1 Introduction 1
Learning Objectives 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
Chapter Summary and Study Guide 27
Review Problems 28
Problems 28
2 Fluid Statics 32
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
2.12.1 Linear Motion 70
2.12.2 Rigid-Body Rotation 72
Chapter Summary and Study Guide 74
References 75
3 Elementary Fluid Dynamics—The Bernoulli Equation 76
Learning Objectives 76
3.1 Newton’s Second Law 76
3.2 F = ma along a Streamline 79
3.3 F = ma Normal to a Streamline 83
3.4 Physical Interpretations and Alternate Forms of the Bernoulli Equation 85
3.5 Static, Stagnation, Dynamic, and Total Pressure 88
3.6 Examples of Use of the Bernoulli Equation 93
3.6.1 Free Jets 93
3.6.2 Confined Flows 96
3.6.3 Flowrate Measurement 102
3.7 The Energy Line and the Hydraulic Grade Line 106
3.8 Restrictions on Use of the Bernoulli Equation 109
3.8.1 Compressibility Effects 109
3.8.2 Unsteady Effects 110
3.8.3 Rotational Effects 111
3.8.4 Other Restrictions 112
Chapter Summary and Study Guide 113
References 114
4 Fluid Kinematics 115
Learning Objectives 115
4.1 The Velocity Field 115
4.1.1 Eulerian and Lagrangian Flow Descriptions 118
4.1.2 One-, Two-, and Three-Dimensional Flows 119
4.1.3 Steady and Unsteady Flows 120
4.1.4 Streamlines, Streaklines, and Pathlines 120
4.2 The Acceleration Field 124
4.2.1 Acceleration and the Material Derivative 124
4.2.2 Unsteady Effects 127
4.2.3 Convective Effects 127
4.2.4 Streamline Coordinates 130
4.3 Control Volume and System Representations 132
4.4 The Reynolds Transport Theorem 134
4.4.1 Derivation of the Reynolds Transport Theorem 136
4.4.2 Physical Interpretation 141
4.4.3 Relationship to Material Derivative 141
4.4.4 Steady Effects 142
4.4.5 Unsteady Effects 142
4.4.6 Moving Control Volumes 143
4.4.7 Selection of a Control Volume 145
Chapter Summary and Study Guide 145
References 146
5 Finite Control Volume Analysis 147
Learning Objectives 147
5.1 Conservation of Mass—The Continuity Equation 148
5.1.1 Derivation of the Continuity Equation 148
5.1.2 Fixed, Nondeforming Control Volume 150
5.1.3 Moving, Nondeforming Control Volume 156
5.1.4 Deforming Control Volume 158
5.2 Newton’s Second Law—The Linear Momentum and Moment-of-Momentum Equations 160
5.2.1 Derivation of the Linear Momentum Equation 160
5.2.2 Application of the Linear Momentum Equation 161
5.2.3 Derivation of the Moment-of-Momentum Equation 174
5.2.4 Application of the Moment-of-Momentum Equation 176
5.3 First Law of Thermodynamics—The Energy Equation 182
5.3.1 Derivation of the Energy Equation 182
5.3.2 Application of the Energy Equation 185
5.3.3 The Mechanical Energy Equation and the Bernoulli Equation 189
5.3.4 Application of the Energy Equation to Nonuniform Flows 195
5.3.5 Comparison of Various Forms of the Energy Equation 197
5.3.6 Combination of the Energy Equation and the Moment-of-Momentum Equation 199
5.4 Second Law of Thermodynamics—Irreversible Flow 200
5.4.1 Semi-infinitesimal Control Volume Statement of the Energy Equation 200
5.4.2 Semi-infinitesimal Control Volume Statement of the Second Law of Thermodynamics 201
5.4.3 Combination of the Equations of the First and Second Laws of Thermodynamics 202
Chapter Summary and Study Guide 203
References 204
6 Differential Analysis of Fluid Flow 205
Learning Objectives 205
6.1 Fluid Element Kinematics 206
6.1.1 Velocity and Acceleration Fields Revisited 206
6.1.2 Linear Motion and Deformation 207
6.1.3 Angular Motion and Deformation 208
6.2 Conservation of Mass 211
6.2.1 Differential Form of Continuity Equation 211
