Fundamentals of Fluid Mechanics

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1 Sixth Edition. Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department of Mechanical Engineering Iowa State University Ames, Iowa, USA WADE W. HUEBSCH Department of Mechanical and Aerospace Engineering West Virginia University Morgantown, West Virginia, USA WILEY John Wiley & Sons, Inc.

2 c ontents i INTRODUCTION 1.1 Some Characteristics of Fluids 1.2 Dimensions, Dimensional Homogeneity, and Units Systems of Units 1.3 Analysis of Fluid Behavior 1.4 Measures of Fluid Mass and Weight Density Specific Weight Specific Gravity 1.5 Ideal Gas Law 1.6 Viscosity 1.7 Compressibility of Fluids Bulk Modulus Compression and Expansion of Gases Speed of Sound 1.8 Vapor Pressure 1.9 Surface Tension 1. A Brief Look Back in History 1.11 Review * 2 FLUID STATICS 2.1 Pressure at a Point 2.2 Basic for Pressure Field 2.3 'Pressure Variation in a Fluid at Rest Incompressible Fluid Compressible Fluid 2.4 Standard Atmosphere 2.5 Measurement of Pressure 2.6 Manometry Piezometer Tube U-Tube Manometer Inclined-Tube Manometer 2.7 Mechanical and Electronic Pressure Measuring Devices Hydrostatic Force on a Plane Surface Pressure Prism Hydrostatic Force on a Curved Surface Buoyancy, Flotation, and Stability Archimedes'Principle Stability Pressure Variation in a Fluid with Rigid-Body Motion Linear Motion Rigid-Body Rotation Review ELEMENTARY FLUID DYNAMICS THE BERNOULLI EQUATION 3.1 Newton's Second Law 3.2 F = ma along a Streamline 3.3 F = ma Normal to a Streamline 3.4 Physical Interpretation 3.5 Static, Stagnation, Dynamic, and Total Pressure 3.6 Examples of Use of the Bernoulli Free Jets Confined Flows Flowrate Measurement 3.7 The Energy Line and the Hydraulic Grade Line 3.8 Restrictions on Use of the Bernoulli Compressibility Effects Unsteady Effects Rotational Effects Other Restrictions 3.9 Review XVII

3 XVIII Contents FLUID KINEMATICS The Velocity Field Eulerian and Lagrangian Flow Descriptions One-, Two-, and Three- Dimensional Flows Steady and Unsteady Flows Streamlines, Streaklines, ' " and Pathlines The Acceleration Field The Material Derivative Unsteady Effects Convective Effects Streamline Coordinates Control Volume and System Representations The Reynolds Transport Theorem Derivation of the Reynolds Transport Theorem Physical Interpretation Relationship to Material Derivative Steady Effects Unsteady Effects Moving Control Volumes Selection of a Control Volume Review Application of the Moment-of- -, First Law of Thermodynamics The Energy Derivation of the Energy Application of the Energy Comparison of the Energy with the Bernoulli Application of the Energy to Nonuniform Flows Combination of the Energy and the Moment-of- Law of Thermodynamics Second Irreversible Flow Semi-infinitesimal Control Volume Statement of the Energy Semi-infinitesimal Control Volume Statement of the Second Law of Thermodynamics Combination of the s of the First and Second Laws of Thermodynamics Application of the Loss Form of the Energy Review' FINITE CONTROL VOLUME ANALYSIS ' c ' Conservation of Mass The Continuity Derivation of the Continuity Fixed, Nondeforming Control Volume Moving, Nondeforming Control Volume Deforming Control Volume 5.2 Newton's Second Law The Linear Momentum and Moment-of- s Derivation of the Linear Application of the Linear Derivation of the Moment-of DIFFERENTIAL ANALYSIS OF FLUID FLOW Fluid Element Kinematics Velocity and Acceleration Fields Revisited Linear Motion and Deformation Angular Motion and Deformation Conservation of Mass Differential Form of Continuity Cylindrical Polar Coordinates The Stream Function Conservation of Linear Momentum Description of Forces Acting on the Differential Element s of Motion Inviscid Flow Euler's s of Motion The Bernoulli 279

