1 Intoduction 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 32

Key Equations 33

References 33

Questions And Problems 33

2 Fluid Statics 40

Learning Objectives 40

2.1 Pressure At A Point 40

2.2 Basic Equation For Pressure Field 41

2.3 Pressure Variation In A Fluid At Rest 43

2.3.1 Incompressible Fluid 44

2.3.2 Compressible Fluid 47

2.4 Standard Atmosphere 48

2.5 Measurement Of Pressure 50

2.6 Manometry 52

2.6.1 Piezometer Tube 52

2.6.2 U-Tube Manometer 53

2.6.3 Inclined-Tube Manometer 55

2.7 Mechanical And Electronic Pressure-Measuring Devices 56

2.8 Hydrostatic Force On A Plane Surface And Pressure Diagram 59

2.8.1 Hydrostatic Force 59

2.8.2 Pressure Diagram 65

2.9 Hydrostatic Force On A Curved Surface 68

2.10 Buoyancy, Flotation, And Stability 70

2.10.1 Archimedes' Principle 70

2.10.2 The Stability Of Bodies In Fluids 73

2.11 Pressure Variation In A Fluid With Rigid-Body Motion 75

2.11.1 Linear Motion 75

2.11.2 Rigid-Body Rotation 77

2.12 Equilibrium Of Moving Fluids (Special Case Of Fluid Statics) 79

Chapter Summary 80

Key Equations 80

References 81

Questions And Problems 81

3 Fluid Kinematics 99

Learning Objectives 99

3.1 The Velocity Field 99

3.1.1 Eulerian And Lagrangian Flow Descriptions 101

3.1.2 One-, Two-, And Threedimensional Flows 103

3.1.3 Steady And Unsteady Flows 104

3.1.4 Flow Patterns: Streamlines, Streaklines, And Pathlines 105

3.2 The Acceleration Field 108

3.2.1 Acceleration And The Material Derivative 109

3.2.2 Unsteady Effects 112

3.2.3 Convective Effects 112

3.2.4 Streamline Coordinates 115

3.3 Control Volume And System Representations 117

3.4 The Reynolds Transport Theorem 119

3.4.1 Derivation Of The Reynolds Transport Theorem 121

3.4.2 Physical Interpretation 125

3.4.3 Relationship To Material Derivative 126

3.4.4 Steady And Unsteady Effects 126

3.4.5 Moving Control Volumes 128

3.4.6 Selection Of A Control Volume 130

Chapter Summary 130

Key Equations 131

References 131

Questions And Problems 131

4 Elementary Fluid Dynamics- The Bernoulli Equation 139

Learning Objectives 139

4.1 Newton's Second Law 139

4.2 F = Ma Along A Streamline 142

4.3 F = Ma Normal To A Streamline 146

4.4 Physical Interpretations And Alternate Forms Of The Bernoulli Equation 148

4.5 Static, Stagnation, Dynamic, And Total Pressure 151

4.6 Applications Of The Bernoulli Equation 156

4.6.1 Free Jets 156

4.6.2 Confined Flows 159

4.6.3 Flowrate Measurement 165

4.7 The Energy Line And The Hydraulic Grade Line 170

4.8 Restrictions On Use Of The Bernoulli Equation 172

4.8.1 Compressibility Effects 172

4.8.2 Unsteady Effects 173

4.8.3 Rotational Effects 174

4.8.4 Other Restrictions 175

Chapter Summary 176

Key Equations 176

References 177

Questions And Problems 177

5 Finite Control Volume Analysis 192

Learning Objectives 192

5.1 Conservation Of Mass-The Continuity Equation 193

5.1.1 Derivation Of The Continuity Equation 193

5.1.2 Fixed, Nondeforming Control Volume 195

5.1.3 Moving, Nondeforming Control Volume 201

5.1.4 Deforming Control Volume 203

5.2 Newton's Second Law-The Linear Momentum And Moment-Of-Momentum Equations 205

5.2.1 Derivation Of The Linear Momentum Equation 205

5.2.2 Application Of The Linear Momentum Equation 206

5.2.3 Derivation Of The Moment-Of-Momentum Equation 219

5.2.4 Application Of The Moment-Ofmomentum Equation 221

5.3 First Law Of Thermodynamics- The Energy Equation 227

5.3.1 Derivation Of The Energy Equation 227

5.3.2 Application Of The Energy Equation 230

5.3.3 The Mechanical Energy Equation And The Bernoulli Equation 234

5.3.4 Application Of The Energy Equation To Nonuniform Flows 240

5.3.5 Comparison Of Various Forms Of The Energy Equation 242

5.3.6 Combination Of The Energy Equation And The Moment-Of-Momentum Equation 244

Chapter Summary 245

Key Equations 245

References 246

Questions And Problems 246

6 Differential Analysis Of Fluid Flow 262

Learning Objectives 262

6.1 Fluid Element Kinematics 263

