Introduction To Fluid Mechanics

1 INTRODUCTION 1

1.1 Some Characteristics of Fluids 3

1.2 Dimensions, Dimensional Homogeneity, and Units 3

1.2.1 Systems of Units 6

1.3 Analysis of Fluid Behavior 9

1.4 Measures of Fluid Mass and Weight 9

1.4.1 Density 9

1.4.2 Specific Weight 10

1.4.3 Specific Gravity 10

1.5 Ideal Gas Law 11

1.6 Viscosity 12

1.7 Compressibility of Fluids 17

1.7.1 Bulk Modulus 17

1.7.2 Compression and Expansion of Gases 18

1.7.3 Speed of Sound 19

1.8 Vapor Pressure 21

1.9 Surface Tension 21

1.10 A Brief Look Back in History 24

1.11 Chapter Summary and Study Guide 27

Review Problems 28

Problems 28

2 FLUID STATICS 32

2.1 Pressure at a Point 33

2.2 Basic Equation for Pressure Field 34

2.3 Pressure Variation in a Fluid at Rest 36

2.3.1 Incompressible Fluid 36

2.3.2 Compressible Fluid 38

2.4 Standard Atmosphere 39

2.5 Measurement of Pressure 39

2.6 Manometry 42

2.6.1 Piezometer Tube 42

2.6.2 U-Tube Manometer 43

2.6.3 Inclined-Tube Manometer 46

2.7 Mechanical and Electronic Pressure-Measuring Devices 47

2.8 Hydrostatic Force on a Plane Surface 47

2.9 Pressure Prism 52

2.10 Hydrostatic Force on a Curved Surface 54

2.11 Buoyancy, Flotation, and Stability 57

2.11.1 Archimedes’ Principle 57

2.11.2 Stability 59

2.12 Pressure Variation in a Fluid with Rigid-Body Motion 60

2.13 Chapter Summary and Study Guide 60

References 61

Review Problems 62

Problems 62

3 ELEMENTARY FLUID DYNAMICS—THE BERNOULLI EQUATION 68

3.1 Newton’s Second Law 69

3.2 F ma Along a Streamline 70

3.3 F ma Normal to a Streamline 74

3.4 Physical Interpretation 75

3.5 Static, Stagnation, Dynamic, and Total Pressure 78

3.6 Examples of Use of the Bernoulli Equation 81

3.6.1 Free Jets 81

3.6.2 Confined Flows 82

3.6.3 Flowrate Measurement 89

3.7 The Energy Line and the Hydraulic Grade Line 92

3.8 Restrictions on the Use of the Bernoulli Equation 94

3.9 Chapter Summary and Study Guide 95

Review Problems 96

Problems 97

4 FLUID KINEMATICS 102

4.1 The Velocity Field 103

4.1.1 Eulerian and Lagrangian Flow Descriptions 105

4.1.2 One-, Two-, and Three-Dimensional Flows 105

4.1.3 Steady and Unsteady Flows 106

4.1.4 Streamlines, Streaklines, and Pathlines 107

4.2 The Acceleration Field 110

4.2.1 The Material Derivative 110

4.2.2 Unsteady Effects 112

4.2.3 Convective Effects 113

4.2.4 Streamline Coordinates 114

4.3 Control Volume and System Representations 115

4.4 The Reynolds Transport Theorem 116

4.4.1 Derivation of the Reynolds Transport Theorem 116

4.4.2 Selection of a Control Volume 120

4.5 Chapter Summary and Study Guide 120

References 121

Review Problems 121

Problems 121

5 FINITE CONTROL VOLUME ANALYSIS 125

5.1 Conservation of Mass—The Continuity Equation 126

5.1.1 Derivation of the Continuity Equation 126

5.1.2 Fixed, Nondeforming Control Volume 127

5.1.3 Moving, Nondeforming Control Volume 131

5.2 Newton’s Second Law—The Linear Momentum and Moment-of-Momentum Equations 133

5.2.1 Derivation of the Linear Momentum Equation 133

