 TABLE A2E Boiling and Freezing Point Properties 905 TABLE A3E Properties of Saturated Water 906 TABLE A4E Properties of Saturated Refrigerant-134a 907 TABLE A5E Properties of Saturated Ammonia 908 TABLE A6E Properties of Saturated Propane 909 TABLE A7E Properties of Liquids 910 TABLE A8E Properties of Liquid Metals 911 TABLE A9E Properties of Air at 1 atm Pressure 912 TABLE A10E Properties of Gases at 1 atm Pressure 913 TABLE A11E Properties of the Atmosphere at High Altitude 915 Glossary 917 Index 931 cen72367_fm.qxd 11/23/04 12:13 PM Page xiii
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15. 15. B A C K G R O U N D Fluid mechanics is an exciting and fascinating subject with unlimited practi- cal applications ranging from microscopic biological systems to automobiles, airplanes, and spacecraft propulsion.Yet fluid mechanics has historically been one of the most challenging subjects for undergraduate students. Unlike ear- lier freshman- and sophomore-level subjects such as physics, chemistry, and engineering mechanics, where students often learn equations and then plug and chug on their calculators, proper analysis of a problem in fluid mechan- ics requires much more. Oftentimes, students must first assess the problem, make and justify assumptions and/or approximations, apply the relevant phys- ical laws in their proper forms, and solve the resulting equations before ever plugging any numbers into their calculators. Many problems in fluid mechan- ics require more than just knowledge of the subject, but also physical intuition and experience. Our hope is that this book, through its careful explanations of concepts and its use of numerous practical examples, sketches, figures, and photographs, bridges the gap between knowledge and proper application of that knowledge. Fluid mechanics is a mature subject; the basic equations and approxima- tions are well established and can be found in numerous introductory fluid mechanics books. The books are distinguished from one another in the way the material is presented. An accessible fluid mechanics book should present the material in a progressive order from simple to more difficult, building each chapter upon foundations laid down in previous chapters. In this way, even the traditionally challenging aspects of fluid mechanics can be learned effectively. Fluid mechanics is by its very nature a highly visual subject, and students learn more readily by visual stimulation. It is therefore imperative that a good fluid mechanics book also provide quality figures, photographs, and visual aids that help to explain the significance and meaning of the mathematical expressions. O B J E C T I V E S This book is intended for use as a textbook in the first fluid mechanics course for undergraduate engineering students in their junior or senior year. Students are assumed to have an adequate background in calculus, physics, engineering mechanics, and thermodynamics. The objectives of this text are To cover the basic principles and equations of fluid mechanics To present numerous and diverse real-world engineering examples to give students a feel for how fluid mechanics is applied in engineering practice To develop an intuitive understanding of fluid mechanics by emphasiz- ing the physics, and by supplying attractive figures and visual aids to reinforce the physics P R E F A C E cen72367_fm.qxd 11/23/04 11:22 AM Page xv
16. 16. The text contains sufficient material to give instructors flexibility as to which topics to emphasize. For example, aeronautics and aerospace engineer- ing instructors may emphasize potential flow, drag and lift, compressible flow, turbomachinery, and CFD, while mechanical and civil engineering instructors may choose to emphasize pipe flows and open-channel flows, respectively. The book has been written with enough breadth of coverage that it can be used for a two-course sequence in fluid mechanics if desired. P H I L O S O P H Y A N D G O A L We have adopted the same philosophy as that of the texts Thermodynamics: An Engineering Approach by Y. A. engel and M. A. Boles, Heat Transfer: A Practical Approach byY. A. engel, and Fundamentals of Thermal-Fluid Sci- ences by Y. A. engel and R. H. Turner, all published by McGraw-Hill. Namely, our goal is to offer an engineering textbook that Communicates directly to the minds of tomorrows engineers in a sim- ple yet precise manner Leads students toward a clear understanding and firm grasp of the basic principles of fluid mechanics Encourages creative thinking and development of a deeper understand- ing and intuitive feel for fluid mechanics Is read by students with interest and enthusiasm rather than merely as an aid to solve problems It is our philosophy that the best way to learn is by practice. Therefore, spe- cial effort is made throughout the book to reinforce material that was pre- sented earlier (both earlier in the chapter and in previous chapters). For example, many of the illustrated example problems and end-of-chapter prob- lems are comprehensive, forcing the student to review concepts learned in pre- vious chapters. Throughout the book, we show examples generated by computational fluid dynamics (CFD), and we provide an introductory chapter on CFD. Our goal is not to teach details about numerical algorithms associated with CFDthis is more properly presented in a separate course, typically at the graduate level. Rather, it is our intent to introduce undergraduate students to the capabilities and limitations of CFD as an engineering tool. We use CFD solutions in much the same way as we use experimental results from a wind tunnel test, i.e., to reinforce understanding of the physics of fluid flows and to provide quality flow visualizations that help to explain fluid behavior. C O N T E N T A N D O R G A N I Z AT I O N This book is organized into 15 chapters beginning with fundamental concepts of fluids and fluid flows and ending with an introduction to computational fluid dynamics, the application of which is rapidly becoming more common- place, even at the undergraduate level. Chapter 1 provides a basic introduction to fluids, classifications of fluid flow, control volume versus system formulations, dimensions, units, sig- nificant digits, and problem-solving techniques. xvi FLUID MECHANICS cen72367_fm.qxd 11/23/04 11:22 AM Page xvi
17. 17. Chapter 2 is devoted to fluid properties such as density, vapor pressure, specific heats, viscosity, and surface tension. Chapter 3 deals with fluid statics and pressure, including manometers and barometers, hydrostatic forces on submerged surfaces, buoyancy and stability, and fluids in rigid-body motion. Chapter 4 covers topics related to fluid kinematics, such as the differ- ences between Lagrangian and Eulerian descriptions of fluid flows, flow patterns, flow visualization, vorticity and rotationality, and the Reynolds transport theorem. Chapter 5 introduces the fundamental conservation laws of mass, momentum, and energy, with emphasis on the proper use of the mass, Bernoulli, and energy equations and the engineering applications of these equations. Chapter 6 applies the Reynolds transport theorem to linear momentum and angular momentum and emphasizes practical engineering applica- tions of the finite control volume momentum analysis. Chapter 7 reinforces the concept of dimensional homogeneity and intro- duces the Buckingham Pi theorem of dimensional analysis, dynamic similarity, and the method of repeating variablesmaterial that is useful throughout the rest of the book and in many disciplines in science and engineering. Chapter 8 is devoted to flow in pipes and ducts. We discuss the differ- ences between laminar and turbulent flow, friction losses in pipes and ducts, and minor losses in piping networks. We also explain how to properly select a pump or fan to match a piping network. Finally, we dis- cuss various experimental devices that are used to measure flow rate and velocity. Chapter 9 deals with differential analysis of fluid flow and includes derivation and application of the continuity equation, the Cauchy equa- tion, and the NavierStokes equation. We also introduce the stream function and describe its usefulness in analysis of fluid flows. Chapter 10 discusses several approximations of the NavierStokes equa- tions and provides example solutions for each approximation, including creeping flow, inviscid flow, irrotational (potential) flow, and boundary layers. Chapter 11 covers forces on bodies (drag and lift), explaining the dis- tinction between friction and pressure drag, and providing drag coeffi- cients for many common geometries. This chapter emphasizes the practical application of wind tunnel measurements coupled with dynamic similarity and dimensional analysis concepts introduced earlier in Chapter 7. Chapter 12 extends fluid flow analysis to compressible flow, where the behavior of gases is greatly affected by the Mach number, and the con- cepts of expansion waves, normal and oblique shock waves, and choked flow are introduced. Chapter 13 deals with open-channel flow and some of the unique fea- tures associated with the flow of liquids with a free surface, such as sur- face waves and hydraulic jumps. PREFACE xvii cen72367_fm.qxd 11/23/04 11:22 AM Page xvii
