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Chapter 1 Introduction 1

1.1 Introduction to Fluid Mechanics 2

Note to Students 2

Scope of Fluid Mechanics 3

Definition of a Fluid 3

1.2 Basic Equations 4

1.3 Methods of Analysis 5

System and Control Volume 6

Differential versus Integral Approach 7

Methods of Description 7

1.4 Dimensions and Units 9

Systems of Dimensions 9

Systems of Units 10

Preferred Systems of Units 11

Dimensional Consistency and “Engineering” Equations 11

1.5 Analysis of Experimental Error 13

1.6 Summary 14

References 14

Chapter 2 Fundamental Concepts 15

2.1 Fluid as a Continuum 16

2.2 Velocity Field 17

One-, Two-, and Three-Dimensional Flows 18

Timelines, Pathlines, Streaklines, and Streamlines 19

2.3 Stress Field 23

2.4 Viscosity 25

Newtonian Fluid 26

Non-Newtonian Fluids 28

2.5 Surface Tension 29

2.6 Description and Classification of Fluid Motions 30

Viscous and Inviscid Flows 32

Laminar and Turbulent Flows 34

Compressible and Incompressible Flows 34

Internal and External Flows 35

2.7 Summary and Useful Equations 36

References 37

Chapter 3 Fluid Statics 38

3.1 The Basic Equation of Fluid Statics 39

3.2 The Standard Atmosphere 42

3.3 Pressure Variation in a Static Fluid 43

Incompressible Liquids: Manometers 43

Gases 48

3.4 Hydrostatic Force on Submerged Surfaces 50

Hydrostatic Force on a Plane Submerged Surface 50

Hydrostatic Force on a Curved Submerged Surface 57

3.5 Buoyancy and Stability 60

3.6 Fluids in Rigid-Body Motion 63

3.7 Summary and Useful Equations 68

References 69

Chapter 4 Basic Equations In Integral Form For a Control Volume 70

4.1 Basic Laws for a System 71

Conservation of Mass 71

Newton’s Second Law 72

The Angular-Momentum Principle 72

The First Law of Thermodynamics 72

The Second Law of Thermodynamics 73

4.2 Relation of System Derivatives to the Control Volume Formulation 73

Derivation 74

Physical Interpretation 76

4.3 Conservation of Mass 77

Special Cases 78

4.4 Momentum Equation for Inertial Control Volume 82

Differential Control Volume Analysis 93

Control Volume Moving with Constant Velocity 97

4.5 Momentum Equation for Control Volume with Rectilinear Acceleration 99

4.6 Momentum Equation for Control Volume with Arbitrary Acceleration 105

4.7 The Angular-Momentum Principle 110

Equation for Fixed Control Volume 110

Equation for Rotating Control Volume 114

4.8 The First and Second Laws of Thermodynamics 118

Rate of Work Done by a Control Volume 119

Control Volume Equation 121

4.9 Summary and Useful Equations 125

Chapter 5 Introduction to Differential Analysis of Fluid Motion 128

5.1 Conservation of Mass 129

Rectangular Coordinate System 129

Cylindrical Coordinate System 133

5.2 Stream Function for Two-Dimensional Incompressible Flow 135

5.3 Motion of a Fluid Particle (Kinematics) 137

Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field 138

Fluid Rotation 144

Fluid Deformation 147

5.4 Momentum Equation 151

Forces Acting on a Fluid Particle 151

Differential Momentum Equation 152

Newtonian Fluid: Navier–Stokes Equations 152

5.5 Summary and Useful Equations 160

References 161

Chapter 6 Incompressible Inviscid Flow 162

6.1 Momentum Equation for Frictionless Flow: Euler’s Equation 163

6.2 Bernoulli Equation: Integration of Euler’s Equation Along a Streamline for Steady Flow 167

Derivation Using Streamline Coordinates 167

Derivation Using Rectangular Coordinates 168

Static, Stagnation, and Dynamic Pressures 169

Applications 171

Cautions on Use of the Bernoulli Equation 176

6.3 The Bernoulli Equation Interpreted as an Energy Equation 177

6.4 Energy Grade Line and Hydraulic Grade Line 181

6.5 Unsteady Bernoulli Equation: Integration of Euler’s Equation Along a Streamline 183

6.6 Irrotational Flow 185

Bernoulli Equation Applied to Irrotational Flow 185

Velocity Potential 186

Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace’s Equation 187

Elementary Plane Flows 189

Superposition of Elementary Plane Flows 191

6.7 Summary and Useful Equations 200

References 201

Chapter 7 Dimensional Analysis and Similitude 202

7.1 Nondimensionalizing the Basic Differential Equations 204

7.2 Buckingham Pi Theorem 206

7.3 Significant Dimensionless Groups in Fluid Mechanics 212

7.4 Flow Similarity and Model Studies 214

Incomplete Similarity 216

Scaling with Multiple Dependent Parameters 221

Comments on Model Testing 224

7.5 Summary and Useful Equations 225

References 226

Chapter 8 Internal Incompressible Viscous Flow 227

8.1 Internal Flow Characteristics 228

Laminar versus Turbulent Flow 228

The Entrance Region 229

Part A. Fully Developed Laminar Flow 230

8.2 Fully Developed Laminar Flow Between Infinite Parallel Plates 230

Both Plates Stationary 230

Upper Plate Moving with Constant Speed, U 236

8.3 Fully Developed Laminar Flow in a Pipe 241

Part B. Flow In Pipes and Ducts 245

8.4 Shear Stress Distribution in Fully Developed Pipe Flow 246

