**CHAPTER 1 INTRODUCTION /1**

1.1 Note to Students /3

1.2 Scope of Fluid Mechanics /4

1.3 Definition of a Fluid /4

1.4 Basic Equations /5

1.5 Methods of Analysis /6

System and Control Volume /7

Differential versus Integral Approach /8

Methods of Description /9

1.6 Dimensions and Units /11

Systems of Dimensions /11

Systems of Units /11

Preferred Systems of Units /13

Dimensional Consistency and “Engineering” Equations /14

1.7 Analysis of Experimental Error /15

1.8 Summary /16

Problems /17

**CHAPTER 2 FUNDAMENTAL CONCEPTS /20**

2.1 Fluid as a Continuum /21

2.2 Velocity Field /23

One-, Two-, and Three-Dimensional Flows /24

Timelines, Pathlines, Streaklines, and Streamlines /25

2.3 Stress Field /29

2.4 Viscosity /31

Newtonian Fluid /32

Non-Newtonian Fluids /34

2.5 Surface Tension /36

2.6 Description and Classification of Fluid Motions /38

Viscous and Inviscid Flows /38

Laminar and Turbulent Flows /41

Compressible and Incompressible Flows /42

Internal and External Flows /43

2.7 Summary and Useful Equations /44

References /46

Problems /46

**CHAPTER 3 FLUID STATICS /55**

3.1 The Basic Equation of Fluid Statics /56

3.2 The Standard Atmosphere /60

3.3 Pressure Variation in a Static Fluid /61

Incompressible Liquids: Manometers /61

Gases /66

3.4 Hydraulic Systems /69

3.5 Hydrostatic Force on Submerged Surfaces /69

Hydrostatic Force on a Plane Submerged Surface /69

Hydrostatic Force on a Curved Submerged Surface /76

*3.6 Buoyancy and Stability /80

3.7 Fluids in Rigid-Body Motion (on the Web) /W-1

3.8 Summary and Useful Equations /83

References /84

Problems /84

**CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME /96**

4.1 Basic Laws for a System /98

Conservation of Mass /98

Newton’s Second Law /98

The Angular-Momentum Principle /99

The First Law of Thermodynamics /99

The Second Law of Thermodynamics /99

4.2 Relation of System Derivatives to the Control Volume Formulation /100

Derivation /101

Physical Interpretation /103

4.3 Conservation of Mass /104

Special Cases /105

4.4 Momentum Equation for Inertial Control Volume /110

*Differential Control Volume Analysis /122

Control Volume Moving with Constant Velocity /126

4.5 Momentum Equation for Control Volume with Rectilinear Acceleration /128

4.6 Momentum Equation for Control Volume with Arbitrary Acceleration (on the Web) /W-6

*4.7 The Angular-Momentum Principle /135

Equation for Fixed Control Volume /135

Equation for Rotating Control Volume (on the Web) /W-11

4.8 The First Law of Thermodynamics /139

Rate of Work Done by a Control Volume /140

Control Volume Equation /142

4.9 The Second Law of Thermodynamics /146

4.10 Summary and Useful Equations /147

Problems /149

**CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION /171**

5.1 Conservation of Mass /172

Rectangular Coordinate System /173

Cylindrical Coordinate System /177

*5.2 Stream Function for Two-Dimensional Incompressible Flow /180

5.3 Motion of a Fluid Particle (Kinematics) /184

Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field /185

Fluid Rotation /190

Fluid Deformation /194

5.4 Momentum Equation /197

Forces Acting on a Fluid Particle /198

Differential Momentum Equation /199

Newtonian Fluid: NavierStokes Equations /199

*5.5 Introduction to Computational Fluid Dynamics /208

The Need for CFD /208

Applications of CFD /209

Some Basic CFD/Numerical Methods Using a Spreadsheet /210

The Strategy of CFD /215

Discretization Using the Finite-Difference Method /216

Assembly of Discrete System and Application of Boundary Conditions /217

Solution of Discrete System /218

Grid Convergence /219

Dealing with Nonlinearity /220

Direct and Iterative Solvers /221

Iterative Convergence /222

Concluding Remarks /223

5.6 Summary and Useful Equations /224

References /226

Problems /226

**CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW /235**

6.1 Momentum Equation for Frictionless Flow: Euler’s Equation /237

6.2 Euler’s Equations in Streamline Coordinates /238

6.3 Bernoulli Equation—Integration of Euler’s Equation Along a Streamline for Steady Flow /241

*Derivation Using Streamline Coordinates /241

*Derivation Using Rectangular Coordinates /242

Static, Stagnation, and Dynamic Pressures /244

Applications /247

Cautions on Use of the Bernoulli Equation /252

6.4 The Bernoulli Equation Interpreted as an Energy Equation /253

6.5 Energy Grade Line and Hydraulic Grade Line /257

*6.6 Unsteady Bernoulli Equation: Integration of Euler’s Equation Along a Streamline (on the Web) /W-16