18. 18. Chapter 14 examines turbomachinery in more detail, including pumps, fans, and turbines. An emphasis is placed on how pumps and turbines work, rather than on their detailed design. We also discuss overall pump and turbine design, based on dynamic similarity laws and simplified velocity vector analyses. Chapter 15 describes the fundamental concepts of computational fluid dynamics (CFD) and shows students how to use commercial CFD codes as a tool to solve complex fluid mechanics problems. We emphasize the application of CFD rather than the algorithms used in CFD codes. Each chapter contains a large number of end-of-chapter homework prob- lems suitable for use by instructors. Most of the problems that involve calcu- lations are in SI units, but approximately 20 percent are written in English units. Finally, a comprehensive set of appendices is provided, giving the ther- modynamic and fluid properties of several materials, not just air and water as in most introductory fluids texts. Many of the end-of-chapter problems require use of the properties found in these appendices. L E A R N I N G T O O L S EMPHASIS ON PHYSICS A distinctive feature of this book is its emphasis on the physical aspects of the subject matter in addition to mathematical representations and manipulations. The authors believe that the emphasis in undergraduate education should remain on developing a sense of underlying physical mechanisms and a mas- tery of solving practical problems that an engineer is likely to face in the real world. Developing an intuitive understanding should also make the course a more motivating and worthwhile experience for the students. EFFECTIVE USE OF ASSOCIATION An observant mind should have no difficulty understanding engineering sci- ences. After all, the principles of engineering sciences are based on our every- day experiences and experimental observations. Therefore, a physical, intuitive approach is used throughout this text. Frequently, parallels are drawn between the subject matter and students everyday experiences so that they can relate the subject matter to what they already know. SELF-INSTRUCTING The material in the text is introduced at a level that an average student can fol- low comfortably. It speaks to students, not over students. In fact, it is self- instructive. Noting that the principles of science are based on experimental observations, most of the derivations in this text are largely based on physical arguments, and thus they are easy to follow and understand. EXTENSIVE USE OF ARTWORK Figures are important learning tools that help the students get the picture, and the text makes effective use of graphics. It contains more figures and illus- trations than any other book in this category. Figures attract attention and stimulate curiosity and interest. Most of the figures in this text are intended to serve as a means of emphasizing some key concepts that would otherwise go unnoticed; some serve as page summaries. xviii FLUID MECHANICS cen72367_fm.qxd 11/23/04 11:22 AM Page xviii
19. 19. CHAPTER OPENERS AND SUMMARIES Each chapter begins with an overview of the material to be covered.A summary is included at the end of each chapter, providing a quick review of basic con- cepts and important relations, and pointing out the relevance of the material. NUMEROUS WORKED-OUT EXAMPLES WITH A SYSTEMATIC SOLUTIONS PROCEDURE Each chapter contains several worked-out examples that clarify the material and illustrate the use of the basic principles. An intuitive and systematic approach is used in the solution of the example problems, while maintaining an informal conversational style. The problem is first stated, and the objectives are identified. The assumptions are then stated, together with their justifica- tions. The properties needed to solve the problem are listed separately. Numerical values are used together with their units to emphasize that numbers without units are meaningless, and unit manipulations are as important as manipulating the numerical values with a calculator. The significance of the findings is discussed following the solutions. This approach is also used con- sistently in the solutions presented in the instructors solutions manual. A WEALTH OF REALISTIC END-OF-CHAPTER PROBLEMS The end-of-chapter problems are grouped under specific topics to make prob- lem selection easier for both instructors and students. Within each group of problems are Concept Questions, indicated by C, to check the studentslevel of understanding of basic concepts. The problems under Review Problems are more comprehensive in nature and are not directly tied to any specific section of a chapter in some cases they require review of material learned in previ- ous chapters. Problems designated as Design and Essay are intended to encourage students to make engineering judgments, to conduct independent exploration of topics of interest, and to communicate their findings in a pro- fessional manner. Problems designated by an E are in English units, and SI users can ignore them. Problems with the are solved using EES, and com- plete solutions together with parametric studies are included on the enclosed DVD. Problems with the are comprehensive in nature and are intended to be solved with a computer, preferably using the EES software that accompa- nies this text. Several economics- and safety-related problems are incorpo- rated throughout to enhance cost and safety awareness among engineering students. Answers to selected problems are listed immediately following the problem for convenience to students. USE OF COMMON NOTATION The use of different notation for the same quantities in different engineering courses has long been a source of discontent and confusion. A student taking both fluid mechanics and heat transfer, for example, has to use the notation Q for volume flow rate in one course, and for heat transfer in the other. The need to unify notation in engineering education has often been raised, even in some reports of conferences sponsored by the National Science Foundation through Foundation Coalitions, but little effort has been made to date in this regard. For example, refer to the final report of the Mini-Conference on Energy Stem Innovations, May 28 and 29, 2003, University of Wisconsin. In this text we made a conscious effort to minimize this conflict by adopting the familiar PREFACE xix cen72367_fm.qxd 11/23/04 11:22 AM Page xix
