Fluid Mechanics: Fundamentals and Applications PDF

 FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS Third Edition i-xxiv_cengel_fm.indd i 12/20/12 10:30 AM This page intentionally left blank ...

 FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS Third Edition i-xxiv_cengel_fm.indd i 12/20/12 10:30 AM This page intentionally left blank  FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS YUNUS A. ÇENGEL THIRD EDITION Department of Mechanical Engineering University of Nevada, Reno JOHN M. CIMBALA Department of Mechanical and Nuclear Engineering The Pennsylvania State University TM i-xxiv_cengel_fm.indd iii 12/20/12 10:30 AM  TM FLUID MECHANICS: FUNDAMENTALS AND APPLICATIONS, THIRD EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Previous editions © 2006 and 2010. 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 1 0 9 8 7 6 5 4 3 ISBN 978-0-07-338032-2 MHID 0-07-338032-6 Senior Vice President, Products & Markets: Kurt L. Strand Vice President, General Manager: Marty Lange Vice President, Content Production & Technology Services: Kimberly Meriwether David Managing Director: Michael Lange Executive Editor: Bill Stenquist Marketing Manager: Curt Reynolds Development Editor: Lorraine Buczek Director, Content Production: Terri Schiesl Project Manager: Melissa M. Leick Buyer: Susan K. Culbertson Media Project Manager: Prashanthi Nadipalli Cover Image: Purestock/SuperStock. Cover Designer: Studio Montage, St. Louis, MO Typeface: 10.5/12 Times Roman Compositor: RPK Editorial Services Printer: R. R. Donnelly—Willard All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. Library of Congress Cataloging-in-Publication Data on File The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill, and McGraw-Hill does not guarantee the accuracy of the information presented at these sites. www.mhhe.com i-xxiv_cengel_fm.indd iv 12/20/12 10:30 AM  Dedication To all students, with the hope of stimulating their desire to explore our marvelous world, of which fluid mechanics is a small but fascinating part. And to our wives Zehra and Suzy for their unending support. i-xxiv_cengel_fm.indd v 12/20/12 10:30 AM  About the Authors Yunus A. Çengel is 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, 7th edition (2011), published by McGraw-Hill. He is also the co-author of the textbook Heat and Mass Transfer: Fundamentals & Applications, 4th Edition (2011), and the coauthor of the textbook Fundamentals of Thermal-Fluid Sciences, 4th edition (2012), 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 Ameri- can Society for Engineering Education (ASEE). John M. Cimbala is Professor of Mechanical Engineering at The Pennsyl- vania State University, University Park. He received his B.S. in Aerospace Engi- neering 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 mechan- ics and heat transfer, turbulence, turbulence modeling, turbomachinery, indoor air quality, and air pollution control. Professor Cimbala completed sabbatical leaves at NASA Langley Research Center (1993-94), where he advanced his knowledge of computational fluid dynamics (CFD), and at Weir American Hydo (2010-11), where he performed CFD analyses to assist in the design of hydroturbines. Dr. Cimbala is the coauthor of three other textbooks: Indoor Air Quality Engi- neering: Environmental Health and Control of Indoor Pollutants (2003), pub- lished by Marcel-Dekker, Inc.; Essentials of Fluid Mechanics: Fundamentals and Applications (2008); and Fundamentals of Thermal-Fluid Sciences, 4th edition (2012), both published by McGraw-Hill. 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). i-xxiv_cengel_fm.indd vi 12/20/12 10:30 AM  Brief Contents chapter one INTRODUCTION AND BASIC CONCEPTS 1 chapter two PROPERTIES OF FLUIDS 37 chapter three PRESSURE AND FLUID STATICS 75 chapter four FLUID KINEMATICS 133 chapter five BERNOULLI AND ENERGY EQUATIONS 185 chapter six MOMENTUM ANALYSIS OF FLOW SYSTEMS 243 chapter seven DIMENSIONAL ANALYSIS AND MODELING 291 chapter eight INTERNAL FLOW 347 chapter nine DIFFERENTIAL ANALYSIS OF FLUID FLOW 437 chapter ten APPROXIMATE SOLUTIONS OF THE NAVIER–STOKES EQUATION 515 chapter eleven EXTERNAL FLOW: DRAG AND LIFT 607 chapter twelve COMPRESSIBLE FLOW 659 chapter thirteen OPEN-CHANNEL FLOW 725 chapter fourteen TURBOMACHINERY 787 chapter fifteen INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS 879 i-xxiv_cengel_fm.indd vii 12/20/12 10:30 AM  Contents Preface xv chapter two PROPERTIES OF FLUIDS 37 chapter one INTRODUCTION AND BASIC CONCEPTS 1 2–1 Introduction 38 Continuum 38 1–1 Introduction 2 2–2 Density and Specific Gravity 39 What Is a Fluid? 