Higher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION

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1 FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS SECOND EDITION Mc Grauu Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto

2 CONTENTS Preface xv ONE INTRODUCTION AND BASIC CONCEPTS 1-1 Introduction 2 What Is a Fluid? 2 Application Areas of Fluid Mechanics The No-Slip Condition A Brief History of Fluid Mechanics Classification of Fluid Flows 9 Viscous versus Inviscid Regions of Flow 10 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 12 One-, Two-, and Three-Dimensional Flows System and Control Volume Importance of Dimensions and Units Some SI and English Units 17 Dimensional Homogeneity 19 Unity Conversion Ratios Mathematical Modeling of Engineering Problems 21 Modeling in Engineering Problem-Solving Technique 23 Step 1: Problem Statement 24 Step 2: Schematic 24 Step 3: Assumptions and Approximations 24 Step 4: Physical Laws 24 Step 5: Properties 24 Step 6: Calculations 25 Step 7: Reasoning, Verification, and Discussion 1-9 Engineering Software Packages 25 Engineering Equation Solver (EES) 26 FlowLab Accuracy, Precision, and Significant Digits 28 Summary 31 References and Suggested Reading 31 Application Spotlight: What Nuclear Blasts and Raindrops Have in Common 32 Problems 33 TWO PROPERTIES OF FLUIDS Introduction 38 Continuum Density and Specific Gravity 39 Density of Ideal Gases Vapor Pressure and Cavitation Energy and Specific Heats Compressibility and Speed of Sound Coefficient of Compressibility 44 Coefficient of Volume Expansion 46 Speed of Sound and Mach Number Viscosity Surface Tension and Capillary Effect Capillary Effect 58 Summary 61 Application Spotlight: Cavitation 62 References and Suggested Reading 63 Problems 63 THREE PRESSURE AND FLUID STATICS Pressure 74 Pressure at a Point 75 Variation of Pressure with Depth Pressure Measurement Devices 79 The Barometer 79 The Manometer 82 Other Pressure Measurement Devices Introduction to Fluid Statics

3 Hydrostatic Forces on Submerged Plane Surfaces 88 Special Case: Submerged Rectangular Plate 90 Hydrostatic Forces on Submerged Curved Surfaces 93 Buoyancy and Stability 97 Stability of Immersed and Floating Bodies 100 Fluids in Rigid-Body Motion 102 Special Case 1: Fluids at Rest 104 Special Case 2: Free Fall of a Fluid Body 104 Acceleration on a Straight Path 105 Rotation in a Cylindrical Container 107 Summary 110 References and Suggested Reading Problems 111 FLUID KINEMATICS FOUR Lagrangian and Eulerian Descriptions 132 Acceleration Field 134 Material Derivative Flow Patterns and Flow Visualization 139 Streamlines and Streamtubes 139 Pathlines 140 Streaklines 142 Timelines 144 Refractive Flow Visualization Techniques 145 Surface Flow Visualization Techniques Plots of Fluid Flow Data 146 Profile Plots 147 Vector Plots 147 Contour Plots Other Kinematic Descriptions 149 Types of Motion or Deformation of Fluid Elements Vorticity and Rotationality 154 Comparison of Two Circular Flows The Reynolds Transport Theorem 158 Alternate Derivation of the Reynolds Transport Theorem 163 Relationship between Material Derivative and RTT 165 Summary 166 Application Spotlight: Fluidic Actuators 167 References and Suggested Reading 168 Problems 168 FIVE IX CONTENTS MASS, BERNOULLI, AND ENERGY EQUATIONS Introduction 184 Conservation of Mass 184 The Linear Momentum Equation 184 Conservation of Energy Conservation of Mass 185 Mass and Volume Flow Rates 185 Conservation of Mass Principle 187 Moving or Deforming Control Volumes 189 Mass Balance for Steady-Flow Processes 189 Special Case: Incompressible Flow Mechanical Energy and Efficiency The Bernoulli Equation 197 Acceleration of a Fluid Particle 197 Derivation of the Bernoulli Equation 198 Force Balance across Streamlines 200 Unsteady, Compressible Flow 200 Static, Dynamic, and Stagnation Pressures 200 Limitations on the Use of the Bernoulli Equation 202 Hydraulic Grade Line (HGL) and Energy Grade Line (EGL) 203 Applications of the Bernoulli Equation General Energy Equation Energy Transfer by Heat, Q Energy Transfer by Work, W ^^ Energy Analysis of Steady Flows 217 Special Case: Incompressible Flow with No Mechanical Work Devices and Negligible Friction 219 Kinetic Energy Correction Factor, a 219 Summary 226 References and Suggested Reading 227 Problems 228 SIX MOMENTUM ANALYSIS OF FLOW SYSTEMS Newton's Laws Choosing A Control Volume Forces Acting On A Control Volume 242