20. 20. thermodynamic notation V . for volume flow rate, thus reserving the notation Q for heat transfer. Also, we consistently use an overdot to denote time rate. We think that both students and instructors will appreciate this effort to promote a common notation. A CHOICE OF SI ALONE OR SI/ENGLISH UNITS In recognition of the fact that English units are still widely used in some industries, both SI and English units are used in this text, with an emphasis on SI. The material in this text can be covered using combined SI/English units or SI units alone, depending on the preference of the instructor. The property tables and charts in the appendices are presented in both units, except the ones that involve dimensionless quantities. Problems, tables, and charts in English units are designated by E after the number for easy recognition, and they can be ignored easily by the SI users. COMBINED COVERAGE OF BERNOULLI AND ENERGY EQUATIONS The Bernoulli equation is one of the most frequently used equations in fluid mechanics, but it is also one of the most misused. Therefore, it is important to emphasize the limitations on the use of this idealized equation and to show how to properly account for imperfections and irreversible losses. In Chapter 5, we do this by introducing the energy equation right after the Bernoulli equation and demonstrating how the solutions of many practical engineering problems differ from those obtained using the Bernoulli equation. This helps students develop a realistic view of the Bernoulli equation. A SEPARATE CHAPTER ON CFD Commercial Computational Fluid Dynamics (CFD) codes are widely used in engineering practice in the design and analysis of flow systems, and it has become exceedingly important for engineers to have a solid understanding of the fundamental aspects, capabilities, and limitations of CFD. Recognizing that most undergraduate engineering curriculums do not have room for a full course on CFD, a separate chapter is included here to make up for this defi- ciency and to equip students with an adequate background on the strengths and weaknesses of CFD. APPLICATION SPOTLIGHTS Throughout the book are highlighted examples called Application Spotlights where a real-world application of fluid mechanics is shown. A unique feature of these special examples is that they are written by guest authors. The Appli- cation Spotlights are designed to show students how fluid mechanics has diverse applications in a wide variety of fields. They also include eye-catching photographs from the guest authors research. GLOSSARY OF FLUID MECHANICS TERMS Throughout the chapters, when an important key term or concept is introduced and defined, it appears in black boldface type. Fundamental fluid mechanics terms and concepts appear in blue boldface type, and these fundamental terms also appear in a comprehensive end-of-book glossary developed by Professor James Brasseur of The Pennsylvania State University. This unique glossary is an excellent learning and review tool for students as they move forward in xx FLUID MECHANICS cen72367_fm.qxd 11/23/04 11:22 AM Page xx
21. 21. their study of fluid mechanics. In addition, students can test their knowledge of these fundamental terms by using the interactive flash cards and other resources located on our accompanying website (www.mhhe.com/cengel). CONVERSION FACTORS Frequently used conversion factors, physical constants, and frequently used properties of air and water at 20C and atmospheric pressure are listed on the front inner cover pages of the text for easy reference. NOMENCLATURE A list of the major symbols, subscripts, and superscripts used in the text are listed on the inside back cover pages of the text for easy reference. S U P P L E M E N T S These supplements are available to adopters of the book: STUDENT RESOURCES DVD Packaged free with every new copy of the text, this DVD provides a wealth of resources for students including Fluid Mechanics Videos, a CFD Animations Library, and EES Software. ONLINE LEARNING CENTER Web support is provided for the book on our Online Learning Center at www.mhhe.com/cengel. Visit this robust site for book and supplement infor- mation, errata, author information, and further resources for instructors and students. ENGINEERING EQUATION SOLVER (EES) Developed by Sanford Klein and William Beckman from the University of WisconsinMadison, this software combines equation-solving capability and engineering property data. EES can do optimization, parametric analysis, and linear and nonlinear regression, and provides publication-quality plotting capabilities. Thermodynamics and transport properties for air, water, and many other fluids are built-in and EES allows the user to enter property data or functional relationships. FLUENT FLOWLAB SOFTWARE AND TEMPLATES As an integral part of Chapter 15, Introduction to Computational Fluid Dynam- ics, we provide access to a student-friendly CFD software package developed by Fluent Inc. In addition, we provide over 40 FLUENT FLOWLAB templates to complement the end-of-chapter problems in Chapter 15. These problems and templates are unique in that they are designed with both a fluid mechanics learn- ing objective and a CFD learning objective in mind. INSTRUCTORS RESOURCE CD-ROM (AVAILABLE TO INSTRUCTORS ONLY) This CD, available to instructors only, offers a wide range of classroom prepa- ration and presentation resources including an electronic solutions manual with PDF files by chapter, all text chapters and appendices as downloadable PDF files, and all text figures in JPEG format. PREFACE xxi cen72367_fm.qxd 11/23/04 11:22 AM Page xxi
22. 22. COSMOS CD-ROM (AVAILABLE TO INSTRUCTORS ONLY) This CD, available to instructors only, provides electronic solutions delivered via our database management tool. McGraw-Hills COSMOS allows instruc- tors to streamline the creation of assignments, quizzes, and tests by using prob- lems and solutions from the textbookas well as their own custom material. A C K N O W L E D G M E N T S The authors would like to acknowledge with appreciation the numerous and valuable comments, suggestions, constructive criticisms, and praise from the following evaluators and reviewers: xxii FLUID MECHANICS Mohammad Ali Kettering University Darryl Alofs University of Missouri, Rolla Farrukh Alvi Florida A & M University & Florida State University Ryoichi Amano University of WisconsinMilwaukee Michael Amitay Rensselaer Polytechnic Institute T. P. Ashokbabu National Institute of Technology, India Idirb Azouz Southern Utah University Kenneth S. Ball University of Texas at Austin James G. Brasseur The Pennsylvania State University Glenn Brown Oklahoma State University John Callister Cornell University Frederick Carranti Syracuse University Kevin W. Cassel Illinois Institute of Technology Haris Catrakis University of California, Irvine Louis N. Cattafesta III University of Florida Soyoung Cha University of Illinois at Chicago Tiao Chang Ohio University Young Cho Drexel University Po-Ya (Abel) Chuang The Pennsylvania State University William H. Colwill American Hydro Corporation A. Terrence Conlisk Jr. The Ohio State University Daniel Cox Texas A&M University John Crepeau University of Idaho Jie Cui Tennessee Technological University Lisa Davids Embry-Riddle Aeronautical University Jerry Drummond The University of Akron Dwayne Edwards University of Kentucky Richard Figliola Clemson University Charles Forsberg Hofstra University Fred K. Forster University of Washington cen72367_fm.qxd 11/23/04 11:22 AM Page xxii
23. 23. PREFACE xxiii Rong Gan The University of Oklahoma Philip Gerhart University of Evansville Fred Gessner University of Washington Sam Han Tennessee Technological University Mark J. Holowach Ballston Spa, NY Neal Houze Purdue University Barbara Hutchings Fluent Incorporated Niu Jianlei Hong Kong Polytechnic University, Hong Kong David Johnson University of Waterloo Matthew Jones Brigham Young University Zbigniew J. Kabala Duke University Fazal Kauser California State Polytechnic University, Pomona Pirouz Kavehpour University of California, Los Angeles Jacob Kazakia Lehigh University Richard Keane University of Illinois at UrbanaChampaign Jamil Khan University of South Carolina N. Nirmala Khandan New Mexico State University Jeyhoon Khodadadi Auburn University Subha Kumpaty Milwaukee School of Engineering James A. Liburdy Oregon State University Chao-An Lin National Tsing Hua University, Taiwan Kraemer Luks The University of Tulsa G. Mahinthakumar North Carolina State University Saeed Manafzadeh University of Illinois at Chicago Daniel Maynes Brigham Young University James M. McDonough University of Kentucky Richard S. Miller Clemson University Shane Moeykens Fluent Incorporated Joseph Morrison NASA Langley Research Center Karim Nasr Kettering University C. O. Ng University of Hong Kong, Hong Kong Wing Ng Virginia Polytechnic Institute Tay Seow Ngie Nanyang Technological University, Singapore John Nicklow Southern Illinois University at Carbondale Nagy Nosseir San Diego State University Emmanuel Nzewi North Carolina A&T State University Ali Ogut Rochester Institute of Technology Michael Olsen Iowa State University cen72367_fm.qxd 11/23/04 11:22 AM Page xxiii