2 Density of Ideal Gases 40 Application Areas of Fluid Mechanics 4 2–3 Vapor Pressure and Cavitation 41 1–2 A Brief History of Fluid Mechanics 6 2–4 Energy and Specific Heats 43 1–3 The No-Slip Condition 8 2–5 Compressibility and Speed of Sound 44 1–4 Classification of Fluid Flows 9 Coefficient of Compressibility 44 Viscous versus Inviscid Regions of Flow 10 Coefficient of Volume Expansion 46 Internal versus External Flow 10 Speed of Sound and Mach Number 48 Compressible versus Incompressible Flow 10 Laminar versus Turbulent Flow 11 2–6 Viscosity 50 Natural (or Unforced) versus Forced Flow 11 2–7 Surface Tension and Capillary Effect 55 Steady versus Unsteady Flow 12 Capillary Effect 58 One-, Two-, and Three-Dimensional Flows 13 Summary 61 1–5 System and Control Volume 14 Application Spotlight: Cavitation 62 1–6 Importance of Dimensions and Units 15 References and Suggested Reading 63 Some SI and English Units 17 Problems 63 Dimensional Homogeneity 19 Unity Conversion Ratios 20 1–7 Modeling in Engineering 21 1–8 Problem-Solving Technique 23 chapter three Step 1: Problem Statement 24 PRESSURE AND FLUID STATICS 75 Step 2: Schematic 24 Step 3: Assumptions and Approximations 24 Step 4: Physical Laws 24 3–1 Pressure 76 Step 5: Properties 24 Pressure at a Point 77 Step 6: Calculations 24 Variation of Pressure with Depth 78 Step 7: Reasoning, Verification, and Discussion 25 3–2 Pressure Measurement Devices 81 1–9 Engineering Software Packages 25 The Barometer 81 Engineering Equation Solver (EES) 26 The Manometer 84 CFD Software 27 Other Pressure Measurement Devices 88 1–10 Accuracy, Precision, and Significant Digits 28 3–3 Introduction to Fluid Statics 89 Summary 31 3–4 Hydrostatic Forces on Submerged References and Suggested Reading 31 Plane Surfaces 89 Application Spotlight: What Nuclear Blasts Special Case: Submerged Rectangular Plate 92 and Raindrops Have in Common 32 3–5 Hydrostatic Forces on Submerged Problems 33 Curved Surfaces 95 i-xxiv_cengel_fm.indd viii 12/20/12 10:30 AM  ix CONTENTS 3–6 Buoyancy and Stability 98 The Linear Momentum Equation 186 Conservation of Energy 186 Stability of Immersed and Floating Bodies 101 3–7 Fluids in Rigid-Body Motion 103 5–2 Conservation of Mass 187 Mass and Volume Flow Rates 187 Special Case 1: Fluids at Rest 105 Conservation of Mass Principle 189 Special Case 2: Free Fall of a Fluid Body 105 Moving or Deforming Control Volumes 191 Acceleration on a Straight Path 106 Mass Balance for Steady-Flow Processes 191 Rotation in a Cylindrical Container 107 Special Case: Incompressible Flow 192 Summary 111 References and Suggested Reading 112 5–3 Mechanical Energy and Efficiency 194 Problems 112 5–4 The Bernoulli Equation 199 Acceleration of a Fluid Particle 199 chapter four Derivation of the Bernoulli Equation 200 Force Balance across Streamlines 202 FLUID KINEMATICS 133 Unsteady, Compressible Flow 202 Static, Dynamic, and Stagnation Pressures 202 Limitations on the Use of the Bernoulli 4–1 Lagrangian and Eulerian Descriptions 134 Equation 204 Acceleration Field 136 Hydraulic Grade Line (HGL) Material Derivative 139 and Energy Grade Line (EGL) 205 4–2 Flow Patterns and Flow Visualization 141 Applications of the Bernoulli Equation 207 Streamlines and Streamtubes 141 5–5 General Energy Equation 214 Pathlines 142 Energy Transfer by Heat, Q 215 Streaklines 144 Energy Transfer by Work, W 215 Timelines 146 Refractive Flow Visualization Techniques 147 5–6 Energy Analysis of Steady Flows 219 Surface Flow Visualization Techniques 148 Special Case: Incompressible Flow with No 4–3 Plots of Fluid Flow Data 148 Mechanical Work Devices and Negligible Profile Plots 149 Friction 221 Vector Plots 149 Kinetic Energy Correction Factor, a 221 Contour Plots 150 Summary 228 4–4 Other Kinematic Descriptions 151 References and Suggested Reading 229 Problems 230 Types of Motion or Deformation of Fluid Elements 151 4–5 Vorticity and Rotationality 156 Comparison of Two Circular Flows 159 4–6 The Reynolds Transport Theorem 160 chapter six Alternate Derivation of the Reynolds Transport MOMENTUM ANALYSIS OF FLOW Theorem 165 SYSTEMS 243 Relationship between Material Derivative and RTT 167 Summary 168 6–1 Newton’s Laws 244 Application Spotlight: Fluidic Actuators 169 6–2 Choosing a Control Volume 245 References and Suggested Reading 170 Problems 170 6–3 Forces Acting on a Control Volume 246 6–4 The Linear Momentum Equation 249 chapter five Special Cases 251 Momentum-Flux Correction Factor, b 251 BERNOULLI AND ENERGY EQUATIONS 185 Steady Flow 253 Flow with No External Forces 254 5–1 Introduction 186 6–5 Review of Rotational Motion and Angular Conservation of Mass 186 Momentum 263 i-xxiv_cengel_fm.indd ix 12/20/12 10:30 AM  x FLUID MECHANICS 6–6 The Angular Momentum Equation 265 8–4 Laminar Flow in Pipes 353 Special Cases 267 Pressure Drop and Head Loss 355 Flow with No External Moments 268 Effect of Gravity on Velocity and Flow Rate Radial-Flow Devices 269 in Laminar Flow 357 Laminar Flow in Noncircular Pipes 358 Application Spotlight: Manta Ray Swimming 273 8–5 Turbulent Flow in Pipes 361 Summary 275 Turbulent Shear Stress 363 References and Suggested Reading 275 Turbulent Velocity Profile 364 Problems 276 The Moody Chart and the Colebrook Equation 367 Types of Fluid Flow Problems 369 8–6 Minor Losses 374 chapter seven 8–7 Piping Networks and Pump Selection 381 Series and Parallel Pipes 381 DIMENSIONAL ANALYSIS Piping Systems with Pumps and Turbines 383 AND MODELING 291 8–8 Flow Rate and Velocity Measurement 391 Pitot and Pitot-Static Probes 391 7–1 Dimensions and Units 292 Obstruction Flowmeters: Orifice, Venturi, and Nozzle Meters 392 7–2 Dimensional Homogeneity 293 Positive Displacement Flowmeters 396 Nondimensionalization of Equations 294 Turbine Flowmeters 397 Variable-Area Flowmeters (Rotameters) 398 7–3 Dimensional Analysis and Similarity 299 Ultrasonic Flowmeters 399 7–4 The Method of Repeating Variables Electromagnetic Flowmeters 401 and The Buckingham Pi Theorem 303 Vortex Flowmeters 402 Thermal (Hot-Wire and Hot-Film) Anemometers 402 Historical Spotlight: Persons Honored Laser Doppler