5.2.2 Application of the Linear Momentum Equation 134

5.2.3 Derivation of the Moment-of-Momentum Equation 144

5.2.4 Application of the Moment-of-Momentum Equation 145

5.3 First Law of Thermodynamics—The Energy Equation 152

5.3.1 Derivation of the Energy Equation 152

5.3.2 Application of the Energy Equation 154

5.3.3 Comparison of the Energy Equation with the Bernoulli Equation 157

5.3.4 Application of the Energy Equation to Nonuniform Flows 162

5.4 Chapter Summary and Study Guide 164

Review Problems 166

Problems 166

6 DIFFERENTIAL ANALYSIS OF FLUID FLOW 175

6.1 Fluid Element Kinematics 176

6.1.1 Velocity and Acceleration Fields Revisited 176

6.1.2 Linear Motion and Deformation 177

6.1.3 Angular Motion and Deformation 179

6.2 Conservation of Mass 182

6.2.1 Differential Form of Continuity Equation 182

6.2.2 Cylindrical Polar Coordinates 184

6.2.3 The Stream Function 185

6.3 Conservation of Linear Momentum 188

6.3.1 Description of Forces Acting on Differential Element 189

6.3.2 Equations of Motion 191

6.4 Inviscid Flow 192

6.4.1 Euler’s Equations of Motion 192

6.4.2 The Bernoulli Equation 193

6.4.3 Irrotational Flow 195

6.4.4 The Bernoulli Equation for Irrotational Flow 196

6.4.5 The Velocity Potential 196

6.5 Some Basic, Plane Potential Flows 199

6.5.1 Uniform Flow 201

6.5.2 Source and Sink 201

6.5.3 Vortex 203

6.5.4 Doublet 207

6.6 Superposition of Basic, Plane Potential Flows 209

6.6.1 Source in a Uniform Stream—Half-Body 209

6.6.2 Flow around a Circular Cylinder 212

6.7 Other Aspects of Potential Flow Analysis 219

6.8 Viscous Flow 219

6.8.1 Stress–Deformation Relationships 219

6.8.2 The Navier–Stokes Equations 220

6.9 Some Simple Solutions for Laminar, Viscous, Incompressible Fluids 221

6.9.1 Steady, Laminar Flow between Fixed Parallel Plates 222

6.9.2 Couette Flow 224

6.9.3 Steady, Laminar Flow in Circular Tubes 227

6.10 Other Aspects of Differential Analysis 229

6.11 Chapter Summary and Study Guide 230

References 232

Review Problems 232

Problems 232

7 SIMILITUDE, DIMENSIONAL ANALYSIS, AND MODELING 238

7.1 Dimensional Analysis 239

7.2 Buckingham Pi Theorem 240

7.3 Determination of Pi Terms 241

7.4 Some Additional Comments about Dimensional Analysis 246

7.4.1 Selection of Variables 247

7.4.2 Determination of Reference Dimensions 247

7.4.3 Uniqueness of Pi Terms 247

7.5 Determination of Pi Terms by Inspection 248

7.6 Common Dimensionless Groups in Fluid Mechanics 249

7.7 Correlation of Experimental Data 250

7.7.1 Problems with One Pi Term 251

7.7.2 Problems with Two or More Pi Terms 252

7.8 Modeling and Similitude 254

7.8.1 Theory of Models 254

7.8.2 Model Scales 258

7.8.3 Distorted Models 259

7.9 Some Typical Model Studies 260

7.9.1 Flow through Closed Conduits 260

7.9.2 Flow around Immersed Bodies 262

7.9.3 Flow with a Free Surface 264

7.10 Chapter Summary and Study Guide 267

References 268

Review Problems 269

Problems 269

8 VISCOUS FLOW IN PIPES 274

8.1 General Characteristics of Pipe Flow 275

8.1.1 Laminar or Turbulent Flow 275