24. 24. xxiv FLUID MECHANICS The authors also acknowledge the guest authors who contributed photographs and write-ups for the Application Spotlights: Roger Pawlowski Lawrence Technological University Bryan Pearce The University of Maine Blair Perot University of Massachusetts Amherst Alexander Povitsky The University of Akron Guy Riefler Ohio University Kurt Rosentrater Northern Illinois University Subrata Roy Kettering University Joseph Sai Texas A&M UniversityKingsville Gregory Selby Old Dominion University Gary S. Settles The Pennsylvania State University Winoto SH National University of Singapore, Singapore Muhammad Sharif The University of Alabama Mark Stone Washington State University Chelakara Subramanian Florida Institute of Technology Constantine Tarawneh The University of TexasPan American Sahnaz Tigrek Middle East Technical University Hsu Chin Tsau Hong Kong University of Science and Technology, Hong Kong M. Erol Ulucakli Lafayette College Oleg Vasilyev University of Missouri Zhi Jian Wang Michigan State University Timothy Wei Rutgers, The State University of New Jersey Minami Yoda Georgia Institute of Technology Mohd Zamri Yusoff Universiti Tenaga Nasional, Malaysia Michael L. Billet The Pennsylvania State University James G. Brasseur The Pennsylvania State University Werner J. A. Dahm University of Michigan Brian Daniels Oregon State University Michael Dickinson California Institute of Technology Gerald C. Lauchle The Pennsylvania State University James A. Liburdy Oregon State University Anupam Pal The Pennsylvania State University Ganesh Raman Illinois Institute of Technology Gary S. Settles The Pennsylvania State University Lorenz Sigurdson University of Alberta cen72367_fm.qxd 11/23/04 11:22 AM Page xxiv
25. 25. Special thanks go to Professor Gary Settles and his associates at Penn State (Lori Dodson-Dreibelbis, J. D. Miller, and Gabrielle Tremblay) for creating the exciting narrated video clips that are found on the DVD that accompanies this book. Similarly, the authors acknowledge several people at Fluent Inc., who helped to make available the wonderful CFD animations that are also found on the DVD and the FLUENT FLOWLAB templates that are available for downloading from the books website: Shane Moeykens, Barbara Hutch- ings, Liz Marshall, Ashish Kulkarni, Ajay Parihar, and R. Murali Krishnan. The authors also thank Professor James Brasseur of Penn State for creating the precise glossary of fluid mechanics terms, Professor Glenn Brown of Oklahoma State for providing many items of historical interest throughout the text, Professor Mehmet Kanoglu of Gaziantep University for preparing the solutions of EES problems, and Professor Tahsin Engin of Sakarya University for contributing several end-of-chapter problems. Finally, special thanks must go to our families, especially our wives, Zehra engel and Suzanne Cimbala, for their continued patience, understanding, and support throughout the preparation of this book, which involved many long hours when they had to handle family concerns on their own because their husbands faces were glued to a computer screen. Yunus A. engel John M. Cimbala PREFACE xxv cen72367_fm.qxd 11/23/04 11:22 AM Page xxv
26. 26. INTRODUCTION AND BASIC CONCEPTS I n this introductory chapter, we present the basic concepts commonly used in the analysis of fluid flow. We start this chapter with a discussion of the phases of matter and the numerous ways of classification of fluid flow, such as viscous versus inviscid regions of flow, internal versus external flow, compressible versus incompressible flow, laminar versus turbulent flow, natural versus forced flow, and steady versus unsteady flow. We also discuss the no-slip condition at solidfluid interfaces and present a brief his- tory of the development of fluid mechanics. After presenting the concepts of system and control volume, we review the unit systems that will be used. We then discuss how mathematical mod- els for engineering problems are prepared and how to interpret the results obtained from the analysis of such models. This is followed by a presenta- tion of an intuitive systematic problem-solving technique that can be used as a model in solving engineering problems. Finally, we discuss accuracy, pre- cision, and significant digits in engineering measurements and calculations. 1 CHAPTER 1 OBJECTIVES When you finish reading this chapter, you should be able to I Understand the basic concepts of fluid mechanics and recognize the various types of fluid flow problems encountered in practice I Model engineering problems and solve them in a systematic manner I Have a working knowledge of accuracy, precision, and significant digits, and recognize the importance of dimensional homogeneity in engineering calculations cen72367_ch01.qxd 10/29/04 2:31 PM Page 1
27. 27. 11 I INTRODUCTION Mechanics is the oldest physical science that deals with both stationary and moving bodies under the influence of forces. The branch of mechanics that deals with bodies at rest is called statics, while the branch that deals with bodies in motion is called dynamics. The subcategory fluid mechanics is defined as the science that deals with the behavior of fluids at rest (fluid sta- tics) or in motion (fluid dynamics), and the interaction of fluids with solids or other fluids at the boundaries. Fluid mechanics is also referred to as fluid dynamics by considering fluids at rest as a special case of motion with zero velocity (Fig. 11). Fluid mechanics itself is also divided into several categories. The study of the motion of fluids that are practically incompressible (such as liquids, especially water, and gases at low speeds) is usually referred to as hydrody- namics. A subcategory of hydrodynamics is hydraulics, which deals with liq- uid flows in pipes and open channels. Gas dynamics deals with the flow of fluids that undergo significant density changes, such as the flow of gases through nozzles at high speeds. The category aerodynamics deals with the flow of gases (especially air) over bodies such as aircraft, rockets, and automo- biles at high or low speeds. Some other specialized categories such as meteo- rology, oceanography, and hydrology deal with naturally occurring flows. What Is a Fluid? You will recall from physics that a substance exists in three primary phases: solid, liquid, and gas. (At very high temperatures, it also exists as plasma.) A substance in the liquid or gas phase is referred to as a fluid. Distinction between a solid and a fluid is made on the basis of the substances ability to resist an applied shear (or tangential) stress that tends to change its shape. A solid can resist an applied shear stress by deforming, whereas a fluid deforms continuously under the influence of shear stress, no matter how small. In solids stress is proportional to strain, but in fluids stress is propor- tional to strain rate. When a constant shear force is applied, a solid eventu- ally stops deforming, at some fixed strain angle, whereas a fluid never stops deforming and approaches a certain rate of strain. Consider a rectangular rubber block tightly placed between two plates. As the upper plate is pulled with a force F while the lower plate is held fixed, the rubber block deforms, as shown in Fig. 12. The angle of deformation a (called the shear strain or angular displacement) increases in proportion to the applied force F. Assuming there is no slip between the rubber and the plates, the upper surface of the rubber is displaced by an amount equal to the displacement of the upper plate while the lower surface remains station- ary. In equilibrium, the net force acting on the plate in the horizontal direc- tion must be zero, and thus a force equal and opposite to F must be acting on the plate. This opposing force that develops at the platerubber interface due to friction is expressed as F tA, where t is the shear stress and A is the contact area between the upper plate and the rubber. When the force is removed, the rubber returns to its original position. This phenomenon would also be observed with other solids such as a steel block provided that the applied force does not exceed the elastic range. If this experiment were repeated with a fluid (with two large parallel plates placed in a large body of water, for example), the fluid layer in contact with the upper plate would 2 FLUID MECHANICS FIGURE 11 Fluid mechanics deals with liquids and gases in motion or at rest. Vol. 16/Photo Disc. Contact area, A Shear stress t = F/A Shear strain, a Force, F a Deformed rubber FIGURE 12 Deformation of a rubber eraser placed between two parallel plates under the influence of a shear force. cen72367_ch01.qxd 11/19/04 10:24 AM Page 2
