# Fluid Mechanics, 9th Edition SI Version

# Fluid Mechanics, 9th Edition SI Version

ISBN: 978-1-118-95898-8

Dec 2015

680 pages

$64.00

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## Description

Through eight editions, Fox & McDonald’s *Fluid Mechanics* has been one of the most widely adopted textbooks in the field. This highly-regarded text continues to provide readers with a balanced and comprehensive approach to mastering critical concepts, incorporating a proven problem-solving methodology that helps readers develop an orderly plan to finding the right solution and relating results to expected physical behavior. The ninth edition features a wealth of example problems integrated throughout the text as well as a variety of new end of chapter problems.

*Fluid Mechanics*integrates case studies at the beginning of each chapter, motivating students by demonstrating how the concepts of fluid mechanics are applied to solve real-world problems. Videos demonstrating various fluid phenomena are integrated throughout the text, building students visualization skills. The coverage of compressible flow has been combined into a single chapter at the end of the book.

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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

Problems 14

**CHAPTER 2 FUNDAMENTAL CONCEPTS 17**

2.1 Fluid as a Continuum 18

2.2 Velocity Field 19

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

Timelines, Pathlines, Streaklines, and Streamlines 21

2.3 Stress Field 25

2.4 Viscosity 27

Newtonian Fluid 28

Non-Newtonian Fluids 30

2.5 Surface Tension 31

2.6 Description and Classification of Fluid Motions 34

Viscous and Inviscid Flows 34

Laminar and Turbulent Flows 36

Compressible and Incompressible Flows 37

Internal and External Flows 38

2.7 Summary and Useful Equations 39

References 40

Problems 40

**CHAPTER 3 FLUID STATICS 46**

3.1 The Basic Equation of Fluid Statics 47

3.2 The Standard Atmosphere 50

3.3 Pressure Variation in a Static Fluid 51

Incompressible Liquids: Manometers 51

Gases 56

3.4 Hydrostatic Force on Submerged Surfaces 58

Hydrostatic Force on a Plane Submerged Surface 58

Hydrostatic Force on a Curved Submerged Surface 65

3.5 Buoyancy and Stability 68

3.6 Fluids in Rigid-Body Motion (on the Web) 71

3.7 Summary and Useful Equations 71

References 72

Problems 72

**CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME 82**

4.1 Basic Laws for a System 84

Conservation of Mass 84

Newton’s Second Law 84

The Angular-Momentum Principle 84

The First Law of Thermodynamics 85

The Second Law of Thermodynamics 85

4.2 Relation of System Derivatives to the Control Volume Formulation 85

Derivation 86

Physical Interpretation 88

4.3 Conservation of Mass 89

Special Cases 90

4.4 Momentum Equation for Inertial Control Volume 94

Differential Control Volume Analysis 105

Control Volume Moving with Constant Velocity 109

4.5 Momentum Equation for Control Volume with Rectilinear Acceleration 111

4.6 Momentum Equation for Control Volume with Arbitrary Acceleration (on the Web) 117

4.7 The Angular-Momentum Principle 117

Equation for Fixed Control Volume 117

4.8 The First and Second Laws of Thermodynamics 121

Rate of Work Done by a Control Volume 122

Control Volume Equation 123

4.9 Summary and Useful Equations 128

Problems 129

**CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION 146**

5.1 Conservation of Mass 147

Rectangular Coordinate System 147

Cylindrical Coordinate System 151

*5.2 Stream Function for Two-Dimensional Incompressible Flow 153

5.3 Motion of a Fluid Particle (Kinematics) 155

Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field 156

Fluid Rotation 162

Fluid Deformation 165

5.4 Momentum Equation 169

Forces Acting on a Fluid Particle 169

Differential Momentum Equation 170

Newtonian Fluid: Navier–Stokes Equations 170

*5.5 Introduction to Computational Fluid Dynamics 178

The Need for CFD 178

Applications of CFD 179

Some Basic CFD/Numerical Methods Using a Spreadsheet 180

The Strategy of CFD 184

Discretization Using the Finite-Difference Method 185

Assembly of Discrete System and Application of Boundary Conditions 186

Solution of Discrete System 187

Grid Convergence 187

Dealing with Nonlinearity 188

Direct and Iterative Solvers 189

Iterative Convergence 190

Concluding Remarks 191

5.6 Summary and Useful Equations 192

References 194

Problems 194

**CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW 200**

6.1 Momentum Equation for Frictionless Flow: Euler’s Equation 201

6.2 Bernoulli Equation: Integration of Euler’s Equation Along a Streamline for Steady Flow 204