*6.7 Irrotational Flow /259

Bernoulli Equation Applied to Irrotational Flow /260

Velocity Potential /261

Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace’s Equation /262

Elementary Plane Flows /264

Superposition of Elementary Plane Flows /267

6.8 Summary and Useful Equations /276

References /279

Problems /279

**CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE /290**

7.1 Nondimensionalizing the Basic Differential Equations /292

7.2 Nature of Dimensional Analysis /294

7.3 Buckingham Pi Theorem /296

7.4 Determining the Π Groups /297

7.5 Significant Dimensionless Groups in Fluid Mechanics /303

7.6 Flow Similarity and Model Studies /305

Incomplete Similarity /308

Scaling with Multiple Dependent Parameters /314

Comments on Model Testing /317

7.7 Summary and Useful Equations /318

References /319

Problems /320

**CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW /328**

8.1 Introduction /330

Laminar versus Turbulent Flow /330

The Entrance Region /331

PART A. FULLY DEVELOPED LAMINAR FLOW /332

8.2 Fully Developed Laminar Flow between Infinite Parallel Plates /332

Both Plates Stationary /332

Upper Plate Moving with Constant Speed, U /338

8.3 Fully Developed Laminar Flow in a Pipe /344

PART B. FLOW IN PIPES AND DUCTS /348

8.4 Shear Stress Distribution in Fully Developed Pipe Flow /349

8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow /351

8.6 Energy Considerations in Pipe Flow /353

Kinetic Energy Coefficient /355

Head Loss /355

8.7 Calculation of Head Loss /357

Major Losses: Friction Factor /357

Minor Losses /361

Pumps, Fans, and Blowers in Fluid Systems /367

Noncircular Ducts /368

8.8 Solution of Pipe Flow Problems /369

Single-Path Systems /370

*Multiple-Path Systems /383

PART C. FLOW MEASUREMENT /387

8.9 Direct Methods /387

8.10 Restriction Flow Meters for Internal Flows /387

The Orifice Plate /391

The Flow Nozzle /391

The Venturi /393

The Laminar Flow Element /394

8.11 Linear Flow Meters /397

8.12 Traversing Methods /399

8.13 Summary and Useful Equations /400

References /402

Problems /403

**CHAPTER 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW /421**

PART A. BOUNDARY LAYERS /423

9.1 The Boundary-Layer Concept /423

9.2 Boundary-Layer Thicknesses /425

9.3 Laminar Flat-Plate Boundary Layer: Exact Solution (on the Web) /W-19

9.4 Momentum Integral Equation /428

9.5 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient /433

Laminar Flow /434

Turbulent Flow /439

Summary of Results for Boundary-Layer Flow with Zero Pressure Gradient /441

9.6 Pressure Gradients in Boundary-Layer Flow /442

PART B. FLUID FLOW ABOUT IMMERSED BODIES /445

9.7 Drag /445

Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow /446

Pure Pressure Drag: Flow over a Flat Plate Normal to the Flow /450

Friction and Pressure Drag: Flow over a Sphere and Cylinder /450

Streamlining /456

9.8 Lift /459

9.9 Summary and Useful Equations /474

References /477

Problems /478

**CHAPTER 10 FLUID MACHINERY /492**

10.1 Introduction and Classification of Fluid Machines /494

Machines for Doing Work on a Fluid /494

Machines for Extracting Work (Power) from a Fluid /496

Scope of Coverage /498

10.2 Turbomachinery Analysis /499

The Angular-Momentum Principle: The Euler Turbomachine Equation /499

Velocity Diagrams /501

Performance: Hydraulic Power /504

Dimensional Analysis and Specific Speed /505

10.3 Pumps, Fans, and Blowers /510

Application of Euler Turbomachine Equation to Centrifugal Pumps /510

Application of the Euler Equation to Axial Flow Pumps and Fans /512

Performance Characteristics /516

Similarity Rules /522

Cavitation and Net Positive Suction Head /526

Pump Selection: Applications to Fluid Systems /529

Blowers and Fans /541

10.4 Positive Displacement Pumps /548

10.5 Hydraulic Turbines /552

Hydraulic Turbine Theory /552