28. 28. move with the plate continuously at the velocity of the plate no matter how small the force F is. The fluid velocity decreases with depth because of fric- tion between fluid layers, reaching zero at the lower plate. You will recall from statics that stress is defined as force per unit area and is determined by dividing the force by the area upon which it acts. The normal component of the force acting on a surface per unit area is called the normal stress, and the tangential component of a force acting on a surface per unit area is called shear stress (Fig. 13). In a fluid at rest, the normal stress is called pressure. The supporting walls of a fluid eliminate shear stress, and thus a fluid at rest is at a state of zero shear stress. When the walls are removed or a liquid container is tilted, a shear develops and the liquid splashes or moves to attain a horizontal free surface. In a liquid, chunks of molecules can move relative to each other, but the volume remains relatively constant because of the strong cohesive forces between the molecules. As a result, a liquid takes the shape of the container it is in, and it forms a free surface in a larger container in a gravitational field. A gas, on the other hand, expands until it encounters the walls of the container and fills the entire available space. This is because the gas mole- cules are widely spaced, and the cohesive forces between them are very small. Unlike liquids, gases cannot form a free surface (Fig. 14). Although solids and fluids are easily distinguished in most cases, this dis- tinction is not so clear in some borderline cases. For example, asphalt appears and behaves as a solid since it resists shear stress for short periods of time. But it deforms slowly and behaves like a fluid when these forces are exerted for extended periods of time. Some plastics, lead, and slurry mixtures exhibit similar behavior. Such borderline cases are beyond the scope of this text. The fluids we will deal with in this text will be clearly recognizable as fluids. Intermolecular bonds are strongest in solids and weakest in gases. One reason is that molecules in solids are closely packed together, whereas in gases they are separated by relatively large distances (Fig. 15). The molecules in a solid are arranged in a pattern that is repeated through- out. Because of the small distances between molecules in a solid, the attrac- tive forces of molecules on each other are large and keep the molecules at 3 CHAPTER 1 Fn Ft F Normal to surface Tangent to surface Force acting on area dA dA FIGURE 13 The normal stress and shear stress at the surface of a fluid element. For fluids at rest, the shear stress is zero and pressure is the only normal stress. Free surface Liquid Gas FIGURE 14 Unlike a liquid, a gas does not form a free surface, and it expands to fill the entire available space. (a) (b) (c) FIGURE 15 The arrangement of atoms in different phases: (a) molecules are at relatively fixed positions in a solid, (b) groups of molecules move about each other in the liquid phase, and (c) molecules move about at random in the gas phase. Shear stress: t Ft dA Normal stress: s Fn dA cen72367_ch01.qxd 10/29/04 2:31 PM Page 3
29. 29. fixed positions. The molecular spacing in the liquid phase is not much differ- ent from that of the solid phase, except the molecules are no longer at fixed positions relative to each other and they can rotate and translate freely. In a liquid, the intermolecular forces are weaker relative to solids, but still strong compared with gases. The distances between molecules generally increase slightly as a solid turns liquid, with water being a notable exception. In the gas phase, the molecules are far apart from each other, and a mole- cular order is nonexistent. Gas molecules move about at random, continu- ally colliding with each other and the walls of the container in which they are contained. Particularly at low densities, the intermolecular forces are very small, and collisions are the only mode of interaction between the mol- ecules. Molecules in the gas phase are at a considerably higher energy level than they are in the liquid or solid phase. Therefore, the gas must release a large amount of its energy before it can condense or freeze. Gas and vapor are often used as synonymous words. The vapor phase of a substance is customarily called a gas when it is above the critical tempera- ture. Vapor usually implies a gas that is not far from a state of condensation. Any practical fluid system consists of a large number of molecules, and the properties of the system naturally depend on the behavior of these mole- cules. For example, the pressure of a gas in a container is the result of momentum transfer between the molecules and the walls of the container. However, one does not need to know the behavior of the gas molecules to determine the pressure in the container. It would be sufficient to attach a pressure gage to the container (Fig. 16). This macroscopic or classical approach does not require a knowledge of the behavior of individual mole- cules and provides a direct and easy way to the solution of engineering problems. The more elaborate microscopic or statistical approach, based on the average behavior of large groups of individual molecules, is rather involved and is used in this text only in the supporting role. Application Areas of Fluid Mechanics Fluid mechanics is widely used both in everyday activities and in the design of modern engineering systems from vacuum cleaners to supersonic aircraft. Therefore, it is important to develop a good understanding of the basic prin- ciples of fluid mechanics. To begin with, fluid mechanics plays a vital role in the human body. The heart is constantly pumping blood to all parts of the human body through the arteries and veins, and the lungs are the sites of airflow in alternating directions. Needless to say, all artificial hearts, breathing machines, and dialysis systems are designed using fluid dynamics. An ordinary house is, in some respects, an exhibition hall filled with appli- cations of fluid mechanics. The piping systems for cold water, natural gas, and sewage for an individual house and the entire city are designed primarily on the basis of fluid mechanics. The same is also true for the piping and duct- ing network of heating and air-conditioning systems. A refrigerator involves tubes through which the refrigerant flows, a compressor that pressurizes the refrigerant, and two heat exchangers where the refrigerant absorbs and rejects heat. Fluid mechanics plays a major role in the design of all these compo- nents. Even the operation of ordinary faucets is based on fluid mechanics. We can also see numerous applications of fluid mechanics in an automo- bile. All components associated with the transportation of the fuel from the 4 FLUID MECHANICS Pressure gage FIGURE 16 On a microscopic scale, pressure is determined by the interaction of individual gas molecules. However, we can measure the pressure on a macroscopic scale with a pressure gage. cen72367_ch01.qxd 10/29/04 2:31 PM Page 4
