Young, Munson and Okiishi's A Brief Introduction to Fluid Mechanics

1 Introduction 1

Learning Objectives 1

1.1 Some Characteristics of Fluids 3

1.2 Dimensions, Dimensional Homogeneity, and Units 4

1.2.1 Systems of Units 7

1.3 Analysis of Fluid Behavior 12

1.4 Measures of Fluid Mass and Weight 12

1.4.1 Density 12

1.4.2 Specific Weight 14

1.4.3 Specific Gravity 14

1.5 Ideal Gas Law 14

1.6 Viscosity 17

1.7 Compressibility of Fluids 23

1.7.1 Bulk Modulus 23

1.7.2 Compression and Expansion of Gases 24

1.7.3 Speed of Sound 25

1.8 Vapor Pressure 26

1.9 Surface Tension 27

1.10 A Brief Look Back in History 30

Chapter Summary and Study Guide 32

References 34

2 Fluid Statics 35

Learning Objectives 35

2.1 Pressure at a Point 35

2.2 Basic Equation for Pressure Field 36

2.3 Pressure Variation in a Fluid at Rest 38

2.3.1 Incompressible Fluid 39

2.3.2 Compressible Fluid 42

2.4 Standard Atmosphere 43

2.5 Measurement of Pressure 45

2.6 Manometry 47

2.6.1 Piezometer Tube 47

2.6.2 U-Tube Manometer 48

2.6.3 Inclined-Tube Manometer 50

2.7 Mechanical and Electronic Pressure-Measuring Devices 51

2.8 Hydrostatic Force on a Plane Surface 54

2.9 Pressure Prism 60

2.10 Hydrostatic Force on a Curved Surface 63

2.11 Buoyancy, Flotation, and Stability 65

2.11.1 Archimedes’ Principle 65

2.11.2 Stability 68

2.12 Pressure Variation in a Fluid with Rigid-Body Motion 70

Chapter Summary and Study Guide 70

References 71

3 Elementary Fluid Dynamics—The Bernoulli Equation 72

Learning Objectives 72

3.1 Newton’s Second Law 72

3.2 F = ma along a Streamline 75

3.3 F = ma Normal to a Streamline 79

3.4 Physical Interpretations and Alternate Forms of the Bernoulli Equation 81

3.5 Static, Stagnation, Dynamic, and Total Pressure 83

3.6 Examples of Use of the Bernoulli Equation 87

3.6.1 Free Jets 87

3.6.2 Confined Flows 90

3.6.3 Flowrate Measurement 96

3.7 The Energy Line and the Hydraulic Grade Line 100

3.8 Restrictions on Use of the Bernoulli Equation 103

Chapter Summary and Study Guide 103

References 105

4 Fluid Kinematics 106

Learning Objectives 106

4.1 The Velocity Field 106

4.1.1 Eulerian and Lagrangian Flow Descriptions 109

4.1.2 One-, Two-, and Three-Dimensional Flows 110

4.1.3 Steady and Unsteady Flows 111

4.1.4 Streamlines, Streaklines, and Pathlines 111

4.2 The Acceleration Field 115

4.2.1 Acceleration and the Material Derivative 115

4.2.2 Unsteady Effects 118

4.2.3 Convective Effects 118

4.2.4 Streamline Coordinates 121

4.3 Control Volume and System Representations 122

4.4 The Reynolds Transport Theorem 123

4.4.1 Derivation of the Reynolds Transport Theorem 125

4.4.2 Selection of a Control Volume 129

Chapter Summary and Study Guide 130

References 131

5 Finite Control Volume Analysis 132

Learning Objectives 132

5.1 Conservation of Mass—The Continuity Equation 132

5.1.1 Derivation of the Continuity Equation 132

5.1.2 Fixed, Nondeforming Control Volume 134

5.1.3 Moving, Nondeforming Control Volume 140

5.2 Newton’s Second Law—The Linear Momentum and Moment-of-Momentum Equations 143

5.2.1 Derivation of the Linear Momentum Equation 143