6.2.2 Cylindrical Polar Coordinates 214
6.2.3 The Stream Function 214
6.3 The Linear Momentum Equation 217
6.3.1 Description of Forces Acting on the Differential Element 218
6.3.2 Equations of Motion 220
6.4 Inviscid Flow 221
6.4.1 Euler’s Equations of Motion 221
6.4.2 The Bernoulli Equation 222
6.4.3 Irrotational Flow 223
6.4.4 The Bernoulli Equation for Irrotational Flow 225
6.4.5 The Velocity Potential 226
6.5 Some Basic, Plane Potential Flows 228
6.5.1 Uniform Flow 230
6.5.2 Source and Sink 230
6.5.3 Vortex 232
6.5.4 Doublet 235
6.6 Superposition of Basic, Plane Potential Flows 237
6.6.1 Source in a Uniform Stream—Half-Body 237
6.6.2 Rankine Ovals 240
6.6.3 Flow Around a Circular Cylinder 242
6.7 Other Aspects of Potential Flow Analysis 248
6.8 Viscous Flow 248
6.8.1 Stress–Deformation Relationships 249
6.8.2 The Navier–Stokes Equations 249
6.9 Some Simple Solutions for Laminar, Viscous, Incompressible Flows 251
6.9.1 Steady, Laminar Flow Between Fixed Parallel Plates 251
6.9.2 Couette Flow 253
6.9.3 Steady, Laminar Flow in Circular Tubes 255
6.9.4 Steady, Axial, Laminar Flow in an Annulus 258
6.10 Other Aspects of Differential Analysis 260
6.10.1 Numerical Methods 260
Chapter Summary and Study Guide 261
References 262
7 Dimensional Analysis, Similitude, and Modeling 263
Learning Objectives 263
7.1 The Need for Dimensional Analysis 264
7.2 Buckingham Pi Theorem 266
7.3 Determination of Pi Terms 267
7.4 Some Additional Comments about Dimensional Analysis 273
7.4.1 Selection of Variables 273
7.4.2 Determination of Reference Dimensions 274
7.4.3 Uniqueness of Pi Terms 276
7.5 Determination of Pi Terms by Inspection 276
7.6 Common Dimensionless Groups in Fluid Mechanics 278
7.7 Correlation of Experimental Data 283
7.7.1 Problems with One Pi Term 283
7.7.2 Problems with Two or More Pi Terms 284
7.8 Modeling and Similitude 286
7.8.1 Theory of Models 287
7.8.2 Model Scales 290
7.8.3 Practical Aspects of Using Models 291
7.9 Some Typical Model Studies 293
7.9.1 Flow Through Closed Conduits 293
7.9.2 Flow Around Immersed Bodies 295
7.9.3 Flow with a Free Surface 299
7.10 Similitude Based on Governing Differential Equations 302
Chapter Summary and Study Guide 305
References 306
8 Viscous Flow in Pipes 307
Learning Objectives 307
8.1 General Characteristics of Pipe Flow 308
8.1.1 Laminar or Turbulent Flow 309
8.1.2 Entrance Region and Fully Developed Flow 311
8.1.3 Pressure and Shear Stress 312
8.2 Fully Developed Laminar Flow 313
8.2.1 From F = ma Applied Directly to a Fluid Element 314
8.2.2 From the Navier–Stokes Equations 318
8.2.3 From Dimensional Analysis 319
8.2.4 Energy Considerations 320
8.3 Fully Developed Turbulent Flow 322
8.3.1 Transition from Laminar to Turbulent Flow 322
8.3.2 Turbulent Shear Stress 324
8.3.3 Turbulent Velocity Profile 329
8.3.4 Turbulence Modeling 332
8.3.5 Chaos and Turbulence 333
8.4 Pipe Flow Losses via Dimensional Analysis 333
8.4.1 Major Losses 333
8.4.2 Minor Losses 339
8.4.3 Noncircular Conduits 348
8.5 Pipe Flow Examples 351
8.5.1 Single Pipes 351
8.5.2 Multiple Pipe Systems 360
8.6 Pipe Flowrate Measurement 364
8.6.1 Pipe Flowrate Meters 364
8.6.2 Volume Flowmeters 369
Chapter Summary and Study Guide 370
References 372
9 Flow over Immersed Bodies 373
Learning Objectives 373
9.1 General External Flow Characteristics 374
9.1.1 Lift and Drag Concepts 375
9.1.2 Characteristics of Flow Past an Object 378
9.2 Boundary Layer Characteristics 382
9.2.1 Boundary Layer Structure and Thickness on a Flat Plate 382
9.2.2 Prandtl/Blasius Boundary Layer Solution 385
9.2.3 Momentum Integral Boundary Layer Equation for a Flat Plate 389