4 FLUID MECHANICS 6 4 The Linear Momentum Equation 245 Special Cases 247 Momentum-Flux Correction Factor, ß 247 Steady Flow 249 Flow with No External Forces Review of Rotational Motion and Angular Momentum The Angular Momentum Equation 261 Special Cases 263 Flow with No External Moments 264 Radial-Flow Devices 265 Summary 269 References and Suggested Reading 270 Problems 270 SEVEN DIMENSIONAL ANALYSIS AND MODELING Dimensions and Units Dimensional Homogeneity 285 Nondimensionalization of Equations Dimensional Analysis and Similarity The Method of Repeating Variables and The Buckingham Pi Theorem 295 Historical Spotlight: Persons Honored by Nondimensional Parameters Experimental Testing, Modeling, and Incomplete Similarity 311 Setup of an Experiment and Correlation of Experimental Data 311 Incomplete Similarity 312 Wind Tunnel Testing 312 Flows with Free Surfaces 315 Application Spotlight: How a Fly Flies 318 Summary 319 References and Suggested Reading 319 Problems 319 INTERNAL FLOW Introduction 338 EIGHT 8-2 Laminar and Turbulent Flows 339 Reynolds Number The Entrance Region 341 Entry Lengths Laminar Flow In Pipes 343 Pressure Drop and Head Loss 345 Effect of Gravity on Velocity and Flow Rate in Laminar Flow 347 Laminar Flow in Noncircular Pipes Turbulent Flow In Pipes 351 Turbulent Shear Stress 353 Turbulent Velocity Profile 354 The Moody Chart and the Colebrook Equation 357 Types of Fluid Flow Problems Minor Losses Piping Networks and Pump Selection 371 Series and Parallel Pipes 371 Piping Systems with Pumps and Turbines Flow Rate and Velocity Measurement 381 Pitot and Pitot-Static Probes 381 Obstruction Flowmeters: Orifice, Venturi, and Nozzle Meters 382 Positive Displacement Flowmeters 386 Turbine Flowmeters 387 Variable-Area Flowmeters (Rotameters) 388 Ultrasonic Flowmeters 389 Electromagnetic Flowmeters 391 Vortex Flowmeters 392 Thermal (Hot-Wire and Hot-Film) Anemometers 392 Laser Doppler Velocimetry 394 Particle Image Velocimetry 396 Application Spotlight: How Orifice Plate Flowmeters Work, or Do Not Work 399 Summary 400 References and Suggested Reading Problems 402 NINE 401 DIFFERENTIAL ANALYSIS OF FLUID FLOW 9-1 Introduction Conservation of Mass The Continuity Equation 420 Derivation Using the Divergence Theorem 421 Derivation Using an Infinitesimal Control Volume 422 Alternative Form of the Continuity Equation 425 Continuity Equation in Cylindrical Coordinates 426 Special Cases of the Continuity Equation The Stream Function 432 The Stream Function in Cartesian Coordinates 432 The Stream Function in Cylindrical Coordinates