Derivation Using Streamline Coordinates 204

Derivation Using Rectangular Coordinates 205

Static, Stagnation, and Dynamic Pressures 207

Applications 209

Cautions on Use of the Bernoulli Equation 214

6.3 The Bernoulli Equation Interpreted as an Energy Equation 215

6.4 Energy Grade Line and Hydraulic Grade Line 219

6.5 Unsteady Bernoulli Equation: Integration of Euler’s Equation Along a Streamline (on the Web) 221

*6.6 Irrotational Flow 221

Bernoulli Equation Applied to Irrotational Flow 221

Velocity Potential 222

Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace’s Equation 223

Elementary Plane Flows 225

Superposition of Elementary Plane Flows 227

6.7 Summary and Useful Equations 236

References 237

Problems 238

**CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE 245**

7.1 Nondimensionalizing the Basic Differential Equations 246

7.2 Nature of Dimensional Analysis 247

7.3 Buckingham Pi Theorem 249

7.4 Significant Dimensionless Groups in Fluid Mechanics 255

7.5 Flow Similarity and Model Studies 257

Incomplete Similarity 259

Scaling with Multiple Dependent Parameters 264

Comments on Model Testing 267

7.6 Summary and Useful Equations 268

References 269

Problems 269

**CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW 275**

8.1 Internal Flow Characteristics 276

Laminar versus Turbulent Flow 276

The Entrance Region 277

PART A. FULLY DEVELOPED LAMINAR FLOW 277

8.2 Fully Developed Laminar Flow Between Infinite Parallel Plates 277

Both Plates Stationary 278

Upper Plate Moving with Constant Speed, U 283

8.3 Fully Developed Laminar Flow in a Pipe 288

PART B. FLOW IN PIPES AND DUCTS 292

8.4 Shear Stress Distribution in Fully Developed Pipe Flow 293

8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow 294

8.6 Energy Considerations in Pipe Flow 297

Kinetic Energy Coefficient 298

Head Loss 298

8.7 Calculation of Head Loss 299

Major Losses: Friction Factor 299

Minor Losses 303

Pumps, Fans, and Blowers in Fluid Systems 308

Noncircular Ducts 309

8.8 Solution of Pipe Flow Problems 309

Single-Path Systems 310

Multiple-Path Systems 322

PART C. FLOW MEASUREMENT 326

8.9 Restriction Flow Meters for Internal Flows 326

The Orifice Plate 329

The Flow Nozzle 330

The Venturi 332

The Laminar Flow Element 332

Linear Flow Meters 335

Traversing Methods 336

8.10 Summary and Useful Equations 337

References 340

Problems 341

**CHAPTER 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW 352**

PART A. BOUNDARY LAYERS 354

9.1 The Boundary-Layer Concept 354

9.2 Laminar Flat-Plate Boundary Layer: Exact Solution (on the Web) 358

9.3 Momentum Integral Equation 358

9.4 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient 362

Laminar Flow 363

Turbulent Flow 367

Summary of Results for Boundary-Layer Flow with Zero Pressure Gradient 370

9.5 Pressure Gradients in Boundary-Layer Flow 370

PART B. FLUID FLOW ABOUT IMMERSED BODIES 373

9.6 Drag 373

Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow 374

Pure Pressure Drag: Flow over a Flat Plate Normal to the Flow 377

Friction and Pressure Drag: Flow over a Sphere and Cylinder 377

Streamlining 383

9.7 Lift 385

9.8 Summary and Useful Equations 399

References 401

Problems 402

**CHAPTER 10 FLUID MACHINERY 412**

10.1 Introduction and Classification of Fluid Machines 413

Machines for Doing Work on a Fluid 413

Machines for Extracting Work (Power) from a Fluid 415

Scope of Coverage 417

10.2 Turbomachinery Analysis 417

The Angular-Momentum Principle: The Euler Turbomachine Equation 417

Velocity Diagrams 419

Performance—Hydraulic Power 422

Dimensional Analysis and Specific Speed 423

10.3 Pumps, Fans, and Blowers 428

Application of Euler Turbomachine Equation to Centrifugal Pumps 428

Application of the Euler Equation to Axial Flow Pumps and Fans 429

Performance Characteristics 432

Similarity Rules 437

Cavitation and Net Positive Suction Head 441

Pump Selection: Applications to Fluid Systems 444

Blowers and Fans 455

10.4 Positive Displacement Pumps 461

10.5 Hydraulic Turbines 464

Hydraulic Turbine Theory 464

Performance Characteristics for Hydraulic Turbines 466

Sizing Hydraulic Turbines for Fluid Systems 470

10.6 Propellers and Wind-Power Machines 474

Propellers 474

Wind-Power Machines 482

10.7 Compressible Flow Turbomachines 490

Application of the Energy Equation to a Compressible Flow Machine 490

Compressors 491

Compressible-Flow Turbines 495

10.8 Summary and Useful Equations 495

References 497

Problems 499

**CHAPTER 11 FLOW IN OPEN CHANNELS 506**

11.1 Basic Concepts and Definitions 508