4 6.4.3 Irrotational Flow The Bernoulli for Irrotational Flow The Velocity Potential 6.5 Some Basic, Plane Potential Flows Uniform Flow Source and Sink Vortex Doublet 6.6 Superposition of Basic, Plane Potential Flows Source in a Uniform Stream Half-Body Rankine Ovals Flow around a Circular Cylinder 6.7 Other Aspects of Potential Flow Analysis 6.8 Viscous Flow Stress-Deformation Relationships The Naiver-Stokes s 6.9 Some Simple Solutions for Viscous, Incompressible Fluids Steady, Laminar Flow between Fixed Parallel Plates Couette Flow Steady, Laminar Flow in Circular Tubes Steady, Axial, Laminar Flow in an Annulus 6. Other Aspects of Differential Analysis 6..1 Numerical Methods 6.11 Review 7 DIMENSIONAL ANALYSIS, SIMILITUDE, AND MODELING 7.1 Dimensional Analysis 7.2 Buckingham Pi Theorem 73 ' Determination of Pi Terms 7.4 Some Additional Comments About Dimensional Analysis Selection of Variables Determination of Reference Dimensions Uniqueness of Pi Terms 7.5 Determination of Pi Terms by Inspection 7.6 Common Dimensionless Groups in Fluid Mechanics 7.7 Correlation of Experimental Data with One Pi Term Contents with Two or More Pi Terms Modeling and Similitude Theory of Models Model Scales Practical Aspects of 288 Using Models Some Typical Model Studies Flow through Closed Conduits Flow around Immersed Bodies Flow with a Free Surface 7. Similitude Based on Governing Differential s Review VISCOUS FLOW IN PIPES 8.1 General Characteristics of Pipe Flow Laminar or Turbulent Flow Entrance Region and Fully Developed Flow Pressure and Shear Stress 8.2 Fully Developed Laminar Flow From F = ma Applied to a Fluid Element From the Navier-Stokes s From Dimensional Analysis Energy Considerations 8.3 Fully Developed Turbulent Flow Transition from Laminar to Turbulent Flow Turbulent Shear Stress Turbulent Velocity Profile Turbulence Modeling Chaos and Turbulence 8.4 Dimensional Analysis of Pipe Flow Major Losses Minor Losses Noncircular Conduits 8.5 Pipe Flow Examples Single Pipes Multiple Pipe Systems 8.6 Pipe Fkwrate Measurement Pipe Flowrate Meters Volume Flow Meters 8.7 Review XIX

5 XX Contents FLOW OVER IMMERSED BODIES 9.1 General External Flow Characteristics Lift and Drag Concepts Characteristics of Flow Past an Object 9.2 Boundary Layer Characteristics Boundary Layer Structure _and Thickness on a Flat Plate * Prandtl/Blasius Boundary Layer Solution Momentum Integral Boundary Layer for a Flat Plate Transition from Laminar to Turbulent Flow Turbulent Boundary Layer Flow Effects of Pressure Gradient Momentum-Integral Boundary Layer with Nonzero Pressure Gradient Drag Lift Friction Drag Pressure Drag Drag Coefficient Data and Examples Surface Pressure Distribution Circulation Review OPEN-CHANNEL.1 General Characteristics of Open- Channel Flow.2 Surface Waves.2.1 Wave Speed '.2.2 Froude Number Effects.3 Energy Considerations.3.1 Specific Energy.3.2 Channel Depth Variations.4 Uniform Depth Channel Flow.4.1 Uniform Flow Approximations.4.2 The Chezy and Manning s.4.3 Uniform Depth Examples.5 Gradually Varied Flow.5.1 Classification of Surface Shapes.5.2 Examples of Gradually Varied Flows Rapidly Varied Flow.6.1 The Hydraulic Jump.6.2 Sharp-Crested Weirs.6.3 Broad-Crested Weirs.6.4 Underflow Gates.7 Review COMPRESSIBLE FLOW 11.1 Ideal Gas Relationships 11.2 Mach Number and Speed of Sound 11.3 Categories of Compressible Flow 11.4 Isentropic Flow of an Ideal Gas Effect of Variations in Flow Cross-Sectional Area Converging-Diverging Duct Flow Constant-Area Duct Flow 11.5 Nonisentropic Flow of an Ideal Gas Adiabatic Constant-Area Duct Flow with Friction (Fanno Flow) Frictionless Constant-Area Duct Flow with Heat Transfer (Rayleigh Flow) Normal Shock Waves 11.6 Analogy between Compressible and Open-Channel Flows 11.7 Two-Dimensional Compressible Flow 11.8 Review 12 TURBOMACHINES 12.1 Introduction 12.2 Basic Energy Considerations 12.3 Basic Angular Momentum Considerations 12.4 The Centrifugal Pump Theoretical Considerations Pump Performance Characteristics Net Positive Suction Head (NPSH) System Characteristics and Pump Selection 12.5 Dimensionless Parameters and Similarity Laws Special Pump Scaling Laws Specific Speed Suction Specific Speed

6 Contents xxi 12.6 Axial-Flow and Mixed-Flow Pumps 12.7 Fans 12.8 Turbines Impulse Turbines Reaction Turbines 12.9 Compressible Flow Turbomachines Compressors Compressible Flow Turbines 12. Review COMPUTATIONAL FLUID DYNAMICS AND FLOWLAB B PHYSICAL PROPERTIES OF FLUIDS C PROPERTIES OF THE U.S. STANDARD ATMOSPHERE D COMPRESSIBLE FLOW DATA FOR AN IDEAL GAS ONLINE APPENDIX LIST,1l COMPREHENSIVE TABLE OF CONVERSION FACTORS VIDEO LIBRARY REVIEW PROBLEMS H LABORATORY PROBLEMS I CFD DRIVEN CAVITY EXAMPLE J FLOWLAB TUTORIAL AND USER'S GUIDE K FLOWLAB PROBLEMS ANSWERS ANS-1 INDEX 1-1 VIDEO INDEX VI-1

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