5 CONTENTS The Compressible Stream Function The Differential Linear Momentum Equation Cauchy's Equation 441 Derivation Using the Divergence Theorem 441 Derivation Using an Infinitesimal Control Volume 442 Alternative Form of Cauchyis Equation 445 Derivation Using Newton's Second Law The Navier-Stokes Equation 446 Introduction 446 Newtonian versus Non-Newtonian Fluids 447 Derivation of the Navier-Stokes Equation for Incompressible, Isothermal Flow 448 Continuity and Navier-Stokes Equations in Cartesian Coordinates 450 Continuity and Navier-Stokes Equations in Cylindrical Coordinates Differential Analysis of Fluid Flow Problems 452 Calculation of the Pressure Field for a Known Velocity Field 452 Exact Solutions of the Continuity and Navier-Stokes Equations 457 Summary 475 References and Suggested Reading 476 Problems 476 TEN APPROXIMATE SOLUTIONS OF THE NAVIER-STOKES EQUATION Introduction Nondimensionalized Equations of Motion The Creeping Flow Approximation 496 Drag on a Sphere in Creeping Flow Approximation for Inviscid Regions of Flow 501 Derivation of the Bernoulli Equation in Inviscid Regions of Flow The Irrotational Flow Approximation 505 Continuity Equation 505 Momentum Equation 507 Derivation of the Bernoulli Equation in Irrotational Regions of Flow 507 Two-Dimensional Irrotational Regions of Flow 510 Superposition in Irrotational Regions of Flow 514 Elementary Planar Irrotational Flows 514 Irrotational Flows Formed by Superposition The Boundary Layer Approximation 530 The Boundary Layer Equations 535 The Boundary Layer Procedure 540 Displacement Thickness 544 Momentum Thickness 547 Turbulent Flat Plate Boundary Layer 548 Boundary Layers with Pressure Gradients 554 The Momentum Integral Technique for Boundary Layers 559 Summary 567 References and Suggested Reading 568 Application Spotlight: Droplet Formation 569 Problems 570 ELVEN EXTERNAL FLOW: DRAG AND LIFT Introduction Drag and Lift Friction and Pressure Drag 590 Reducing Drag by Streamlining 591 Flow Separation Drag Coefficients of Common Geometries 593 Biological Systems and Drag 597 Drag Coefficients of Vehicles 598 Superposition Parallel Flow Over Flat Plates 601 Friction Coefficient Flow Over Cylinders and Spheres 606 Effect of Surface Roughness Lift 610 Finite-Span Wings and Induced Drag 614 Lift Generated by Spinning 615 Summary 619 References and Suggested Reading 620 Application Spotlight: Drag Reduction 621 Problems 622 COMPRESSIBLE FLOW Stagnation Properties 636 TWELVE 12-2 One-Dimensional Isentropic Flow 639 Variation of Fluid Velocity with Flow Area 642

6 Property Relations for Isentropic Flow of Ideal Gases Isentropic Flow Through Nozzles 646 Converging Nozzles 646 Converging-Diverging Nozzles Shock Waves and Expansion Waves 655 Normal Shocks 655 Oblique Shocks 661 Prandtl-Meyer Expansion Waves Duct Flow With Heat Transfer and Negligible Friction (Rayleigh Flow) 669 Property Relations for Rayleigh Flow 675 Choked Rayleigh Flow Adiabatic Duct Flow With Friction (Fanno Flow) 678 Property Relations for Fanno Flow 681 Choked Fanno Flow 684 Application Spotlight: Shock-Wave/ Boundary-Layer Interactions 688 Summary 689 References and Suggested Reading 690 Problems 690 OPEN-CHANNEL FLOW 701 THIRTEEN 13-1 Classification of Open-Channel Flows 702 Uniform and Varied Flows 702 Laminar and Turbulent Flows in Channels Froude Number and Wave Speed 705 Speed of Surface Waves Specific Energy Conservation of Mass and Energy Equations Uniform Flow in Channels 713 Critical Uniform Flow 715 Superposition Method for Nonuniform Perimeters Best Hydraulic Cross Sections 719 Rectangular Channels 721 Trapezoidal Channels Gradually Varied Flow 723 Liquid Surface Profiles in Open Channels, y(x) 725 Some Representative Surface Profiles 728 Numerical Solution of Surface Profile Rapidly Varied Flow and The Hydraulic Jump Flow Control and Measurement 737 Underflow Gates 738 Overflow Gates 740 Summary 747 References and Suggested Reading 748 Problems 748 TURBOMACHINERY 761 FOURTEEN 14-1 Classifications and Terminology Pumps 764 Pump Performance Curves and Matching a Pump to a Piping System 765 Pump Cavitation and Net Positive Suction Head 771 Pumps in Series and Parallel 774 Positive-Displacement Pumps 777 Dynamic Pumps 780 Centrifugal Pumps 780 Axial Pumps Pump Scaling Laws 799 Dimensional Analysis 799 Pump Specific Speed 801 Affinity Laws Turbines 807 Positive-Displacement Turbines 808 Dynamic Turbines 808 Impulse Turbines 809 Reaction Turbines 811 Gas and Steam Turbines 822 Wind Turbines Turbine Scaling Laws 831 Dimensionless Turbine Parameters 831 Turbine Specific Speed 833 Application Spotlight: Rotary Fuel Atomizers 837 Summary 838 References and Suggested Reading 838 Problems 839 FIFTEEN INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS Introduction and Fundamentals 854 Motivation 854 Equations of Motion 854