Velocimetry 404 by Nondimensional Parameters 311 Particle Image Velocimetry 406 Introduction to Biofluid Mechanics 408 7–5 Experimental Testing, Modeling, and Incomplete Similarity 319 Application Spotlight: PIV Applied to Cardiac Setup of an Experiment and Correlation of Flow 416 Experimental Data 319 Summary 417 Incomplete Similarity 320 References and Suggested Reading 418 Wind Tunnel Testing 320 Problems 419 Flows with Free Surfaces 323 Application Spotlight: How a Fly Flies 326 Summary 327 chapter nine References and Suggested Reading 327 Problems 327 DIFFERENTIAL ANALYSIS OF FLUID FLOW 437 9–1 Introduction 438 9–2 Conservation of Mass—The Continuity chapter eight Equation 438 Derivation Using the Divergence Theorem 439 INTERNAL FLOW 347 Derivation Using an Infinitesimal Control Volume 440 Alternative Form of the Continuity Equation 443 8–1 Introduction 348 Continuity Equation in Cylindrical Coordinates 444 Special Cases of the Continuity Equation 444 8–2 Laminar and Turbulent Flows 349 Reynolds Number 350 9–3 The Stream Function 450 The Stream Function in Cartesian Coordinates 450 8–3 The Entrance Region 351 The Stream Function in Cylindrical Coordinates 457 Entry Lengths 352 The Compressible Stream Function 458 i-xxiv_cengel_fm.indd x 12/20/12 10:30 AM  xi CONTENTS 9–4 The Differential Linear Momentum Equation— 10–6 The Boundary Layer Approximation 554 Cauchy’s Equation 459 The Boundary Layer Equations 559 Derivation Using the Divergence Theorem 459 The Boundary Layer Procedure 564 Derivation Using an Infinitesimal Control Volume 460 Displacement Thickness 568 Alternative Form of Cauchy’s Equation 463 Momentum Thickness 571 Derivation Using Newton’s Second Law 463 Turbulent Flat Plate Boundary Layer 572 Boundary Layers with Pressure Gradients 578 9–5 The Navier–Stokes Equation 464 The Momentum Integral Technique for Boundary Layers 583 Introduction 464 Summary 591 Newtonian versus Non-Newtonian Fluids 465 References and Suggested Reading 592 Derivation of the Navier–Stokes Equation for Incompressible, Isothermal Flow 466 Application Spotlight: Droplet Formation 593 Continuity and Navier–Stokes Equations in Cartesian Problems 594 Coordinates 468 Continuity and Navier–Stokes Equations in Cylindrical Coordinates 469 chapter eleven 9–6 Differential Analysis of Fluid Flow Problems 470 EXTERNAL FLOW: DRAG AND LIFT 607 Calculation of the Pressure Field for a Known Velocity Field 470 11–1 Introduction 608 Exact Solutions of the Continuity and Navier–Stokes 11–2 Drag and Lift 610 Equations 475 Differential Analysis of Biofluid Mechanics Flows 493 11–3 Friction and Pressure Drag 614 Application Spotlight: The No-Slip Boundary Reducing Drag by Streamlining 615 Flow Separation 616 Condition 498 Summary 499 11–4 Drag Coefficients of Common Geometries 617 References and Suggested Reading 499 Biological Systems and Drag 618 Problems 499 Drag Coefficients of Vehicles 621 Superposition 623 11–5 Parallel Flow Over Flat Plates 625 chapter ten Friction Coefficient 627 APPROXIMATE SOLUTIONS OF THE NAVIER– 11–6 Flow Over Cylinders And Spheres 629 STOKES EQUATION 515 Effect of Surface Roughness 632 11–7 Lift 634 10–1 Introduction 516 Finite-Span Wings and Induced Drag 638 10–2 Nondimensionalized Equations of Motion 517 Lift Generated by Spinning 639 10–3 The Creeping Flow Approximation 520 Summary 643 References and Suggested Reading 644 Drag on a Sphere in Creeping Flow 523 Application Spotlight: Drag Reduction 645 10–4 Approximation for Inviscid Regions of Flow 525 Problems 646 Derivation of the Bernoulli Equation in Inviscid Regions of Flow 526 10–5 The Irrotational Flow Approximation 529 chapter twelve Continuity Equation 529 Momentum Equation 531 COMPRESSIBLE FLOW 659 Derivation of the Bernoulli Equation in Irrotational Regions of Flow 531 12–1 Stagnation Properties 660 Two-Dimensional Irrotational Regions of Flow 534 Superposition in Irrotational Regions of Flow 538 12–2 One-Dimensional Isentropic Flow 663 Elementary Planar Irrotational Flows 538 Variation of Fluid Velocity with Flow Area 665 Irrotational Flows Formed by Superposition 545 Property Relations for Isentropic Flow of Ideal Gases 667 i-xxiv_cengel_fm.indd xi 12/20/12 10:30 AM  xii FLUID MECHANICS 12–3 Isentropic Flow Through Nozzles 669 13–9 Flow Control and Measurement 761 Converging Nozzles 670 Underflow Gates 762 Converging–Diverging Nozzles 674 Overflow Gates 764 12–4 Shock Waves and Expansion Waves 678 Application Spotlight: Bridge Scour 771 Normal Shocks 678 Summary 772 Oblique Shocks 684 References and Suggested Reading 773 Prandtl–Meyer Expansion Waves 688 Problems 773 12–5 Duct Flow With Heat Transfer and Negligible Friction (Rayleigh Flow) 693 chapter fourteen Property Relations for Rayleigh Flow 699 Choked Rayleigh Flow 700 TURBOMACHINERY 787 12–6 Adiabatic Duct Flow With Friction 14–1 Classifications and Terminology 788 (Fanno Flow) 702 Property Relations for Fanno Flow 705 14–2 Pumps 790 Choked Fanno Flow 708 Pump Performance Curves and Matching a Pump to a Piping System 791 Application Spotlight: Shock-Wave/ Pump Cavitation and Net Positive Suction Head 797 Boundary-Layer Interactions 712 Pumps in Series and Parallel 800 Summary 713 Positive-Displacement Pumps 803 References and Suggested Reading 714 Dynamic Pumps 806 Problems 714 Centrifugal Pumps 806 Axial Pumps 816 14–3 Pump Scaling Laws 824 Dimensional