30. 30. fuel tank to the cylindersthe fuel line, fuel pump, fuel injectors, or carbu- retorsas well as the mixing of the fuel and the air in the cylinders and the purging of combustion gases in exhaust pipes are analyzed using fluid mechanics. Fluid mechanics is also used in the design of the heating and air-conditioning system, the hydraulic brakes, the power steering, automatic transmission, and lubrication systems, the cooling system of the engine block including the radiator and the water pump, and even the tires. The sleek streamlined shape of recent model cars is the result of efforts to mini- mize drag by using extensive analysis of flow over surfaces. On a broader scale, fluid mechanics plays a major part in the design and analysis of aircraft, boats, submarines, rockets, jet engines, wind turbines, biomedical devices, the cooling of electronic components, and the trans- portation of water, crude oil, and natural gas. It is also considered in the design of buildings, bridges, and even billboards to make sure that the struc- tures can withstand wind loading. Numerous natural phenomena such as the rain cycle, weather patterns, the rise of ground water to the top of trees, winds, ocean waves, and currents in large water bodies are also governed by the principles of fluid mechanics (Fig. 17). 5 CHAPTER 1 Piping and plumbing systems Photo by John M. Cimbala. Cars Photo by John M. Cimbala. Power plants Vol. 57/Photo Disc. Aircraft and spacecraft Vol. 1/Photo Disc. Human body Vol. 110/Photo Disc. Wind turbines Vol. 17/Photo Disc. Natural flows and weather Vol. 16/Photo Disc. Industrial applications Courtesy UMDE Engineering, Contracting, and Trading. Used by permission. FIGURE 17 Some application areas of fluid mechanics. Boats Vol. 5/Photo Disc. cen72367_ch01.qxd 10/29/04 2:31 PM Page 5
31. 31. 12 I THE NO-SLIP CONDITION Fluid flow is often confined by solid surfaces, and it is important to under- stand how the presence of solid surfaces affects fluid flow. We know that water in a river cannot flow through large rocks, and goes around them. That is, the water velocity normal to the rock surface must be zero, and water approaching the surface normally comes to a complete stop at the sur- face. What is not so obvious is that water approaching the rock at any angle also comes to a complete stop at the rock surface, and thus the tangential velocity of water at the surface is also zero. Consider the flow of a fluid in a stationary pipe or over a solid surface that is nonporous (i.e., impermeable to the fluid). All experimental observa- tions indicate that a fluid in motion comes to a complete stop at the surface and assumes a zero velocity relative to the surface. That is, a fluid in direct contact with a solid sticks to the surface due to viscous effects, and there is no slip. This is known as the no-slip condition. The photo in Fig. 18 obtained from a video clip clearly shows the evolu- tion of a velocity gradient as a result of the fluid sticking to the surface of a blunt nose. The layer that sticks to the surface slows the adjacent fluid layer because of viscous forces between the fluid layers, which slows the next layer, and so on. Therefore, the no-slip condition is responsible for the development of the velocity profile. The flow region adjacent to the wall in which the viscous effects (and thus the velocity gradients) are significant is called the boundary layer. The fluid property responsible for the no-slip condition and the development of the boundary layer is viscosity and is dis- cussed in Chap. 2. A fluid layer adjacent to a moving surface has the same velocity as the surface. A consequence of the no-slip condition is that all velocity profiles must have zero values with respect to the surface at the points of contact between a fluid and a solid surface (Fig. 19). Another consequence of the no-slip condition is the surface drag, which is the force a fluid exerts on a surface in the flow direction. When a fluid is forced to flow over a curved surface, such as the back side of a cylinder at sufficiently high velocity, the boundary layer can no longer remain attached to the surface, and at some point it separates from the surfacea process called flow separation (Fig. 110). We emphasize that the no-slip condition applies everywhere along the surface, even down- stream of the separation point. Flow separation is discussed in greater detail in Chap. 10. 6 FLUID MECHANICS FIGURE 18 The development of a velocity profile due to the no-slip condition as a fluid flows over a blunt nose. Hunter Rouse: Laminar and Turbulent Flow Film. Copyright IIHR-Hydroscience & Engineering, The University of Iowa. Used by permission. Relative velocities of fluid layers Uniform approach velocity, V Zero velocity at the surface Plate FIGURE 19 A fluid flowing over a stationary surface comes to a complete stop at the surface because of the no-slip condition. Separation point FIGURE 110 Flow separation during flow over a curved surface. From G. M. Homsy et al, Multi-Media Fluid Mechanics, Cambridge Univ. Press (2001). ISBN 0-521-78748-3. Reprinted by permission. cen72367_ch01.qxd 10/29/04 2:32 PM Page 6
32. 32. A similar phenomenon occurs for temperature. When two bodies at differ- ent temperatures are brought into contact, heat transfer occurs until both bodies assume the same temperature at the points of contact. Therefore, a fluid and a solid surface have the same temperature at the points of contact. This is known as no-temperature-jump condition. 13 I A BRIEF HISTORY OF FLUID MECHANICS1 One of the first engineering problems humankind faced as cities were devel- oped was the supply of water for domestic use and irrigation of crops. Our urban lifestyles can be retained only with abundant water, and it is clear from archeology that every successful civilization of prehistory invested in the construction and maintenance of water systems. The Roman aqueducts, some of which are still in use, are the best known examples. However, per- haps the most impressive engineering from a technical viewpoint was done at the Hellenistic city of Pergamon in present-day Turkey. There, from 283 to 133 BC, they built a series of pressurized lead and clay pipelines (Fig. 111), up to 45 km long that operated at pressures exceeding 1.7 MPa (180 m of head). Unfortunately, the names of almost all these early builders are lost to history. The earliest recognized contribution to fluid mechanics the- ory was made by the Greek mathematician Archimedes (285212 BC). He formulated and applied the buoyancy principle in historys first nondestruc- tive test to determine the gold content of the crown of King Hiero I. The Romans built great aqueducts and educated many conquered people on the benefits of clean water, but overall had a poor understanding of fluids the- ory. (Perhaps they shouldnt have killed Archimedes when they sacked Syracuse.) During the Middle Ages the application of fluid machinery slowly but steadily expanded. Elegant piston pumps were developed for dewatering mines, and the watermill and windmill were perfected to grind grain, forge metal, and for other tasks. For the first time in recorded human history sig- nificant work was being done without the power of a muscle supplied by a person or animal, and these inventions are generally credited with enabling the later industrial revolution. Again the creators of most of the progress are unknown, but the devices themselves were well documented by several technical writers such as Georgius Agricola (Fig. 112). The Renaissance brought continued development of fluid systems and machines, but more importantly, the scientific method was perfected and adopted throughout Europe. Simon Stevin (15481617), Galileo Galilei (15641642), Edme Mariotte (16201684), and Evangelista Torricelli (16081647) were among the first to apply the method to fluids as they investigated hydrostatic pressure distributions and vacuums. That work was integrated and refined by the brilliant mathematician, Blaise Pascal (1623 1662). The Italian monk, Benedetto Castelli (15771644) was the first per- son to publish a statement of the continuity principle for fluids. Besides for- mulating his equations of motion for solids, Sir Isaac Newton (16431727) applied his laws to fluids and explored fluid inertia and resistance, free jets, and viscosity. That effort was built upon by the Swiss Daniel Bernoulli 7 CHAPTER 1 1 This section is contributed by Professor Glenn Brown of Oklahoma State University. FIGURE 111 Segment of Pergamon pipeline. Each clay pipe section was 13 to 18 cm in diameter. Courtesy Gunther Garbrecht. Used by permission. FIGURE 112 A mine hoist powered by a reversible water wheel. G. Agricola, De Re Metalica, Basel, 1556. cen72367_ch01.qxd 10/29/04 2:32 PM Page 7