7 CONTENTS Solution Procedure 855 Additional Equations of Motion 857 Grid Generation and Grid Independence 857 Boundary Conditions 863 Practice Makes Perfect Laminar CFD Calculations 867 Pipe Flow Entrance Region at Re = Flow around a Circular Cylinder at Re = Turbulent CFD Calculations 877 Flow around a Circular Cylinder at Re = 10, Flow around a Circular Cylinder at Re = Design of the Stator for a Vane-Axial Flow Fan CFD With Heat Transfer 890 Temperature Rise through a Cross-Flow Heat Exchanger 890 Cooling of an Array of Integrated Circuit Chips Compressible Flow CFD Calculations 897 Compressible Flow through a Converging-Diverging Nozzle 898 Oblique Shocks over a Wedge Open-Channel Flow CFD Calculations 903 Flow over a Bump on the Bottom of a Channel 904 Flow through a Sluice Gate (Hydraulic Jump) 905 Application Spotlight: A Virtual Stomach 906 Summary 907 References and Suggested Reading 907 Problems 908 APPENDIX 1 PROPERTY TABLES AND CHARTS (SI UNITS) 921 TABLE A-1 TABLE A-2 Molar Mass, Gas Constant, and Ideal- Gas Specfic Heats of Some Substances 922 Boiling and Freezing Point Properties 923 TABLE A-3 Properties of Saturated Water 924 TABLE A-4 Properties of Saturated Refrigerant-134a 925 TABLE A-5 Properties of Saturated Ammonia 926 TABLE A-6 Properties of Saturated Propane 927 TABLE A-7 Properties of Liquids 928 TABLE A-8 Properties of Liquid Metals 929 TABLE A-9 TABLE A-10 TABLE A-11 TABLE A-13 TABLE A-14 TABLE A-15 TABLE A-16 Properties of Air at 1 atm Pressure 930 APPENDIX 2 Properties of Gases at 1 atm Pressure 931 Properties of the Atmosphere at High Altitude 933 One-Dimensional Isentropic Compressible Flow Functions for an Ideal Gas with k= One-Dimensional Normal Shock Functions for an Ideal Gas with it = Rayleigh Flow Functions for an Ideal Gas with k= Fanno flow Functions for an Ideal Gas with к = PROPERTY TABLES AND CHARTS (ENGLISH UNITS) 939 TABLE A-1 E TABLE A-2E Molar Mass, Gas Constant, and Ideal-Gas Specific Heats of Some Substances 940 Boiling and Freezing Point Properties 941 TABLE A-3E Properties of Saturated Water 942 TABLE A-4E Properties of Saturated Refrigerant-134a 943 TABLE A-5E Properties of Saturated Ammonia 944 TABLE A-6E Properties of Saturated Propane 945 TABLE A-7E Properties of Liquids 946 TABLE A-8E Properties of Liquid Metals 947 TABLE A-9E Properties of Air at 1 Atm Pressure 948 TABLE A-10E Properties of Gases at 1 Atm Pressure 949 TABLE A-11E Properties of the Atmosphere at High Altitude 951 Glossary 953 Index 967

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