8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow 247

8.6 Energy Considerations in Pipe Flow 251

Kinetic Energy Coefficient 252

Head Loss 252

8.7 Calculation of Head Loss 253

Major Losses: Friction Factor 253

Minor Losses 258

Pumps, Fans, and Blowers in Fluid Systems 262

Noncircular Ducts 262

8.8 Solution of Pipe Flow Problems 263

Single-Path Systems 264

Multiple-Path Systems 276

Part C. Flow Measurement 279

8.9 Restriction Flow Meters for Internal Flows 279

The Orifice Plate 282

The Flow Nozzle 286

The Venturi 286

The Laminar Flow Element 287

Linear Flow Meters 288

Traversing Methods 289

8.10 Summary and Useful Equations 290

References 292

Chapter 9 External Incompressible Viscous Flow 293

Part A. Boundary Layers 295

9.1 The Boundary Layer Concept 295

9.2 Laminar Flat Plate Boundary Layer: Exact Solution 299

9.3 Momentum Integral Equation 302

9.4 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient 306

Laminar Flow 307

Turbulent Flow 311

9.5 Pressure Gradients in Boundary Layer Flow 314

Part B. Fluid Flow About Immersed Bodies 316

9.6 Drag 316

Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow 317

Pure Pressure Drag: Flow over a Flat Plate Normal to the Flow 320

Friction and Pressure Drag: Flow over a Sphere and Cylinder 320

Streamlining 326

9.7 Lift 328

9.8 Summary and Useful Equations 340

References 342

Chapter 10 Fluid Machinery 343

10.1 Introduction and Classification of Fluid Machines 344

Machines for Doing Work on a Fluid 344

Machines for Extracting Work (Power) from a Fluid 346

Scope of Coverage 348

10.2 Turbomachinery Analysis 348

The Angular Momentum Principle: The Euler Turbomachine Equation 348

Velocity Diagrams 350

Performance—Hydraulic Power 352

Dimensional Analysis and Specific Speed 353

10.3 Pumps, Fans, and Blowers 358

Application of Euler Turbomachine Equation to Centrifugal Pumps 358

Application of the Euler Equation to Axial Flow Pumps and Fans 359

Performance Characteristics 362

Similarity Rules 367

Cavitation and Net Positive Suction Head 371

Pump Selection: Applications to Fluid Systems 374

Blowers and Fans 380

10.4 Positive Displacement Pumps 384

10.5 Hydraulic Turbines 387

Hydraulic Turbine Theory 387

Performance Characteristics for Hydraulic Turbines 389

10.6 Propellers and Wind Turbines 395

Propellers 395

Wind Turbines 400

10.7 Compressible Flow Turbomachines 406

Application of the Energy Equation to a Compressible Flow Machine 406

Compressors 407

Compressible-Flow Turbines 410

10.8 Summary and Useful Equations 410

References 412

Chapter 11 Flow In Open Channels 414

11.1 Basic Concepts and Definitions 416

Simplifying Assumptions 416

Channel Geometry 418

Speed of Surface Waves and the Froude Number 419

11.2 Energy Equation for Open-Channel Flows 423

Specific Energy 425

Critical Depth: Minimum Specific Energy 426

11.3 Localized Effect of Area Change (Frictionless Flow) 431

Flow over a Bump 431

11.4 The Hydraulic Jump 435

Depth Increase Across a Hydraulic Jump 438

Head Loss Across a Hydraulic Jump 439

11.5 Steady Uniform Flow 441

The Manning Equation for Uniform Flow 443

Energy Equation for Uniform Flow 448

Optimum Channel Cross Section 450

11.6 Flow with Gradually Varying Depth 451

Calculation of Surface Profiles 452

11.7 Discharge Measurement Using Weirs 455

Suppressed Rectangular Weir 455

Contracted Rectangular Weirs 456

Triangular Weir 456

Broad-Crested Weir 457

11.8 Summary and Useful Equations 458

References 459

Chapter 12 Introduction to Compressible Flow 460

12.1 Review of Thermodynamics 461

12.2 Propagation of Sound Waves 467

Speed of Sound 467

Types of Flow—The Mach Cone 471

12.3 Reference State: Local Isentropic Stagnation Properties 473

Local Isentropic Stagnation Properties for the Flow of an Ideal Gas 474

12.4 Critical Conditions 480

12.5 Basic Equations for One-Dimensional Compressible Flow 480

Continuity Equation 481

Momentum Equation 481

First Law of Thermodynamics 481

Second Law of Thermodynamics 482

Equation of State 483

12.6 Isentropic Flow of an Ideal Gas: Area Variation 483

Subsonic Flow, M <1 485

Supersonic Flow, M >1 486

Sonic Flow, M =1 486

Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas 487

Isentropic Flow in a Converging Nozzle 492

Isentropic Flow in a Converging-Diverging Nozzle 496

12.7 Normal Shocks 501

Basic Equations for a Normal Shock 501

Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas 503

12.8 Supersonic Channel Flow with Shocks 507

12.9 Summary and Useful Equations 509

References 511

Problems P-1

Appendix A Fluid Property Data A-1

Appendix B Videos For Fluid Mechanics A-13

Appendix C Selected Performance Curves For Pumps and Fans A-15

Appendix D Flow Functions For Computation of Compressible Flow A-26

Appendix E Analysis of Experimental Uncertainty A-29

Appendix F Introduction to Computational Fluid Dynamics A-35

Index I-1

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