Analysis 824 chapter thirteen Pump Specific Speed 827 Affinity Laws 829 OPEN-CHANNEL FLOW 725 14–4 Turbines 833 Positive-Displacement Turbines 834 13–1 Classification of Open-Channel Flows 726 Dynamic Turbines 834 Uniform and Varied Flows 726 Impulse Turbines 835 Laminar and Turbulent Flows in Channels 727 Reaction Turbines 837 Gas and Steam Turbines 847 13–2 Froude Number and Wave Speed 729 Wind Turbines 847 Speed of Surface Waves 731 14–5 Turbine Scaling Laws 855 13–3 Specific Energy 733 Dimensionless Turbine Parameters 855 13–4 Conservation of Mass and Energy Turbine Specific Speed 857 Equations 736 Application Spotlight: Rotary Fuel Atomizers 861 13–5 Uniform Flow in Channels 737 Summary 862 Critical Uniform Flow 739 References and Suggested Reading 862 Superposition Method for Nonuniform Perimeters 740 Problems 863 13–6 Best Hydraulic Cross Sections 743 Rectangular Channels 745 Trapezoidal Channels 745 chapter fifteen 13–7 Gradually Varied Flow 747 INTRODUCTION TO COMPUTATIONAL FLUID Liquid Surface Profiles in Open Channels, y(x) 749 DYNAMICS 879 Some Representative Surface Profiles 752 Numerical Solution of Surface Profile 754 15–1 Introduction and Fundamentals 880 13–8 Rapidly Varied Flow and The Hydraulic Motivation 880 Jump 757 Equations of Motion 880 i-xxiv_cengel_fm.indd xii 12/20/12 10:30 AM  xiii CONTENTS Solution Procedure 881 TABLE A–10 Properties of Gases at 1 atm Additional Equations of Motion 883 Pressure 949 Grid Generation and Grid Independence 883 Boundary Conditions 888 TABLE A–11 Properties of the Atmosphere at High Practice Makes Perfect 893 Altitude 951 15–2 Laminar CFD Calculations 893 FIGURE A–12 The Moody Chart for the Friction Factor Pipe Flow Entrance Region at Re 5 500 893 for Fully Developed Flow in Circular Flow around a Circular Cylinder at Re 5 150 897 Pipes 952 15–3 Turbulent CFD Calculations 902 TABLE A–13 One-Dimensional Isentropic Flow around a Circular Cylinder at Re 5 10,000 905 Compressible Flow Functions for an Flow around a Circular Cylinder at Re 5 107 907 Ideal Gas with k 5 1.4 953 Design of the Stator for a Vane-Axial Flow Fan 907 TABLE A–14 One-Dimensional Normal Shock 15–4 CFD With Heat Transfer 915 Functions for an Ideal Gas with Temperature Rise through a Cross-Flow Heat Exchanger 915 k 5 1.4 954 Cooling of an Array of Integrated Circuit Chips 917 TABLE A–15 Rayleigh Flow Functions for an Ideal 15–5 Compressible Flow CFD Calculations 922 Gas with k 5 1.4 955 Compressible Flow through a Converging–Diverging Nozzle 923 TABLE A–16 Fanno Flow Functions for an Ideal Gas Oblique Shocks over a Wedge 927 with k 5 1.4 956 15–6 Open-Channel Flow CFD Calculations 928 Flow over a Bump on the Bottom of a Channel 929 Flow through a Sluice Gate (Hydraulic Jump) 930 appendix 2 Application Spotlight: A Virtual Stomach 931 PROPERTY TABLES AND CHARTS Summary 932 (ENGLISH UNITS) 957 References and Suggested Reading 932 Problems 933 TABLE A–1E Molar Mass, Gas Constant, and Ideal-Gas Specific Heats of Some Substances 958 appendix 1 TABLE A–2E Boiling and Freezing Point PROPERTY TABLES AND CHARTS Properties 959 (SI UNITS) 939 TABLE A–3E Properties of Saturated Water 960 TABLE A–4E Properties of Saturated TABLE A–1 Molar Mass, Gas Constant, and Refrigerant-134a 961 Ideal-Gas Specfic Heats of Some TABLE A–5E Properties of Saturated Ammonia 962 Substances 940 TABLE A–6E Properties of Saturated Propane 963 TABLE A–2 Boiling and Freezing Point Properties 941 TABLE A–7E Properties of Liquids 964 TABLE A–3 Properties of Saturated Water 942 TABLE A–8E Properties of Liquid Metals 965 TABLE A–4 Properties of Saturated TABLE A–9E Properties of Air at 1 atm Refrigerant-134a 943 Pressure 966 TABLE A–5 Properties of Saturated Ammonia 944 TABLE A–10E Properties of Gases at 1 atm Pressure 967 TABLE A–6 Properties of Saturated Propane 945 TABLE A–11E Properties of the Atmosphere at High TABLE A–7 Properties of Liquids 946 Altitude 969 TABLE A–8 Properties of Liquid Metals 947 TABLE A–9 Properties of Air at 1 atm Glossary 971 Pressure 948 Index 983 i-xxiv_cengel_fm.indd xiii 12/20/12 10:30 AM This page intentionally left blank  Preface BACKGROUND Fluid mechanics is an exciting and fascinating subject with unlimited practi- cal applications ranging from microscopic biological systems to automobiles, airplanes, and spacecraft propulsion. Fluid mechanics has also historically been one of the most challenging subjects for undergraduate students because proper analysis of fluid mechanics problems requires not only knowledge of the concepts but also physical intuition and experience. Our hope is that this book, through its careful explanations of concepts and its use of numer- ous practical examples, sketches, figures, and photographs, bridges the gap between knowledge and the 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 any introductory textbook. Our book is distinguished from other introductory books because we present the subject in a progressive order from simple to more difficult, building each chapter upon foundations laid down in earlier chapters. We provide more dia- grams and photographs that other books because fluid mechanics, is by its nature, a highly visual subject. Only by illustrating the concepts discussed, can students fully appreciate the mathematical significance of the material. OBJECTIVES This book has been written for the first fluid