6.1.1 Velocity And Acceleration Fields Revisited 263

6.1.2 Linear Motion And Deformation 264

6.1.3 Angular Motion And Deformation 265

6.2 Conservation Of Mass 268

6.2.1 Differential Form Of Continuity Equation 268

6.2.2 Cylindrical Polar Coordinates 271

6.2.3 The Stream Function 271

6.3 The Linear Momentum Equation 274

6.3.1 Description Of Forces Acting On The Differential Element 275

6.3.2 Equations Of Motion 277

6.4 Inviscid Flow 278

6.4.1 Euler's Equations Of Motion 278

6.4.2 The Bernoulli Equation 279

6.4.3 Irrotational Flow 280

6.4.4 The Bernoulli Equation For Irrotational Flow 282

6.4.5 The Velocity Potential 283

6.5 Some Basic, Plane Potential Flows 285

6.5.1 Uniform Flow 287

6.5.2 Source And Sink 287

6.5.3 Vortex 289

6.5.4 Doublet 292

6.6 Superposition Of Basic, Plane Potential Flows 294

6.6.1 Source In A Uniform Stream-Half-Body 294

6.6.2 Rankine Ovals 297

6.6.3 Flow Around A Circular Cylinder 299

6.7 Other Aspects Of Potential Flow 305

6.8 Viscous Flow 305

6.8.1 Stress-Deformation Relationships 306

6.8.2 The Navier-Stokes Equations 306

6.9 Some Simple Solutions For Laminar, Viscous, Incompressible Flows 308

6.9.1 Steady, Laminar Flow Between Fixed Parallel Plates 308

6.9.2 Couette Flow 310

6.9.3 Steady, Laminar Flow In Circular Tubes 312

6.9.4 Steady, Axial, Laminar Flow In An Annulus 315

6.10 Other Aspects Of Differential Analysis 317

6.10.1 Numerical Methods 317

Chapter Summary 318

Key Equations 318

References 319

Questions And Problems 319

7 Dimensional Analysis, Similitude, And Modeling 329

Learning Objectives 329

7.1 The Need For Dimensional Analysis 330

7.2 Buckingham Pi Theorem 332

7.3 Determination Of Pi Terms 333

7.4 Some Directions About Dimensional Analysis 339

7.4.1 Selection Of Variables 339

7.4.2 Determination Of Reference Dimensions 340

7.4.3 Uniqueness Of Pi Terms 340

7.5 Determination Of Pi Terms By Inspection 342

7.6 Common Dimensionless Groups In Fluid Mechanics 344

7.7 Correlation Of Experimental Data 349

7.7.1 Problems With One Pi Term 349

7.7.2 Problems With Two Or More Pi Terms 350

7.8 Modeling And Similitude 352

7.8.1 Theory Of Models 353

7.8.2 Model Scales 356

7.8.3 Practical Aspects Of Using Models 357

7.9 Typical Model Studies 359

7.9.1 Flow Through Closed Conduits 359

7.9.2 Flow Around Immersed Bodies 361

7.9.3 Flow With A Free Surface 365

7.10 Similitude Based On Governing Differential Equations 368

Chapter Summary 371

Key Equations 371

References 372

Questions And Problems 372

8 Viscous Flow In Pipes 382

Learning Objectives 382

8.1 General Characteristics Of Pipe Flow 383

8.1.1 Laminar Or Turbulent Flow 384

8.1.2 Entrance Region And Fully Developed Flow 386

8.1.3 Pressure And Shear Stress 387

8.2 Fully Developed Laminar Flow 388

8.2.1 From F = Ma Applied Directly To A Fluid Element 389

8.2.2 From The Navier-Stokes Equations 393

8.2.3 From Dimensional Analysis 394

8.2.4 Energy Considerations 395

8.3 Fully Developed Turbulent Flow 397

8.3.1 Transition From Laminar To Turbulent Flow 397

8.3.2 Turbulent Shear Stress 399

8.3.3 Turbulent Velocity Profile 404

8.3.4 Turbulence Modeling 407

8.3.5 Chaos And Turbulence 408

8.4 Pipe Flow Losses Via Dimensional Analysis 408

8.4.1 Major Losses 408

8.4.2 Minor Losses 414

8.4.3 Noncircular Conduits 423

8.5 Pipe Flow Examples 426

8.5.1 Single Pipes 426

8.5.2 Multiple Pipe Systems 435

8.6 Pipe Flowrate Measurement 439

8.6.1 Pipe Flowrate Meters 439

8.6.2 Volume Flowmeters 444

8.6.3 Multiphase Flow Measurement In Pipes 445

8.6.4 Water Hammer And Their Measurements In Pipes 445

Chapter Summary 447

Key Equations 448

References 448

Questions And Problems 449

9 Flow Over Immersed Bodies 462

Learning Objectives 462

9.1 General External Flow Characteristics 463

9.1.1 Lift And Drag Concepts 464

9.1.2 Characteristics Of Flow Past An Object 467

9.2 Boundary Layer Characteristics 471

9.2.1 Boundary Layer Structure And Thickness On A Flat Plate 471

9.2.2 Prandtl / Blasius Boundary Layer Solution 474