5.2.2 Application of the Linear Momentum Equation 144

5.2.3 Derivation of the Moment-of-Momentum Equation 157

5.2.4 Application of the Moment-of-Momentum Equation 159

5.3 First Law of Thermodynamics—The Energy Equation 165

5.3.1 Derivation of the Energy Equation 165

5.3.2 Application of the Energy Equation 168

5.3.3 The Mechanical Energy Equation and the Bernoulli Equation 172

5.3.4 Application of the Energy Equation to Nonuniform Flows 177

5.3.5 Comparison of Various Forms of the Energy Equation 178

Chapter Summary and Study Guide 182

References 183

6 Differential Analysis of Fluid Flow 184

Learning Objectives 184

6.1 Fluid Element Kinematics 185

6.1.1 Velocity and Acceleration Fields Revisited 185

6.1.2 Linear Motion and Deformation 186

6.1.3 Angular Motion and Deformation 187

6.2 Conservation of Mass 190

6.2.1 Differential Form of Continuity Equation 190

6.2.2 Cylindrical Polar Coordinates 192

6.2.3 The Stream Function 193

6.3 The Linear Momentum Equation 196

6.3.1 Description of Forces Acting on the Differential Element 197

6.3.2 Equations of Motion 199

6.4 Inviscid Flow 200

6.4.1 Euler’s Equations of Motion 200

6.4.2 The Bernoulli Equation 201

6.4.3 Irrotational Flow 202

6.4.4 The Bernoulli Equation for Irrotational Flow 203

6.4.5 The Velocity Potential 203

6.5 Some Basic, Plane Potential Flows 206

6.5.1 Uniform Flow 208

6.5.2 Source and Sink 208

6.5.3 Vortex 210

6.5.4 Doublet 213

6.6 Superposition of Basic, Plane Potential Flows 215

6.6.1 Source in a Uniform Stream—Half-Body 215

6.6.2 Flow Around a Circular Cylinder 218

6.7 Other Aspects of Potential Flow Analysis 224

6.8 Viscous Flow 225

6.8.1 Stress–Deformation Relationships 225

6.8.2 The Navier–Stokes Equations 226

6.9 Some Simple Solutions for Laminar, Viscous, Incompressible Flows 227

6.9.1 Steady, Laminar Flow Between Fixed Parallel Plates 228

6.9.2 Couette Flow 230

6.9.3 Steady, Laminar Flow in Circular Tubes 232

6.10 Other Aspects of Differential Analysis 234

Chapter Summary and Study Guide 235

References 237

7 Dimensional Analysis, Similitude, and Modeling 238

Learning Objectives 238

7.1 The Need for Dimensional Analysis 239

7.2 Buckingham Pi Theorem 241

7.3 Determination of Pi Terms 241

7.4 Some Additional Comments about Dimensional Analysis 247

7.4.1 Selection of Variables 247

7.4.2 Determination of Reference Dimensions 248

7.4.3 Uniqueness of Pi Terms 249

7.5 Determination of Pi Terms by Inspection 250

7.6 Common Dimensionless Groups in Fluid Mechanics 251

7.7 Correlation of Experimental Data 253

7.7.1 Problems with One Pi Term 253

7.7.2 Problems with Two or More Pi Terms 254

7.8 Modeling and Similitude 257

7.8.1 Theory of Models 257

7.8.2 Model Scales 260

7.8.3 Practical Aspects of Using Models 261

7.9 Some Typical Model Studies 262

7.9.1 Flow Through Closed Conduits 262

7.9.2 Flow Around Immersed Bodies 264

7.9.3 Flow with a Free Surface 267

Chapter Summary and Study Guide 269

References 271

8 Viscous Flow in Pipes 272

Learning Objectives 272

8.1 General Characteristics of Pipe Flow 273

8.1.1 Laminar or Turbulent Flow 273

8.1.2 Entrance Region and Fully Developed Flow 275