mechanics course for under- graduate engineering students. There is sufficient material for a two-course sequence, if desired. We assume that readers will have an adequate back- ground in calculus, physics, engineering mechanics, and thermodynamics. The objectives of this text are To present the basic principles and equations of fluid mechanics. To show numerous and diverse real-world engineering examples to give the student the intuition necessary for correct application of fluid mechanics principles in engineering applications. To develop an intuitive understanding of fluid mechanics by emphasiz- ing the physics, and reinforcing that understanding through illustrative figures and photographs. The book contains enough material to allow considerable flexibility in teach- ing the course. Aeronautics and aerospace engineers might emphasize poten- tial flow, drag and lift, compressible flow, turbomachinery, and CFD, while mechanical or civil engineering instructors might choose to emphasize pipe flows and open-channel flows, respectively. NEW TO THE THIRD EDITION In this edition, the overall content and order of presentation has not changed significantly except for the following: the visual impact of all figures and photographs has been enhanced by a full color treatment. We also added new i-xxiv_cengel_fm.indd xv 12/20/12 10:30 AM  xvi FLUID MECHANICS photographs throughout the book, often replacing existing diagrams with pho- tographs in order to convey the practical real-life applications of the material. Several new Application Spotlights have been added to the end of selected chapters. These introduce students to industrial applications and exciting research projects being conducted by leaders in the field about material pre- sented in the chapter. We hope these motivate students to see the relevance and application of the materials they are studying. New sections on Biofluids have been added to Chapters 8 and 9, written by guest author Keefe Manning of The Pennsylvania State University, along with bio-related examples and homework problems in those chapters. New solved example problems were added to some chapters and several new end-of-chapter problems or modifications to existing problems were made to make them more versatile and practical. Most significant is the addi- tion of Fundamentals of Engineering (FE) exam-type problems to help students prepare to take their Professional Engineering exams. Finally, the end-of- chapter problems that require Computational Fluid Dynamics (CFD) have been moved to the text website (www.mhhe.com/cengel) where updates based on software or operating system changes can be better managed. PHILOSOPHY AND GOAL The Third Edition of Fluid Mechanics: Fundamentals and Applications has the same goals and philosophy as the other texts by lead author Yunus Çengel. Communicates directly with tomorrow’s engineers in a simple 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 a guide to solve homework problems The best way to learn is by practice. Special effort is made throughout the book to reinforce the material that was presented earlier (in each chapter as well as in material from previous chapters). Many of the illustrated example problems and end-of-chapter problems are comprehensive and encourage students to review and revisit concepts and intuitions gained previously. Throughout the book, we show examples generated by computational fluid dynamics (CFD). We also provide an introductory chapter on the subject. Our goal is not to teach the details about numerical algorithms associated with CFD—this is more properly presented in a separate course. Rather, our intent is 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 experimental results are used from wind tunnel tests (i.e., to reinforce understanding of the physics of fluid flows and to provide quality flow visual- izations that help explain fluid behavior). With dozens of CFD end-of-chapter problems posted on the website, instructors have ample opportunity to intro- duce the basics of CFD throughout the course. i-xxiv_cengel_fm.indd xvi 12/20/12 10:30 AM  xvii PREFACE CONTENT AND ORGANIZATION This book is organized into 15 chapters beginning with fundamental concepts of fluids, fluid properties, and fluid flows and ending with an introduction to computational fluid dynamics. Chapter 1 provides a basic introduction to fluids, classifications of fluid flow, control volume versus system formulations, dimensions, units, significant digits, and problem-solving techniques. Chapter 2 is devoted to fluid properties such as density, vapor pressure, specific heats, speed of sound, 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 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 variables—material 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 dif- ferences 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 discuss various experimental devices that are used to measure flow rate and velocity, and provide a brief introduction to biofluid mechanics. Chapter 9 deals with differential analysis of fluid flow and includes der- ivation and application of the continuity equation, the Cauchy equation, and the Navier-Stokes equation. We also introduce the stream function and describe its usefulness in analysis of fluid flows, and we provide a brief introduction to biofluids. Finally, we point out some of the unique aspects of differential analysis related to biofluid mechanics. Chapter 10 discusses several approximations of the Navier–Stokes equa- tion 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 distinction between friction and pressure drag, and providing drag i-xxiv_cengel_fm.indd xvii 12/20/12 10:30 AM  xviii FLUID MECHANICS coefficients 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. In this chapter, the concepts 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 surface waves and hydraulic jumps. 