# INTRODUCTION TO FLUID MECHANICS

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1 INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC.

2 CONTENTS CHAPTER 1 INTRODUCTION /1 1-1 Note to Students /I 1-2 Definition of a Fluid /3 1-3 Scope of Fluid Mechanics I A 1-4 Basic Equations /4 1-5 Methods of Analysis /5 System and Control Volume /5 Differential versus Integral Approach /8 Methods of Description /8 1-6 Dimensions and Units /10 Systems of Dimensions /11 Systems of Units /11 Preferred Systems of Units / Summary /13 Problems /13 CHAPTER 2 FUNDAMENTAL CONCEPTS / Fluid as a Continuum / Velocity Field /19 One-, Two-, and Three- Dimensional Flows /20 Timelines, Pathlines, Streaklines, and Streamlines / Stress Field / Viscosity /26 Newtonian Fluid /28 Non-Newtonian Fluids / Surface Tension / Description and Classification of Fluid Motion /35 Viscous and Inviscid Flows /35 Laminar and Turbulent Flows /38 Compressible and Incompressible Flows /39 Internal and External Flows / Summary /42 References /42 Problems /42 CHAPTER 3 FLUID STATICS / The Basic Equation of Fluid Statics / The Standard Atmosphere / Pressure Variation in a Static Fluid /57 Incompressible Liquids: Manometers /57 Gases /63 vii

3 Viil CONTENTS 3-4 Hydraulic Systems / Hydrostatic Fouce on Submerged Surfaces /66 Hydrostatic Force on a Plane Submerged Surface /66 Hydrostatic Force on a Curved Submerged Surface /74 *3.6 Buoyancy and Stability / Fluids in Rigid-Body Motion (CD-ROM) /S Summary /82 References /82 Problems /83 CHAPTER 4 CHAPTER 5 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME / Basic Laws for a System /99 Conservation of Mass /99 Newton's Second Law /100 The Angular-Momentum Principle /100 The First Law of Thermodynamics /100 The Second Law of Thermodynamics / Relation of System Derivatives to the Control Volume Formulation / 101 Derivation /102 Physical Interpretation / Conservation of Mass /105 Special Cases / Momentum Equation for Inertial Control Volume /112 *Differential Control Volume Analysis /124 Control Volume Moving with Constant Velocity / Momentum Equation for Control Volume with Rectilinear Acceleration / Momentum Equation for Control Volume with Arbitrary Acceleration (CD-ROM) /S-7 *4-7 The Angular-Momentum Principle /139 Equation for Fixed Control Volume /139 Equation for Rotating Control Volume (CD-ROM) /S The First Law of Thermodynamics /144 Rate of Work Done by a Control Volume /144 Control Volume Equation / The Second Law of Thermodynamics / Summary /152 Problems /152 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION / Conservation of Mass /184 Rectangular Coordinate System /184 Cylindrical Coordinate System /189 *5-2 Stream Function for Two-Dimensional Incompressible Flow / Motion of a Fluid Particle (Kinematics) /197 Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field /197 Fluid Rotation /203 Fluid Deformation /207

4 CONTENTS IX 5-4 Momentum Equation /211 Forces Acting on a Fluid Particle /212 Differential Momentum Equation 1213 Newtonian Fluid: Navier-Stokes Equations / Summary /222 References /223 Problems /223 CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW / Momentum Equation for Frictionless Flow: Euler's Equation / Euler's Equations in Streamline Coordinates / Bernoulli Equation-Integration of Euler's Equation along a Streamline for Steady Flow /237 Derivation Using Streamline Coordinates /237 Derivation Using Rectangular Coordinates /238 Static, Stagnation, and Dynamic Pressures /239 Applications /243 Cautions on Use of the Bernoulli Equation / The Bernoulli Equation Interpreted as an Energy Equation / Energy Grade Line and Hydraulic Grade Line / Unsteady Bernoulli Equation - Integration of Euler's Equation along a Streamline (CD-ROM) IS Irrotational Flow (CD-ROM) /S-20 Bernoulli Equation Applied to Irrotational Flow (CD-ROM) /S-21 Velocity Potential (CD-ROM) /S-22 Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace's Equation (CD-ROM) /S-23 Elementary Plane Flows (CD-ROM) /S-25 Superposition of Elementary Plane Flows (CD-ROM) /S Summary /256 References /257 Problems /257 CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE / Nondimensionalizing the Basic Differential Equations / Nature of Dimensional Analysis / Buckingham Pi Theorem / Determining the Pi Groups / Significant Dimensionless Groups in Fluid Mechanics / Flow Similarity and Model Studies /286 Incomplete Similarity /289 Scaling with Multiple Dependent Parameters /295 Comments on Model Testing /298 Summary /299 References /300 Problems /301 CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW / Introduction /310 PART A. FULLY DEVELOPED LAMINAR FLOW /312

