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CHAPTER 1 INTRODUCTION 1

1-1 Note to Students 1

1-2 Definition of a Fluid 3

1-3 Scope of Fluid Mechanics 4

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 13

1-7 Summary 13

Problems 13

CHAPTER 2 FUNDAMENTAL CONCEPTS 17

2-1 Fluid as a Continuum 17

2-2 Velocity Field 19

One-, Two-, and Three- Dimensional Flows 20

Timelines, Pathlines, Streaklines, and Streamlines 21

2-3 Stress Field 24

2-4 Viscosity 26

Newtonian Fluid 28

Non-Newtonian Fluids 30

2-5 Surface Tension 32

2-6 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 40

2-7 Summary 42

References 42

Problems 42

CHAPTER 3 FLUID STATICS 52

3-1 The Basic Equation of Fluid Statics 52

3-2 The Standard Atmosphere 56

3-3 Pressure Variation in a Static Fluid 57

Incompressible Liquids: Manometers 57

Gases 63

3-4 Hydraulic Systems 66

3-5 Hydrostatic Force 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 78

3-8 Summary 82

References 82

Problems 83

CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME 99

4-1 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 101

4-2 Relation of System Derivatives to the Control Volume Formulation 101

Derivation 102

Physical Interpretation 104

4-3 Conservation of Mass 105

Special Cases 106

4-4 Momentum Equation for Inertial Control Volume 112

Differential Control Volume Analysis 124

Control Volume Moving with Constant Velocity 129

4-5 Momentum Equation for Control Volume with Rectilinear Acceleration 131

4-7 The Angular-Momentum Principle 139

Equation for Fixed Control Volume 139

4-8 The First Law of Thermodynamics 144

Rate of Work Done by a Control Volume 144

Control Volume Equation 146

4-9 The Second Law of Thermodynamics 151

4-10 Summary 152

Problems 152

CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION 184

5-1 Conservation of Mass 184

Rectangular Coordinate System 184

Cylindrical Coordinate System 189

5-2 Stream Function for Two-Dimensional Incompressible Flow 193

5-3 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

5-4 Momentum Equation 211

Forces Acting on a Fluid Particle 212

Differential Momentum Equation 213

Newtonian Fluid: Navier-Stokes Equations 213

5-5 Summary 222

References 223

Problems 223

CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW 232

6-1 Momentum Equation for Frictionless Flow: Euler's Equation 232

6-2 Euler's Equations in Streamline Coordinates 233

6-3 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 248

6-4 The Bernoulli Equation Interpreted as an Energy Equation 249

6-5 Energy Grade Line and Hydraulic Grade Line 254

6-8 Summary 256

References 257

Problems 257

CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE 273

7-1 Nondimensionalizing the Basic Differential Equations 273

7-2 Nature of Dimensional Analysis 275

7-3 Buckingham Pi Theorem 277

7-4 Determining the Pi Groups 278

7-5 Significant Dimensionless Groups in Fluid Mechanics 284

7-6 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 310

8-1 Introduction 310

PART A. FULLY DEVELOPED LAMINAR FLOW 312

8-2 Fully Developed Laminar Flow between Infinite Parallel Plates 312

Both Plates Stationary 312

Upper Plate Moving with Constant Speed, U 318

8-3 Fully Developed Laminar Flow in a Pipe 324

PART B. FLOW IN PIPES AND DUCTS 328

8-4 Shear Stress Distribution in Fully Developed Pipe Flow 329

8-5 Turbulent Velocity Profiles in Fully Developed Pipe Flow 330

8-6 Energy Considerations in Pipe Flow 334

Kinetic Energy coefficient 335

Head Loss 335

8-7 Calculation of Head Loss 336

Major Loss: Friction Factor 336

Minor Losses 341

Pumps, Fans, and Blowers in Fluid Systems 347

Noncircular Ducts 348

8-8 Solution of Pipe Flow Problems 349

Single-Path Systems 350

Multiple-Path Systems 364

PART C. FLOW MEASUREMENT 369

8-9 Direct Methods 369

8-10 Restriction Flow Meters for Internal Flows 370

The Orifice Plate 373

The Flow Nozzle 374

The Venturi 376

The Laminar Flow Element 376

8-11 Linear flow Meters 380

8-12 Traversing Methods 382

8-13 Summary 383

References 383

Problems 385

CHAPTER 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW 409

PART A. BOUNDARY LAYERS 410

9-1 The Boundary-Layer Concept 410

9-2 Boundary-Layer Thicknesses 412

9-4 Momentum Integral Equation 415

9-5 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient 421

Laminar Flow 422

Turbulent Flow 426

9-6 Pressure Gradients in Boundary-Layer Flow 430

PART B. FLUID FLOW ABOUT IMMERSED BODIES 433

9-7 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 445

9-8 Lift 447

9-9 Summary 464

CHAPTER 10 FLUID MACHINERY 487

10-1 Introduction and Classification of Fluid Machines 487

Machines for Doing Work on a Fluid 488

Machines for Extracting Work (Power) from a Fluid 489

10-2 Scope of Coverage 490

10-3 Turbomachinery Analysis 491

The Angular-Momentum Principle 491

Euler Turbomachine Equation 491

Velocity Diagrams 493

Hydraulic Power 501

10-4 Performance Characteristics 502

Performance Parameters 503

Dimensional Analysis and Specific Speed 514

Similarity Rules 519

Cavitation and Net Positive Suction Head 524

10-5 Applications to Fluid Systems 528

Machines for Doing Work on a Fluid 529

Machines for Extracting Work (Power) from a Fluid 561

10-6 Summary 571

References 572

Problems 574

CHAPTER 11 INTRODUCTION TO COMPRESSIBLE FLOW 589

11-1 Review of Thermodynamics 589

11-2 Propagation of Sound Waves 596

Speed of Sound 596

Types of Flow - The Mach Cone 600

11-3 Reference State: Local Isentropic Stagnation Properties 602

Local Isentopic Stagnation Properties for the Flow of an Ideal Gas 603

11-4 Critical Conditions 610

11-5 Summary 611

References 611

Problems 611

CHAPTER 12 COMPRESSIBLE FLOW 617

12-1 Basic Equations for One-Dimensional Compressible Flow 617

12-2 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 637

12-3 Flow in a Constant-Area Duct with Friction 643

Basic Equations for Adiabatic Flow 644

Adiabatic Flow: The Fanno Line 645

Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas 649

12-4 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 664

12-5 Normal Shocks 669

Basic Equations for a Normal Shock 670

Normal Shock Flow Functions for One-Dimensional Flow of an Ideal Gas 672

12-6 Supersonic Channel Flow with Shocks 678

Flow in a Converging-Diverging Nozzle 678

12-7 Oblique Shocks and Expansion Waves 680

Oblique Shocks 680

Isentropic Expansion Waves 690

12-8 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

Answers to Selected Problems 765

Index 779