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 dyamics (CFD) and shows students how to use commercial CFD codes as tools to solve complex fluid mechanics problems. We emphasize the application of CFD rather than the algorithms used in CFD codes. Each chapter contains a wealth of end-of-chapter homework problems. Most of the problems that require calculation use the SI system of units, how- ever about 20 percent use English units. A comprehensive set of appendices is provided, giving the thermodynamic and fluid properties of several materials, in addition to air and water, along with some useful plots and tables. Many of the end-of-chapter problems require the use of material properties from the appendices to enhance the realism of the problems. LEARNING TOOLS 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 mastery 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 experi- ence for the students. EFFECTIVE USE OF ASSOCIATION An observant mind should have no difficulty understanding engineering sciences. After all, the principles of engineering sciences are based on our everyday experiences and experimental observations. Therefore, a physi- cal, 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. i-xxiv_cengel_fm.indd xviii 12/20/12 10:30 AM  xix PREFACE SELF-INSTRUCTING The material in the text is introduced at a level that an average student can follow 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 AND PHOTOGRAPHS Figures are important learning tools that help the students “get the picture,” and the text makes effective use of graphics. It contains more figures, photo- graphs, and illustrations 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. CONSISTENT COLOR SCHEME FOR FIGURES The figures have a consistent color scheme applied for all arrows. Blue: ( ) motion related, like velocity vectors Green: ( ) force and pressure related, and torque Black: ( ) distance related arrows and dimensions Red: ( ) energy related, like heat and work Purple: ( ) acceleration and gravity vectors, vorticity, and miscellaneous NUMEROUS WORKED-OUT EXAMPLES All chapters contain numerous worked-out examples that both clarify the material and illustrate the use of basic principles in a context that helps devel- ops the student’s intuition. An intuitive and systematic approach is used in the solution of all example problems. The solution methodology starts with a statement of the problem, and all objectives are identified. The assumptions and approximations are then stated together with their justifications. Any properties needed to solve the problem are listed separately. Numerical values are used together with numbers to emphasize that without units, numbers are meaningless. The significance of each example’s result is discussed following the solution. This methodical approach is also followed and provided in the solutions to the end-of-chapter problems, available to instructors. A WEALTH OF REALISTIC END-OF-CHAPTER PROBLEMS The end-of-chapter problems are grouped under specific topics to make problem selection easier for both instructors and students. Within each group of problems are Concept Questions, indicated by “C,” to check the students’ level of understanding of basic concepts. Problems under Funda- mentals of Engineering (FE) Exam Problems are designed to help students prepare for the Fundamentals of Engineering exam, as they prepare for their Professional Engineering license. 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 i-xxiv_cengel_fm.indd xix 12/20/12 10:30 AM  xx FLUID MECHANICS of material learned in previous 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 professional manner. Problems designated by an “E” are in English units, and SI users can ignore them. Problems with the icon are solved using EES, and complete solutions together with paramet- ric studies are included the text website. Problems with the icon are com- prehensive in nature and are intended to be solved with a computer, prefer- ably using the EES software. Several economics- and safety-related problems are incorporated 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 thermodynamic notation V̇ 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 pro- mote 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 equa- tion. This helps students develop a realistic view of the Bernoulli equation. i-xxiv_cengel_fm.indd xx 12/20/12 10:30 AM  xxi PREFACE 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 fea- ture of these special examples is that they are written by guest authors. The Application 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 red 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 their study of fluid mechanics. In addition, students can test their knowl- edge 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 