5 X CONTENTS 8-2 Fully Developed Laminar Flow between Infinite Parallel Plates /312 Both Plates Stationary /312 Upper Plate Moving with Constant Speed, U / Fully Developed Laminar Flow in a Pipe /324 PART B. FLOW IN PIPES AND DUCTS / Shear Stress Distribution in Fully Developed Pipe Flow / Turbulent Velocity Profiles in Fully Developed Pipe Flow / Energy Considerations in Pipe Flow /334 Kinetic Energy coefficient /335 Head Loss / Calculation of Head Loss /336 Major Loss: Friction Factor /336 Minor Losses /341 Pumps, Fans, and Blowers in Fluid Systems /347 Noncircular Ducts / Solution of Pipe Flow Problems /349 Single-Path Systems /350 *Multiple-Path Systems /364 PART C. FLOW MEASUREMENT / Direct Methods / Restriction Flow Meters for Internal Flows /370 The Orifice Plate /373 The Flow Nozzle /374 The Venturi /376 The Laminar Flow Element / LinearflowMeters / Traversing Methods / Summary /383 References /383 Problems /385 CHAPTER 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW /409 PART A. BOUNDARY LAYERS / The Boundary-Layer Concept / Boundary-Layer Thicknesses / Laminar Flat-Plate Boundary Layer: Exact Solution (CD-ROM) /S Momentum Integral Equation / Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient /421 Laminar Flow /422 Turbulent Flow / Pressure Gradients in Boundary-Layer Flow /430 PARTB. FLUID FLOW ABOUT IMMERSED BODIES / Drag /433 Flow over a Flat Plate Parallel to the Flow: Friction Drag /434 Flow over a Flat Plate Normal to the Flow: Pressure Drag /437 Flow over a Sphere and Cylinder: Friction and Pressure Drag /438 Streamlining / Lift / Summary /464

6 CONTENTS XI References /465 Problems 4/466 CHAPTER 10 FLUID MACHINERY / Introduction and Classification of Fluid Machines /487 Machines for Doing Work on a Fluid /488 Machines for Extracting Work (Power) from a Fluid / Scope of Coverage / Turbomachinery Analysis /491 The Angular-Momentum Principle /491 Euler Turbomachine Equation /491 Velocity Diagrams /493 Hydraulic Power / Performance Characteristics /502 Performance Parameters /503 Dimensional Analysis and Specific Speed /514 Similarity Rules /519 Cavitation and Net Positive Suction Head / Applications to Fluid Systems /528 Machines for Doing Work on a Fluid /529 Machines for Extracting Work (Power) from a Fluid / Summary /571 References /572 Problems /574 CHAPTER 11 INTRODUCTION TO COMPRESSIBLE FLOW / Review of Thermodynamics / Propagation of Sound Waves /596 Speed of Sound /596 Types of Flow - The Mach Cone / Reference State: Local Isentropic Stagnation Properties /602 Local Isentopic Stagnation Properties for the Flow of an Ideal Gas / Critical Conditions / Summary /611 References /611 Problems /611 CHAPTER 12 COMPRESSIBLE FLOW / Basic Equations for One-Dimensional Compressible Flow / Isentropic Flow of an Ideal Gas - Area Variation /621 Subsonic Flow, M < 1 /623 Supersonic Flow, M > 1 /623 Sonic Flow, M = 1 /624 Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas /625 Isentropic Flow in a Converging Nozzle /631 Isentropic Flow in a Converging-Diverging Nozzle / Flow in a Constant-Area Duct with Friction /643 Basic Equations for Adiabatic Flow /644

7 XII CONTENTS Adiabatic Flow: The Fanno Line /645 Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas /649 Isothermal Flow (CD-ROM) /S Frictionless Flow in a Constant-Area Duct with Heat Exchange /657 Basic Equations for Flow with Heat Exchange /658 The Rayleigh Line /659 Rayleigh-Line Flow Functions for One-Dimensional Flow of an Ideal Gas / Normal Shocks /669 Basic Equations for a Normal Shock /670 Normal Shock Flow Functions for One-Dimensional Flow of an Ideal Gas / Supersonic Channel Flow with Shocks /678 Flow in a Converging-Diverging Nozzle /678 Supersonic Diffuser (CD-ROM) /S-46 Supersonic Wind Tunnel Operation (CD-ROM) /S-48 Supersonic Flow with Friction in a Constant-Area Channel (CD-ROM) /S-49 Supersonic Flow with Heat Addition in a Constant-Area Channel (CD-ROM) /S Oblique Shocks and Expansion Waves /680 Oblique Shocks /680 Isentropic Expansion Waves / Summary /699 References /699 Problems /700 APPENDIX A FLUID PROPERTY DATA /716 APPENDIX B EQUATIONS OF MOTION IN CYLINDRICAL COORDINATES /730 APPENDIX C VIDEOS FOR FLUID MECHANICS /731 APPENDIX D SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS /733 APPENDIX E FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW /744 APPENDIX F ANALYSIS OF EXPERIMENTAL UNCERTAINTY /755 APPENDIX G SI UNITS, PREFIXES, AND CONVERSION FACTORS /762 APPENDIX H A BRIEF REVIEW OF MICROSOFT EXCEL (CD-ROM) /S-53 Answers to Selected Problems /765 Index /779

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