Simplifying Assumptions 508

Channel Geometry 510

Speed of Surface Waves and the Froude Number 511

11.2 Energy Equation for Open-Channel Flows 515

Specific Energy 517

Critical Depth: Minimum Specific Energy 520

11.3 Localized Effect of Area Change (Frictionless Flow) 523

Flow over a Bump 523

11.4 The Hydraulic Jump 527

Depth Increase Across a Hydraulic Jump 530

Head Loss Across a Hydraulic Jump 531

11.5 Steady Uniform Flow 533

The Manning Equation for Uniform Flow 535

Energy Equation for Uniform Flow 540

Optimum Channel Cross Section 542

11.6 Flow with Gradually Varying Depth 543

Calculation of Surface Profiles 544

11.7 Discharge Measurement Using Weirs 547

Suppressed Rectangular Weir 547

Contracted Rectangular Weirs 548

Triangular Weir 548

Broad-Crested Weir 549

11.8 Summary and Useful Equations 550

References 551

Problems 552

**CHAPTER 12 INTRODUCTION TO COMPRESSIBLE FLOW 555**

12.1 Review of Thermodynamics 556

12.2 Propagation of Sound Waves 562

Speed of Sound 562

Types of Flow—The Mach Cone 566

12.3 Reference State: Local Isentropic Stagnation Properties 569

Local Isentropic Stagnation Properties for the Flow of an Ideal Gas 570

12.4 Critical Conditions 576

12.5 Basic Equations for One-Dimensional Compressible Flow 576

Continuity Equation 576

Momentum Equation 577

First Law of Thermodynamics 577

Second Law of Thermodynamics 578

Equation of State 578

12.6 Isentropic Flow of an Ideal Gas: Area Variation 579

Subsonic Flow, M <1 581

Supersonic Flow, M >1 582

Sonic Flow, M =1 582

Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas 583

Isentropic Flow in a Converging Nozzle 588

Isentropic Flow in a Converging-Diverging Nozzle 592

12.7 Normal Shocks 597

Basic Equations for a Normal Shock 598

Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas 600

12.8 Supersonic Channel Flow with Shocks 604

12.8 Supersonic Channel Flow with Shocks (continued, at www.wiley.com/college/fox) 606

12.9 Flow in a Constant–Area Duct with Friction (www.wiley.com/college/fox) 606

12.10 Frictionless Flow in a Constant–Area Duct with Heat Exchange (www.wiley.com/college/fox) 606

12.11 Oblique Shocks and Expansion Waves (www.wiley.com/college/fox) 606

12.12 Summary and Useful Equations 606

References 609

Problems 609

APPENDIX A FLUID PROPERTY DATA 613

APPENDIX B VIDEOS FOR FLUID MECHANICS 624

APPENDIX C SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS 626

APPENDIX D FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW 641

APPENDIX E ANALYSIS OF EXPERIMENTAL UNCERTAINTY 644

APPENDIX F ADDITIONAL COMPRESSIBLE FLOW FUNCTIONS (WWW.WILEY.COM/COLLEGE/FOX) WF-1

APPENDIX G A BRIEF REVIEW OF MICROSOFT EXCEL (WWW.WILEY.COM/COLLEGE/FOX) WG-1

Answers to Selected Problems 650

Index 660

- Real-World Case Studies: A new case study begins each chapter, providing students with motivation and demonstrating how fluid mechanics concepts are applied to solve real-world problems.
- Restructured and Updated Chapters: Including chapters related to Internal Incompressible Viscous Flow, Flow Measurement, Compressible Flow
- Chapters 12 and 13 of the previous edition have been combined into one comprehensive chapter on Compressible Fluids

- This text is well regarded as an undergraduate textbook for its comprehensive treatment of all the main areas of fluid mechanics, as well as its level of presentation.
- Provides a proven, consistent problem-solving methodology: A consistent problem methodology is demonstrated in every example, demonstrating best practices for students.
- Includes over 100 detailed example problems illustrate important fluid mechanics concepts and incorporate problem-solving techniques that allow students to see the advantages of using a systematic procedure.
- More than 1,700 end-of-chapter problems with varying degrees of difficulty give instructors many options when creating assignments.
- Integration with Excel®: The problem-solving approach is integrated with Excel so instructors can focus more class time on fundamental concepts. 51 Example Excel® workbooks are available to present a variety of fluid mechanics phenomena, especially the effects produced when varying input parameters.
*CFD:*The section on basic concepts of computational fluid dynamics in Chapter 5 now includes material on using the spreadsheet for numerical analysis of simple 1D and 2D flows and includes an introduction to the Euler method.- Extensive explanations of theoretical derivations give instructors the choice to either review theory in class or assign it as homework so that lecture time can be more flexible.