properties of air and water at 20°C 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. SUPPLEMENTS These supplements are available to adopters of the book: Text Website Web support is provided for the book on the text specific website at www. mhhe.com/cengel. Visit this robust site for book and supplement information, errata, author information, and further resources for instructors and students. i-xxiv_cengel_fm.indd xxi 12/20/12 10:30 AM  xxii FLUID MECHANICS Engineering Equation Solver (EES) Developed by Sanford Klein and William Beckman from the University of Wisconsin–Madison, 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 plot- ting 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. ACKNOWLEDGMENTS The authors would like to acknowledge with appreciation the numerous and valuable comments, suggestions, constructive criticisms, and praise from the following evaluators and reviewers of the third edition: Bass Abushakra Jonathan Istok Milwaukee School of Engineering Oregon State University John G. Cherng Tim Lee University of Michigan—Dearborn McGill University Peter Fox Nagy Nosseir Arizona State University San Diego State University Sathya Gangadbaran Robert Spall Embry Riddle Aeronautical University Utah State University We also thank those who were acknowledged in the first and second editions of this book, but are too numerous to mention again here. Special thanks go to Gary S. Settles and his associates at Penn State (Lori Dodson- Dreibelbis, J. D. Miller, and Gabrielle Tremblay) for creating the excit- ing narrated video clips that are found on the book’s website. The authors also thank James Brasseur of Penn State for creating the precise glossary of fluid mechanics terms, Glenn Brown of Oklahoma State for provid- ing many items of historical interest throughout the text, guest authors David F. Hill (parts of Chapter 13) and Keefe Manning (sections on biofluids), Mehmet Kanoglu of University of Gaziantep for preparing FE Exam prob- lems and the solutions of EES problems, and Tahsin Engin of Sakarya Uni- versity for contributing several end-of-chapter problems. We also acknowledge the Korean translation team, who in the translation process, pointed out several errors and inconsistencies in the first and second editions that have now been corrected. The team includes Yun-ho Choi, Ajou University; Nae-Hyun Kim, University of Incheon; Woonjean Park, Korea University of Technology & Education; Wonnam Lee, Dankook University; Sang-Won Cha, Suwon University; Man Yeong Ha, Pusan National University; and Yeol Lee, Korea Aerospace University. Finally, special thanks must go to our families, especially our wives, Zehra Çengel 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. Çengel John M. Cimbala i-xxiv_cengel_fm.indd xxii 12/20/12 10:30 AM  Online Resources for Students and Instructors Online Resources available at www.mhhe.com/cengel Your home page for teaching and studying fluid mechanics, the Fluid Mechanics: Fundamentals and Applications text-specific website offers resources for both instructors and students. For the student, this website offer various resources, including: FE Exam Interactive Review Quizzes—chapter-based self-quizzes provide hints for solutions and correct solution methods, and help students prepare for the NCEES Fundamentals of Engineering Examination. Glossary of Key Terms in Fluid Mechanics—full text and chapter-based glossaries. Weblinks—helpful weblinks to relevant fluid mechanics sites. For the instructor, this password-protected website offers various resources, including: Electronic Solutions Manual—provides PDF files with detailed solutions to all text homework problems. Image Library—provide electronic files for text figures for easy integration into your course presentations, exams, and assignments. Sample Syllabi—make it easier for you to map out your course using this text for different course durations (one quarter, one semester, etc.) and for different disciplines (ME approach, Civil approach, etc.). Transition Guides—compare coverage to other popular introductory fluid mechanics books at the section level to aid transition to teaching from our text. Links to ANSYS Workbench®, FLUENT FLOWLAB®, and EES (Engineering Equa- tion Solver) download sites—the academic versions of these powerful soft- ware programs are available free to departments of educational institutions who adopt this text. CFD homework problems and solutions designed for use with various CFD packages. McGraw-Hill Connect® Engineering provides online presentation, assign- ment, and assessment solutions. It connects your students with the tools and resources they’ll need to achieve success. With Connect Engineering, you can deliver assignments, quizzes, and tests online. A robust set of questions and activities are presented and aligned with the textbook’s learning outcomes. As an instructor, you can edit existing questions and author entirely new prob- lems. Track individual student performance—by question, assignment, or in relation to the class overall—with detailed grade reports. Integrate grade reports easily with Learning Management Systems (LMS), such as WebCT and Blackboard—and much more. ConnectPlus Engineering provides stu- dents with all the advantages of Connect Engineering, plus 24/7 online access to an eBook. This media-rich