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 Archimedesâ 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 Dynamicsâ" The Bernoulli Equation 139
Learning Objectives 139
4.1 Newtonâs 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 Massâ"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 Newtonâs Second Lawâ"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 Thermodynamicsâ" 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 Eulerâs 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 Streamâ"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 Stressâ"Deformation Relationships 306
6.8.2 The Navierâ"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 Navierâ"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
9.2.3 Momentum Integral Boundary Layer Equation For A Flat Plate 478
9.2.4 Transition From Laminar To Turbulent Flow 483
9.2.5 Turbulent Boundary Layer Flow 485
9.2.6 Effects Of Pressure Gradient 488
9.2.7 Momentum Integral Boundary Layer Equation With Nonzero Pressure Gradient 493
9.3 Drag 494
9.3.1 Friction Drag 494
9.3.2 Pressure Drag 496
9.3.3 Drag Coefficient Data And Examples 498
9.4 Lift 511
9.4.1 Surface Pressure Distribution 513
9.4.2 Circulation 518
Chapter Summary 523
Key Equations 524
References 524
Questions And Problems 525
10 Open-Channel Flow 535
Learning Objectives 535
10.1 General Characteristics Of Open-Channel Flow 535
10.2 Surface Waves 537
10.2.1 Wave Speed 537
10.2.2 Froude Number Effects 540
10.3 Energy Considerations 542
10.3.1 Energy Balance 542
10.3.2 Specific Energy 543
10.4 Uniform Flow 546
10.4.1 Uniform Flow Approximations 546
10.4.2 The Chezy And Manning Equations 547
10.4.3 Uniform Flow Examples 549
10.5 Most Efficient Channel Section 555
10.5.1 Trapezoidal Channel Section 555
10.5.2 Triangular Channel Section 557
10.6 Gradually Varied Flow 560
10.7 Rapidly Varied Flow 561
10.7.1 The Hydraulic Jump 562
10.7.2 Sharp-Crested Weirs 567
10.7.3 Broad-Crested Weirs 570
10.7.4 Underflow (Sluice) Gates 572
Chapter Summary 573
Key Equations 573
References 574
Questions And Problems 574
11 Compressible Flow 581
Learning Objectives 581
11.1 Ideal Gas Thermodynamics 582
11.2 Stagnation Properties 587
11.3 Mach Number And Speed Of Sound 588
11.4 Compressible Flow Regimes 593
11.5 Shock Waves 597
11.5.1 Normal Shock 597
11.6 Isentropic Flow 603
11.6.1 Steady Isentropic Flow Of An Ideal Gas 603
11.6.2 Incompressible Flow And The Bernoulli Equation 606
11.6.3 The Critical State 608
11.7 One-Dimensional Flow In A Variable Area Duct 608
11.7.1 General Considerations 609
11.7.2 Isentropic Flow Of An Ideal Gas With Area Change 612
11.7.3 Operation Of A Converging Nozzle 618
11.7.4 Operation Of A Convergingâ"Diverging Nozzle 620
11.8 Constant-Area Duct Flow With Friction 624
11.8.1 Preliminary Consideration: Comparison With Incompressible Duct Flow 624
11.8.2 The Fanno Line 625
11.8.3 Adiabatic Frictional Flow (Fanno Flow) Of An Ideal Gas 628
11.9 Frictionless Flow In A Constant-Area Duct With Heating Or Cooling 636
11.9.1 The Rayleigh Line 636
11.9.2 Frictionless Flow Of An Ideal Gas With Heating Or Cooling (Rayleigh Flow) 639
11.9.3 Rayleigh Lines, Fanno Lines, And Normal Shocks 642
11.10 Analogy Between Compressible And Open -Channel Flows 643
11.11 Two-Dimensional Supersonic Flow 644
11.12 Effects Of Compressibility In External Flow 646
Chapter Summary 649
Key Equations 650
References 652
Questions And Problems 652
12 Turbomachines 657
Learning Objectives 657
12.1 Introduction 658
12.2 Basic Energy Considerations 659
12.3 Angular Momentum Considerations 663
12.4 The Centrifugal Pump 665
12.4.1 Theoretical Considerations 666
12.4.2 Pump Performance Characteristics 670
12.4.3 Net Positive Suction Head (Npsh) 672
12.4.4 System Characteristics, Pump-System Matching, And Pump Selection 674
12.5 Dimensionless Parameters And Similarity Laws 678
12.5.1 Special Pump Scaling Laws 680
12.5.2 Specific Speed 681
12.5.3 Suction Specific Speed 682
12.6 Axial-Flow And Mixed-Flow Pumps 683
12.7 Turbines 685
12.7.1 Impulse Turbines 685
12.7.2 Reaction Turbines 692
12.8 Fans 695
12.9 Compressible Flow Turbomachines 696
12.9.1 Compressors 697
12.9.2 Compressible Flow Turbines 700
Chapter Summary 702
Key Equations 703
References 704
Questions And Problems 704
Appendix A Computational Fluid Dynamics 713
Appendix B Physical Properties Of Fluids 731
Appendix C Properties Of The U.S. Standard Atmosphere 736
Appendix D Compressible Flow Functions For An Ideal Gas With K = 1.4 738
Appendix E Comprehensive Table Of Conversion Factors 746
Index I- 1