8.2 Fully Developed Laminar Flow 276

8.2.1 From F = ma Applied Directly to a Fluid Element 276

8.2.2 From the Navier–Stokes Equations 281

8.3 Fully Developed Turbulent Flow 281

8.3.1 Transition from Laminar to Turbulent Flow 281

8.3.2 Turbulent Shear Stress 283

8.3.3 Turbulent Velocity Profile 284

8.4 Pipe Flow Losses via Dimensional Analysis 286

8.4.1 Major Losses 286

8.4.2 Minor Losses 291

8.4.3 Noncircular Conduits 301

8.5 Pipe Flow Examples 304

8.5.1 Single Pipes 304

8.5.2 Multiple Pipe Systems 313

8.6 Pipe Flowrate Measurement 316

Chapter Summary and Study Guide 319

References 321

9 Flow over Immersed Bodies 322

Learning Objectives 322

9.1 General External Flow Characteristics 322

9.1.1 Lift and Drag Concepts 323

9.1.2 Characteristics of Flow Past an Object 325

9.2 Boundary Layer Characteristics 330

9.2.1 Boundary Layer Structure and Thickness on a Flat Plate 330

9.2.2 Prandtl / Blasius Boundary Layer Solution 333

9.2.3 Momentum Integral Boundary Layer Equation for a Flat Plate 335

9.2.4 Transition from Laminar to Turbulent Flow 337

9.2.5 Turbulent Boundary Layer Flow 339

9.2.6 Effects of Pressure Gradient 343

9.3 Drag 346

9.3.1 Friction Drag 346

9.3.2 Pressure Drag 346

9.3.3 Drag Coefficient Data and Examples 347

9.4 Lift 358

9.4.1 Surface Pressure Distribution 360

9.4.2 Circulation 363

Chapter Summary and Study Guide 365

References 367

10 Open-Channel Flow 368

Learning Objectives 368

10.1 General Characteristics of Open-Channel Flow 368

10.2 Surface Waves 369

10.2.1 Wave Speed 370

10.2.2 Froude Number Effects 372

10.3 Energy Considerations 373

10.3.1 Energy Balance 373

10.3.2 Specific Energy 374

10.4 Uniform Flow 377

10.4.1 Uniform Flow Approximations 377

10.4.2 The Chezy and Manning Equations 378

10.4.3 Uniform Flow Examples 381

10.5 Gradually Varied Flow 386

10.6 Rapidly Varied Flow 386

10.6.1 The Hydraulic Jump 387

10.6.2 Sharp-Crested Weirs 391

10.6.3 Broad-Crested Weirs 393

10.6.4 Underflow (Sluice) Gates 395

Chapter Summary and Study Guide 397

References 398

11 Turbomachines 399

Learning Objectives 399

11.1 Introduction 400

11.2 Basic Energy Considerations 401

11.3 Angular Momentum Considerations 405

11.4 The Centrifugal Pump 406

11.4.1 Theoretical Considerations 407

11.4.2 Pump Performance Characteristics 410

11.4.3 System Characteristics, Pump-System Matching, and Pump Selection 412

11.5 Dimensionless Parameters and Similarity Laws 416

11.5.1 Specific Speed 418

11.6 Axial-Flow and Mixed-Flow Pumps 419

11.7 Fans 422

11.8 Turbines 422

11.8.1 Impulse Turbines 423

11.8.2 Reaction Turbines 430

11.9 Compressible Flow Turbomachines 433

Chapter Summary and Study Guide 433

References 435

Appendix A Computational Fluid Dynamics 436

Appendix B Physical Properties of Fluids 448

Appendix C Properties of the U.S. Standard Atmosphere 453

Appendix D Comprehensive Table of Conversion Factors 455

Questions and Problems SP-1

Chapter 1 SP-1

Chapter 2 SP-9

Chapter 3 SP-26

Chapter 4 SP-41

Chapter 5 SP-48

Chapter 6 SP-66

Chapter 7 SP-76

Chapter 8 SP-84

Chapter 9 SP-96

Chapter 10 SP-105

Chapter 11 SP-110

Index I-1