version of the book is available through the McGraw-Hill Connect platform and allows seamless integration of text, media, and assessments. To learn more, visit www.mcgrawhillconnect.com. i-xxiv_cengel_fm.indd xxiii 12/20/12 10:30 AM This page intentionally left blank  CHAPTER INTRODUCTION AND BASIC CONCEPTS 1 n this introductory chapter, we present the basic concepts commonly I 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 exter- OBJECTIVES When you finish reading this chapter, you should be able to Understand the basic concepts nal flow, compressible versus incompressible flow, laminar versus turbulent of fluid mechanics flow, natural versus forced flow, and steady versus unsteady flow. We also discuss the no-slip condition at solid–fluid interfaces and present a brief his- Recognize the various types of fluid flow problems encountered tory of the development of fluid mechanics. in practice After presenting the concepts of system and control volume, we review Model engineering problems the unit systems that will be used. We then discuss how mathematical mod- and solve them in a systematic els for engineering problems are prepared and how to interpret the results manner obtained from the analysis of such models. This is followed by a presenta- Have a working knowledge tion of an intuitive systematic problem-solving technique that can be used as of accuracy, precision, and a model in solving engineering problems. Finally, we discuss accuracy, pre- significant digits, and recognize cision, and significant digits in engineering measurements and calculations. the importance of dimensional homogeneity in engineering calculations Schlieren image showing the thermal plume produced by Professor Cimbala as he welcomes you to the fascinating world of fluid mechanics. Michael J. Hargather and Brent A. Craven, Penn State Gas Dynamics Lab. Used by Permission. 1 001-036_cengel_ch01.indd 1 12/14/12 12:12 PM  2 INTRODUCTION AND BASIC CONCEPTS 1–1 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 statics) 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. 1–1). Fluid mechanics itself is also divided into several categories. The study of the motion of fluids that can be approximated as incompressible (such as liq- uids, especially water, and gases at low speeds) is usually referred to as hydro- dynamics. A subcategory of hydrodynamics is hydraulics, which deals with liquid 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. FIGURE 1–1 Fluid mechanics deals with liquids and gases in motion or at rest. What Is a Fluid? © D. Falconer/PhotoLink /Getty RF 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 substance’s abil- ity 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 Contact area, Shear stress fluid deforms continuously under the influence of a shear stress, no matter A t = F/A how small. In solids, stress is proportional to strain, but in fluids, stress is Force, F proportional to strain rate. When a constant shear force is applied, a solid a eventually stops deforming at some fixed strain angle, whereas a fluid never Deformed rubber stops deforming and approaches a constant rate of strain. Consider a rectangular rubber block tightly placed between two plates. As Shear the upper plate is pulled with a force F while the lower plate is held fixed, strain, a the rubber block deforms, as shown in Fig. 1–2. The angle of deformation a (called the shear strain or angular displacement) increases in proportion to FIGURE 1–2 the applied force F. Assuming there is no slip between the rubber and the Deformation of a rubber block placed plates, the upper surface of the rubber is displaced by an amount equal to between two parallel plates under the the displacement of the upper plate while the lower surface remains station- influence of a shear force. The shear ary. In equilibrium, the net force acting on the upper plate in the horizontal stress shown is that on the rubber—an equal but opposite shear stress acts on direction must be zero, and thus a force equal and opposite to F must be the upper plate. acting on the plate. This opposing force that develops at the plate–rubber interface due to friction is expressed as F 5 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 phenome- non 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 001-036_cengel_ch01.indd 2 12/20/12 3:29 PM  3 CHAPTER 1 would move with the plate continuously at the velocity of the plate no mat- Normal ter how small the force F. The fluid velocity would decrease with depth to surface because of friction between fluid layers, reaching zero at the lower plate. Force acting You will recall from statics that stress is defined as force per unit area Fn F on area dA and is determined by dividing the force by the area upon which it acts. The normal component of a force acting on a surface per unit area is called the Tangent normal stress, and the tangential component of a force acting on a surface Ft to surface dA per unit area is called shear stress (Fig. 1–3). In a fluid at rest, the normal stress is called pressure. A fluid at rest is at a state of zero shear stress. Fn When the walls are removed or a liquid container is tilted, a shear develops Normal stress: s 5 dA as the liquid moves to re-establish a horizontal free surface. Ft In a liquid, groups of molecules can move relative to each other, but the