Performance Characteristics for Hydraulic Turbines /554

Sizing Hydraulic Turbines for Fluid Systems /558

10.6 Propellers and Wind-Power Machines /562

Propellers /563

Wind-Power Machines /571

10.7 Compressible Flow Turbomachines /581

Application of the Energy Equation to a Compressible Flow Machine /581

Compressors /582

Compressible-Flow Turbines /586

10.8 Summary and Useful Equations /586

References /589

Problems /591

**CHAPTER 11 FLOW IN OPEN CHANNELS /600**

11.1 Basic Concepts and Definitions /603

Simplifying Assumptions /604

Channel Geometry /605

Speed of Surface Waves and the Froude Number /606

11.2 Energy Equation for Open-Channel Flows /610

Specific Energy /613

Critical Depth: Minimum Specific Energy /616

11.3 Localized Effect of Area Change (Frictionless Flow) /619

Flow over a Bump /620

11.4 The Hydraulic Jump /625

Depth Increase Across a Hydraulic Jump /627

Head Loss Across a Hydraulic Jump /628

11.5 Steady Uniform Flow /631

The Manning Equation for Uniform Flow /633

Energy Equation for Uniform Flow /639

Optimum Channel Cross Section /640

11.6 Flow with Gradually Varying Depth /641

Calculation of Surface Profiles /643

11.7 Discharge Measurement Using Weirs /646

Suppressed Rectangular Weir /646

Contracted Rectangular Weirs /647

Triangular Weir /648

Broad-Crested Weir /648

11.8 Summary and Useful Equations /650

References /652

Problems /653

**CHAPTER 12 INTRODUCTION TO COMPRESSIBLE FLOW /657**

12.1 Review of Thermodynamics /659

12.2 Propagation of Sound Waves /665

Speed of Sound /665

Types of Flow—The Mach Cone /670

12.3 Reference State: Local Isentropic Stagnation Properties /673

Local Isentropic Stagnation Properties for the Flow of an Ideal Gas /674

12.4 Critical Conditions /681

12.5 Summary and Useful Equations /681

References /683

Problems /683

**CHAPTER 13 COMPRESSIBLE FLOW /689**

13.1 Basic Equations for One-Dimensional Compressible Flow /691

13.2 Isentropic Flow of an Ideal Gas: Area Variation /694

Subsonic Flow, M , 1 /697

Supersonic Flow, M . 1 /697

Sonic Flow, M 5 1 /698

Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas /699

Isentropic Flow in a Converging Nozzle /704

Isentropic Flow in a Converging-Diverging Nozzle /709

13.3 Normal Shocks /715

Basic Equations for a Normal Shock /716

Fanno and Rayleigh Interpretation of Normal Shock /718

Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas /719

13.4 Supersonic Channel Flow with Shocks /724

Flow in a Converging-Diverging Nozzle /724

Supersonic Diffuser (on the Web) /W-24

Supersonic Wind Tunnel Operation (on the Web) /W-25

Supersonic Flow with Friction in a Constant-Area Channel (on the Web) /W-26

Supersonic Flow with Heat Addition in a Constant-Area Channel (on the Web) /W-26

13.5 Flow in a Constant-Area Duct with Friction /727

Basic Equations for Adiabatic Flow /727

Adiabatic Flow: The Fanno Line /728

Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas /732

Isothermal Flow (on the Web) /W-29

13.6 Frictionless Flow in a Constant-Area Duct with Heat Exchange /740

Basic Equations for Flow with Heat Exchange /740

The Rayleigh Line /741

Rayleigh-Line Flow Functions for One-Dimensional Flow of an Ideal Gas /746

13.7 Oblique Shocks and Expansion Waves /750

Oblique Shocks /750

Isentropic Expansion Waves /759

13.8 Summary and Useful Equations /768

References /771

Problems /772

APPENDIX A FLUID PROPERTY DATA /785

APPENDIX B EQUATIONS OF MOTION IN CYLINDRICAL COORDINATES /798

APPENDIX C VIDEOS FOR FLUID MECHANICS /800

APPENDIX D SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS /803

APPENDIX E FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW /818

APPENDIX F ANALYSIS OF EXPERIMENTAL UNCERTAINTY /829

APPENDIX G SI UNITS, PREFIXES, AND CONVERSION FACTORS /836

APPENDIX H A BRIEF REVIEW OF MICROSOFT EXCEL (ON THE WEB) /W-33

Answers to Selected Problems /838

Index /867