33. 33. (17001782) and his associate Leonard Euler (17071783). Together, their work defined the energy and momentum equations. Bernoullis 1738 classic treatise Hydrodynamica may be considered the first fluid mechanics text. Finally, Jean dAlembert (17171789) developed the idea of velocity and acceleration components, a differential expression of continuity, and his paradox of zero resistance to steady uniform motion. The development of fluid mechanics theory up through the end of the eighteenth century had little impact on engineering since fluid properties and parameters were poorly quantified, and most theories were abstractions that could not be quantified for design purposes. That was to change with the development of the French school of engineering led by Riche de Prony (17551839). Prony (still known for his brake to measure power) and his associates in Paris at the Ecole Polytechnic and the Ecole Ponts et Chaussees were the first to integrate calculus and scientific theory into the engineering curriculum, which became the model for the rest of the world. (So now you know whom to blame for your painful freshman year.) Antonie Chezy (17181798), Louis Navier (17851836), Gaspard Coriolis (17921843), Henry Darcy (18031858), and many other contributors to fluid engineering and theory were students and/or instructors at the schools. By the mid nineteenth century fundamental advances were coming on several fronts. The physician Jean Poiseuille (17991869) had accurately measured flow in capillary tubes for multiple fluids, while in Germany Gotthilf Hagen (17971884) had differentiated between laminar and turbu- lent flow in pipes. In England, Lord Osborn Reynolds (18421912) contin- ued that work and developed the dimensionless number that bears his name. Similarly, in parallel to the early work of Navier, George Stokes (1819 1903) completed the general equations of fluid motion with friction that take their names. William Froude (18101879) almost single-handedly developed the procedures and proved the value of physical model testing. American expertise had become equal to the Europeans as demonstrated by James Franciss (18151892) and Lester Peltons (18291908) pioneering work in turbines and Clemens Herschels (18421930) invention of the Ven- turi meter. The late nineteenth century was notable for the expansion of fluid theory by Irish and English scientists and engineers, including in addition to Reynolds and Stokes, William Thomson, Lord Kelvin (18241907), William Strutt, Lord Rayleigh (18421919), and Sir Horace Lamb (18491934). These individuals investigated a large number of problems including dimen- sional analysis, irrotational flow, vortex motion, cavitation, and waves. In a broader sense their work also explored the links between fluid mechanics, thermodynamics, and heat transfer. The dawn of the twentieth century brought two monumental develop- ments. First in 1903, the self-taught Wright brothers (Wilbur, 18671912; Orville, 18711948) through application of theory and determined experi- mentation perfected the airplane. Their primitive invention was complete and contained all the major aspects of modern craft (Fig. 113). The NavierStokes equations were of little use up to this time because they were too difficult to solve. In a pioneering paper in 1904, the German Ludwig Prandtl (18751953) showed that fluid flows can be divided into a layer near the walls, the boundary layer, where the friction effects are significant and an outer layer where such effects are negligible and the simplified Euler 8 FLUID MECHANICS FIGURE 113 The Wright brothers take flight at Kitty Hawk. National Air and Space Museum/ Smithsonian Institution. cen72367_ch01.qxd 10/29/04 2:32 PM Page 8
34. 34. and Bernoulli equations are applicable. His students, Theodore von Krmn (18811963), Paul Blasius (18831970), Johann Nikuradse (18941979), and others, built on that theory in both hydraulic and aerodynamic applica- tions. (During World War II, both sides benefited from the theory as Prandtl remained in Germany while his best student, the Hungarian born Theodore von Krmn, worked in America.) The mid twentieth century could be considered a golden age of fluid mechanics applications. Existing theories were adequate for the tasks at hand, and fluid properties and parameters were well defined. These sup- ported a huge expansion of the aeronautical, chemical, industrial, and water resources sectors; each of which pushed fluid mechanics in new directions. Fluid mechanics research and work in the late twentieth century were domi- nated by the development of the digital computer in America. The ability to solve large complex problems, such as global climate modeling or to opti- mize the design of a turbine blade, has provided a benefit to our society that the eighteenth-century developers of fluid mechanics could never have imagined (Fig. 114). The principles presented in the following pages have been applied to flows ranging from a moment at the microscopic scale to 50 years of simulation for an entire river basin. It is truly mind-boggling. Where will fluid mechanics go in the twenty-first century? Frankly, even a limited extrapolation beyond the present would be sheer folly. However, if history tells us anything, it is that engineers will be applying what they know to benefit society, researching what they dont know, and having a great time in the process. 14 I CLASSIFICATION OF FLUID FLOWS Earlier we defined fluid mechanics as the science that deals with the behav- ior of fluids at rest or in motion, and the interaction of fluids with solids or other fluids at the boundaries. There is a wide variety of fluid flow problems encountered in practice, and it is usually convenient to classify them on the basis of some common characteristics to make it feasible to study them in groups. There are many ways to classify fluid flow problems, and here we present some general categories. Viscous versus Inviscid Regions of Flow When two fluid layers move relative to each other, a friction force develops between them and the slower layer tries to slow down the faster layer. This internal resistance to flow is quantified by the fluid property viscosity, which is a measure of internal stickiness of the fluid. Viscosity is caused by cohesive forces between the molecules in liquids and by molecular colli- sions in gases. There is no fluid with zero viscosity, and thus all fluid flows involve viscous effects to some degree. Flows in which the frictional effects are significant are called viscous flows. However, in many flows of practical interest, there are regions (typically regions not close to solid surfaces) where viscous forces are negligibly small compared to inertial or pressure forces. Neglecting the viscous terms in such inviscid flow regions greatly simplifies the analysis without much loss in accuracy. The development of viscous and inviscid regions of flow as a result of inserting a flat plate parallel into a fluid stream of uniform velocity is shown in Fig. 115. The fluid sticks to the plate on both sides because of 9 CHAPTER 1 FIGURE 114 The Oklahoma Wind Power Center near Woodward consists of 68 turbines, 1.5 MW each. Courtesy Steve Stadler, Oklahoma Wind Power Initiative. Used by permission. Inviscid flow region Viscous flow region Inviscid flow region FIGURE 115 The flow of an originally uniform fluid stream over a flat plate, and the regions of viscous flow (next to the plate on both sides) and inviscid flow (away from the plate). Fundamentals of Boundary Layers, National Committee from Fluid Mechanics Films, Education Development Center. cen72367_ch01.qxd 11/16/04 11:33 AM Page 9