9.2.4 Transition from Laminar to Turbulent Flow 394
9.2.5 Turbulent Boundary Layer Flow 396
9.2.6 Effects of Pressure Gradient 399
9.2.7 Momentum Integral Boundary Layer Equation with Nonzero Pressure Gradient 404
9.3 Drag 405
9.3.1 Friction Drag 405
9.3.2 Pressure Drag 407
9.3.3 Drag Coefficient Data and Examples 409
9.4 Lift 422
9.4.1 Surface Pressure Distribution 424
9.4.2 Circulation 429
Chapter Summary and Study Guide 434
References 435
10 Open-Channel Flow 437
Learning Objectives 437
10.1 General Characteristics of Open-Channel Flow 437
10.2 Surface Waves 439
10.2.1 Wave Speed 439
10.2.2 Froude Number Effects 442
10.3 Energy Considerations 444
10.3.1 Energy Balance 444
10.3.2 Specific Energy 445
10.4 Uniform Flow 448
10.4.1 Uniform Flow Approximations 448
10.4.2 The Chezy and Manning Equations 449
10.4.3 Uniform Flow Examples 451
10.5 Gradually Varied Flow 457
10.6 Rapidly Varied Flow 458
10.6.1 The Hydraulic Jump 460
10.6.2 Sharp-Crested Weirs 464
10.6.3 Broad-Crested Weirs 467
10.6.4 Underflow (Sluice) Gates 470
Chapter Summary and Study Guide 471
References 472
11 Compressible Flow 473
Learning Objectives 473
11.1 Ideal Gas Thermodynamics 474
11.2 Stagnation Properties 479
11.3 Mach Number and Speed of Sound 480
11.4 Compressible Flow Regimes 485
11.5 Shock Waves 489
11.5.1 Normal Shock 489
11.6 Isentropic Flow 495
11.6.1 Steady Isentropic Flow of an Ideal Gas 495
11.6.2 Incompressible Flow and the Bernoulli Equation 498
11.6.3 The Critical State 500
11.7 One-Dimensional Flow in a Variable Area Duct 500
11.7.1 General Considerations 501
11.7.2 Isentropic Flow of an Ideal Gas with Area Change 504
11.7.3 Operation of a Converging Nozzle 510
11.7.4 Operation of a Converging–Diverging Nozzle 512
11.8 Constant-Area Duct Flow with Friction 516
11.8.1 Preliminary Consideration: Comparison with Incompressible Duct Flow 516
11.8.2 The Fanno Line 517
11.8.3 Adiabatic Frictional Flow (Fanno Flow) of an Ideal Gas 520
11.9 Frictionless Flow in a Constant-Area Duct with Heating or Cooling 528
11.9.1 The Rayleigh Line 528
11.9.2 Frictionless Flow of an Ideal Gas with Heating or Cooling (Rayleigh Flow) 531
11.9.3 Rayleigh Lines, Fanno Lines, and Normal Shocks 534
11.10 Analogy Between Compressible and Open-Channel Flows 535
11.11 Two-Dimensional Supersonic Flow 536
11.12 Effects of Compressibility in External Flow 538
Chapter Summary and Study Guide 541
References 544
12 Turbomachines 545
Learning Objectives 545
12.1 Introduction 546
12.2 Basic Energy Considerations 547
12.3 Angular Momentum Considerations 551
12.4 The Centrifugal Pump 553
12.4.1 Theoretical Considerations 554
12.4.2 Pump Performance Characteristics 558
12.4.3 Net Positive Suction Head (NPSH) 560
12.4.4 System Characteristics, Pump-System Matching, and Pump Selection 562
12.5 Dimensionless Parameters and Similarity Laws 566
12.5.1 Special Pump Scaling Laws 568
12.5.2 Specific Speed 569
12.5.3 Suction Specific Speed 570
12.6 Axial-Flow and Mixed-Flow Pumps 571
12.7 Fans 573
12.8 Turbines 574
12.8.1 Impulse Turbines 575
12.8.2 Reaction Turbines 582
12.9 Compressible Flow Turbomachines 585
12.9.1 Compressors 585
12.9.2 Compressible Flow Turbines 589
Chapter Summary and Study Guide 591
References 593
Appendix A Computational Fluid Dynamics 594
Appendix B Physical Properties of Fluids 613
Appendix C Properties of the U.S. Standard Atmosphere 618
Appendix D Compressible Flow Functions for an Ideal Gas with k = 1.4 620
Appendix E Comprehensive Table of Conversion Factors 628
Questions, Problems, And Reserve Problems 635
Index I-1