8.1.2 Entrance Region and Fully Developed Flow 277

8.2 Fully Developed Laminar Flow 278

8.2.1 From F ma Applied Directly to a Fluid Element 278

8.2.2 From the Navier–Stokes Equations 282

8.3 Fully Developed Turbulent Flow 282

8.3.1 Transition from Laminar to Turbulent Flow 283

8.3.2 Turbulent Shear Stress 284

8.3.3 Turbulent Velocity Profile 285

8.4 Dimensional Analysis of Pipe Flow 285

8.4.1 Major Losses 286

8.4.2 Minor Losses 290

8.4.3 Noncircular Conduits 298

8.5 Pipe Flow Examples 299

8.5.1 Single Pipes 300

8.5.2 Multiple Pipe Systems 307

8.6 Pipe Flowrate Measurement 309

8.7 Chapter Summary and Study Guide 313

References 314

Review Problems 315

Problems 315

9 FLOW OVER IMMERSED BODIES 321

9.1 General External Flow Characteristics 322

9.1.1 Lift and Drag Concepts 322

9.1.2 Characteristics of Flow Past an Object 325

9.2 Boundary Layer Characteristics 328

9.2.1 Boundary Layer Structure and Thickness on a Flat Plate 328

9.2.2 Prandtl/Blasius Boundary Layer Solution 330

9.2.3 Momentum Integral Boundary Layer Equation for a Flat Plate 332

9.2.4 Transition from Laminar to Turbulent Flow 334

9.2.5 Turbulent Boundary Layer Flow 336

9.2.6 Effects of Pressure Gradient 338

9.3 Drag 341

9.3.1 Friction Drag 342

9.3.2 Pressure Drag 342

9.3.3 Drag Coefficient Data and Examples 343

9.4 Lift 357

9.4.1 Surface Pressure Distribution 357

9.4.2 Circulation 361

9.5 Chapter Summary and Study Guide 363

References 364

Review Problems 364

Problems 364

10 OPEN-CHANNEL FLOW 370

10.1 General Characteristics of Open-Channel Flow 370

10.2 Surface Waves 371

10.2.1 Wave Speed 372

10.2.2 Froude Number Effects 374

10.3 Energy Considerations 374

10.3.1 Specific Energy 375

10.4 Uniform Depth Channel Flow 378

10.4.1 Uniform Flow Approximations 378

10.4.2 The Chezy and Manning Equations 378

10.4.3 Uniform Depth Examples 381

10.5 Gradually Varied Flow 385

10.6 Rapidly Varied Flow 386

10.6.1 The Hydraulic Jump 386

10.6.2 Sharp-Crested Weirs 390

10.6.3 Broad-Crested Weirs 393

10.6.4 Underflow Gates 395

10.7 Chapter Summary and Study Guide 397

References 398

Review Problems 398

Problems 398

11 TURBOMACHINES 403

11.1 Introduction 404

11.2 Basic Energy Considerations 404

11.3 Basic Angular Momentum Considerations 408

11.4 The Centrifugal Pump 410

11.4.1 Theoretical Considerations 410

11.4.2 Pump Performance Characteristics 414

11.4.3 System Characteristics and Pump Selection 416

11.5 Dimensionless Parameters and Similarity Laws 419

11.5.1 Specific Speed 422

11.6 Axial-Flow and Mixed-Flow Pumps 423

11.7 Turbines 426

11.7.1 Impulse Turbines 427

11.7.2 Reaction Turbines 433

11.8 Compressible Flow Turbomachines 436

11.9 Chapter Summary and Study Guide 437

References 438

Review Problems 439

Problems 439

A COMPUTATIONAL FLUID DYNAMICS AND FLOWLAB 443

B PHYSICAL PROPERTIES OF FLUIDS 458

C PROPERTIES OF THE U.S. STANDARD ATMOSPHERE 463

D REYNOLDS TRANSPORT THEOREM 465

E COMPREHENSIVE TABLE OF CONVERSION FACTORS 470

ONLINE APPENDIX LIST 474