35. 35. the no-slip condition, and the thin boundary layer in which the viscous effects are significant near the plate surface is the viscous flow region. The region of flow on both sides away from the plate and unaffected by the presence of the plate is the inviscid flow region. Internal versus External Flow A fluid flow is classified as being internal or external, depending on whether the fluid is forced to flow in a confined channel or over a surface. The flow of an unbounded fluid over a surface such as a plate, a wire, or a pipe is external flow. The flow in a pipe or duct is internal flow if the fluid is completely bounded by solid surfaces. Water flow in a pipe, for example, is internal flow, and airflow over a ball or over an exposed pipe during a windy day is external flow (Fig. 116). The flow of liquids in a duct is called open-channel flow if the duct is only partially filled with the liquid and there is a free surface. The flows of water in rivers and irrigation ditches are examples of such flows. Internal flows are dominated by the influence of viscosity throughout the flow field. In external flows the viscous effects are limited to boundary lay- ers near solid surfaces and to wake regions downstream of bodies. Compressible versus Incompressible Flow A flow is classified as being compressible or incompressible, depending on the level of variation of density during flow. Incompressibility is an approx- imation, and a flow is said to be incompressible if the density remains nearly constant throughout. Therefore, the volume of every portion of fluid remains unchanged over the course of its motion when the flow (or the fluid) is incompressible. The densities of liquids are essentially constant, and thus the flow of liq- uids is typically incompressible. Therefore, liquids are usually referred to as incompressible substances. A pressure of 210 atm, for example, causes the density of liquid water at 1 atm to change by just 1 percent. Gases, on the other hand, are highly compressible. A pressure change of just 0.01 atm, for example, causes a change of 1 percent in the density of atmospheric air. When analyzing rockets, spacecraft, and other systems that involve high- speed gas flows, the flow speed is often expressed in terms of the dimen- sionless Mach number defined as where c is the speed of sound whose value is 346 m/s in air at room tem- perature at sea level. A flow is called sonic when Ma 1, subsonic when Ma 1, supersonic when Ma 1, and hypersonic when Ma 1. Liquid flows are incompressible to a high level of accuracy, but the level of variation in density in gas flows and the consequent level of approxima- tion made when modeling gas flows as incompressible depends on the Mach number. Gas flows can often be approximated as incompressible if the density changes are under about 5 percent, which is usually the case when Ma 0.3. Therefore, the compressibility effects of air can be neglected at speeds under about 100 m/s. Note that the flow of a gas is not necessarily a compressible flow. Ma V c Speed of flow Speed of sound 10 FLUID MECHANICS FIGURE 116 External flow over a tennis ball, and the turbulent wake region behind. Courtesy NASA and Cislunar Aerospace, Inc. cen72367_ch01.qxd 10/29/04 2:32 PM Page 10
36. 36. Small density changes of liquids corresponding to large pressure changes can still have important consequences. The irritating water hammer in a water pipe, for example, is caused by the vibrations of the pipe generated by the reflection of pressure waves following the sudden closing of the valves. Laminar versus Turbulent Flow Some flows are smooth and orderly while others are rather chaotic. The highly ordered fluid motion characterized by smooth layers of fluid is called laminar. The word laminar comes from the movement of adjacent fluid particles together in laminates. The flow of high-viscosity fluids such as oils at low velocities is typically laminar. The highly disordered fluid motion that typically occurs at high velocities and is characterized by veloc- ity fluctuations is called turbulent (Fig. 117). The flow of low-viscosity fluids such as air at high velocities is typically turbulent. The flow regime greatly influences the required power for pumping. A flow that alternates between being laminar and turbulent is called transitional. The experiments conducted by Osborn Reynolds in the 1880s resulted in the establishment of the dimensionless Reynolds number, Re, as the key parameter for the determination of the flow regime in pipes (Chap. 8). Natural (or Unforced) versus Forced Flow A fluid flow is said to be natural or forced, depending on how the fluid motion is initiated. In forced flow, a fluid is forced to flow over a surface or in a pipe by external means such as a pump or a fan. In natural flows, any fluid motion is due to natural means such as the buoyancy effect, which manifests itself as the rise of the warmer (and thus lighter) fluid and the fall of cooler (and thus denser) fluid (Fig. 118). In solar hot-water systems, for example, the thermosiphoning effect is commonly used to replace pumps by placing the water tank sufficiently above the solar collectors. Steady versus Unsteady Flow The terms steady and uniform are used frequently in engineering, and thus it is important to have a clear understanding of their meanings. The term steady implies no change at a point with time. The opposite of steady is unsteady. The term uniform implies no change with location over a speci- fied region. These meanings are consistent with their everyday use (steady girlfriend, uniform distribution, etc.). The terms unsteady and transient are often used interchangeably, but these terms are not synonyms. In fluid mechanics, unsteady is the most gen- eral term that applies to any flow that is not steady, but transient is typi- cally used for developing flows. When a rocket engine is fired up, for exam- ple, there are transient effects (the pressure builds up inside the rocket engine, the flow accelerates, etc.) until the engine settles down and operates steadily. The term periodic refers to the kind of unsteady flow in which the flow oscillates about a steady mean. Many devices such as turbines, compressors, boilers, condensers, and heat exchangers operate for long periods of time under the same conditions, and they are classified as steady-flow devices. (Note that the flow field near the rotating blades of a turbomachine is of course unsteady, but we consider the overall flow field rather than the details at some localities when we classify 11 CHAPTER 1 Laminar Transitional Turbulent FIGURE 117 Laminar, transitional, and turbulent flows. Courtesy ONERA, photograph by Werl. FIGURE 118 In this schlieren image of a girl in a swimming suit, the rise of lighter, warmer air adjacent to her body indicates that humans and warm- blooded animals are surrounded by thermal plumes of rising warm air. G. S. Settles, Gas Dynamics Lab, Penn State University. Used by permission. cen72367_ch01.qxd 10/29/04 2:32 PM Page 11
37. 37. devices.) During steady flow, the fluid properties can change from point to point within a device, but at any fixed point they remain constant. There- fore, the volume, the mass, and the total energy content of a steady-flow device or flow section remain constant in steady operation. Steady-flow conditions can be closely approximated by devices that are intended for continuous operation such as turbines, pumps, boilers, con- densers, and heat exchangers of power plants or refrigeration systems. Some cyclic devices, such as reciprocating engines or compressors, do not satisfy the steady-flow conditions since the flow at the inlets and the exits is pulsat- ing and not steady. However, the fluid properties vary with time in a peri- odic manner, and the flow through these devices can still be analyzed as a steady-flow process by using time-averaged values for the properties. Some fascinating visuali