Introduction to fluid mechanics

Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 13
CHAPTER 1 INTRODUCTION......Page 23
1.1 Note to Students......Page 25
1.3 Definition of a Fluid......Page 26
1.4 Basic Equations......Page 27
1.5 Methods of Analysis......Page 28
System and Control Volume......Page 29
Differential versus Integral Approach......Page 30
Methods of Description......Page 31
Systems of Units......Page 33
Preferred Systems of Units......Page 35
Dimensional Consistency and “Engineering” Equations......Page 36
1.7 Analysis of Experimental Error......Page 37
1.8 Summary......Page 38
Problems......Page 39
CHAPTER 2 FUNDAMENTAL CONCEPTS......Page 42
2.1 Fluid as a Continuum......Page 43
2.2 Velocity Field......Page 45
One-, Two-, and Three-Dimensional Flows......Page 46
Timelines, Pathlines, Streaklines, and Streamlines......Page 47
2.3 Stress Field......Page 51
2.4 Viscosity......Page 53
Newtonian Fluid......Page 54
Non-Newtonian Fluids......Page 56
2.5 Surface Tension......Page 58
Viscous and Inviscid Flows......Page 60
Laminar and Turbulent Flows......Page 63
Compressible and Incompressible Flows......Page 64
Internal and External Flows......Page 65
2.7 Summary and Useful Equations......Page 66
Problems......Page 68
CHAPTER 3 FLUID STATICS......Page 77
3.1 The Basic Equation of Fluid Statics......Page 78
3.2 The Standard Atmosphere......Page 82
Incompressible Liquids: Manometers......Page 83
Gases......Page 88
Hydrostatic Force on a Plane Submerged Surface......Page 91
Hydrostatic Force on a Curved Submerged Surface......Page 98
*3.6 Buoyancy and Stability......Page 102
3.7 Fluids in Rigid-Body Motion (on the Web)......Page 104
3.8 Summary and Useful Equations......Page 105
Problems......Page 106
CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME......Page 118
Newton’s Second Law......Page 120
The Second Law of Thermodynamics......Page 121
4.2 Relation of System Derivatives to the Control Volume Formulation......Page 122
Derivation......Page 123
Physical Interpretation......Page 125
4.3 Conservation of Mass......Page 126
Special Cases......Page 127
4.4 Momentum Equation for Inertial Control Volume......Page 132
*Differential Control Volume Analysis......Page 144
Control Volume Moving with Constant Velocity......Page 148
4.5 Momentum Equation for Control Volume with Rectilinear Acceleration......Page 150
Equation for Fixed Control Volume......Page 157
4.8 The First Law of Thermodynamics......Page 161
Rate of Work Done by a Control Volume......Page 162
Control Volume Equation......Page 164
4.9 The Second Law of Thermodynamics......Page 168
4.10 Summary and Useful Equations......Page 169
Problems......Page 171
CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION......Page 193
5.1 Conservation of Mass......Page 194
Rectangular Coordinate System......Page 195
Cylindrical Coordinate System......Page 199
*5.2 Stream Function for Two-Dimensional Incompressible Flow......Page 202
5.3 Motion of a Fluid Particle (Kinematics)......Page 206
Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field......Page 207
Fluid Rotation......Page 212
Fluid Deformation......Page 216
5.4 Momentum Equation......Page 219
Forces Acting on a Fluid Particle......Page 220
Newtonian Fluid: Navier–Stokes Equations......Page 221
The Need for CFD......Page 230
Applications of CFD......Page 231
Some Basic CFD/Numerical Methods Using a Spreadsheet......Page 232
The Strategy of CFD......Page 237
Discretization Using the Finite-Difference Method......Page 238
Assembly of Discrete System and Application of Boundary Conditions......Page 239
Solution of Discrete System......Page 240
Grid Convergence......Page 241
Dealing with Nonlinearity......Page 242
Direct and Iterative Solvers......Page 243
Iterative Convergence......Page 244
Concluding Remarks......Page 245
5.6 Summary and Useful Equations......Page 246
Problems......Page 248
CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW......Page 257
6.1 Momentum Equation for Frictionless Flow: Euler’s Equation......Page 259
6.2 Euler’s Equations in Streamline Coordinates......Page 260
*Derivation Using Streamline Coordinates......Page 263
*Derivation Using Rectangular Coordinates......Page 264
Static, Stagnation, and Dynamic Pressures......Page 266
Applications......Page 269
Cautions on Use of the Bernoulli Equation......Page 274
6.4 The Bernoulli Equation Interpreted as an Energy Equation......Page 275
6.5 Energy Grade Line and Hydraulic Grade Line......Page 279
*6.7 Irrotational Flow......Page 281
Bernoulli Equation Applied to Irrotational Flow......Page 282
Velocity Potential......Page 283
Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace’s Equation......Page 284
Elementary Plane Flows......Page 286
Superposition of Elementary Plane Flows......Page 289
6.8 Summary and Useful Equations......Page 298
Problems......Page 301
CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE......Page 312
7.1 Nondimensionalizing the Basic Differential Equations......Page 314
7.2 Nature of Dimensional Analysis......Page 316
7.3 Buckingham Pi Theorem......Page 318
7.4 Determining the Π 
Groups......Page 319
7.5 Significant Dimensionless Groups in Fluid Mechanics......Page 325
7.6 Flow Similarity and Model Studies......Page 327
Incomplete Similarity......Page 330
Scaling with Multiple Dependent Parameters......Page 336
Comments on Model Testing......Page 339
7.7 Summary and Useful Equations......Page 340
References......Page 341
Problems......Page 342
CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW......Page 350
Laminar versus Turbulent Flow......Page 352
The Entrance Region......Page 353
8.2 Fully Developed Laminar Flow between Infinite Parallel Plates......Page 354
8.3 Fully Developed Laminar Flow in a Pipe......Page 366
PART B. FLOW IN PIPES AND DUCTS......Page 370
8.4 Shear Stress Distribution in Fully Developed Pipe Flow......Page 371
8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow......Page 373
8.6 Energy Considerations in Pipe Flow......Page 375
8.7 Calculation of Head Loss......Page 379
8.8 Solution of Pipe Flow Problems......Page 391
8.10 Restriction Flow Meters for Internal Flows......Page 409
8.11 Linear Flow Meters......Page 419
8.12 Traversing Methods......Page 421
8.13 Summary and Useful Equations......Page 422
References......Page 424
Problems......Page 425
CHAPTER 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW......Page 443
9.1 The Boundary-Layer Concept......Page 445
9.2 Boundary-Layer Thicknesses......Page 447
9.4 Momentum Integral Equation......Page 450
9.5 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient......Page 455
9.6 Pressure Gradients in Boundary-Layer Flow......Page 464
9.7 Drag......Page 467
9.8 Lift......Page 481
9.9 Summary and Useful Equations......Page 496
References......Page 499
Problems......Page 500
CHAPTER 10 FLUID MACHINERY......Page 514
Machines for Doing Work on a Fluid......Page 516
Machines for Extracting Work (Power) from a Fluid......Page 518
Scope of Coverage......Page 520
The Angular-Momentum Principle: The Euler Turbomachine Equation......Page 521
Velocity Diagrams......Page 523
Performance: Hydraulic Power......Page 526
Dimensional Analysis and Specific Speed......Page 527
Application of Euler Turbomachine Equation to Centrifugal Pumps......Page 532
Application of the Euler Equation to Axial Flow Pumps and Fans......Page 534
Performance Characteristics......Page 538
Similarity Rules......Page 544
Cavitation and Net Positive Suction Head......Page 548
Pump Selection: Applications to Fluid Systems......Page 551
Blowers and Fans......Page 563
10.4 Positive Displacement Pumps......Page 570
Hydraulic Turbine Theory......Page 574
Performance Characteristics for Hydraulic Turbines......Page 576
Sizing Hydraulic Turbines for Fluid Systems......Page 580
10.6 Propellers and Wind-Power Machines......Page 584
Propellers......Page 585
Wind-Power Machines......Page 593
Application of the Energy Equation to a Compressible Flow Machine......Page 603
Compressors......Page 604
10.8 Summary and Useful Equations......Page 608
References......Page 611
Problems......Page 613
CHAPTER 11 FLOW IN OPEN CHANNELS......Page 622
11.1 Basic Concepts and Definitions......Page 625
Simplifying Assumptions......Page 626
Channel Geometry......Page 627
Speed of Surface Waves and the Froude Number......Page 628
11.2 Energy Equation for Open-Channel Flows......Page 632
Specific Energy......Page 635
Critical Depth: Minimum Specific Energy......Page 638
11.3 Localized Effect of Area Change (Frictionless Flow)......Page 641
Flow over a Bump......Page 642
11.4 The Hydraulic Jump......Page 647
Depth Increase Across a Hydraulic Jump......Page 649
Head Loss Across a Hydraulic Jump......Page 650
11.5 Steady Uniform Flow......Page 653
The Manning Equation for Uniform Flow......Page 655
Energy Equation for Uniform Flow......Page 661
Optimum Channel Cross Section......Page 662
11.6 Flow with Gradually Varying Depth......Page 663
Calculation of Surface Profiles......Page 665
Suppressed Rectangular Weir......Page 668
Contracted Rectangular Weirs......Page 669
Broad-Crested Weir......Page 670
11.8 Summary and Useful Equations......Page 672
References......Page 674
Problems......Page 675
CHAPTER 12 INTRODUCTION TO COMPRESSIBLE FLOW......Page 679
12.1 Review of Thermodynamics......Page 681
Speed of Sound......Page 687
Types of Flow—The Mach Cone......Page 692
12.3 Reference State: Local Isentropic Stagnation Properties......Page 695
Local Isentropic Stagnation Properties for the Flow of an Ideal Gas......Page 696
12.5 Summary and Useful Equations......Page 703
Problems......Page 705
CHAPTER 13 COMPRESSIBLE FLOW......Page 711
13.1 Basic Equations for One-Dimensional Compressible Flow......Page 713
13.2 Isentropic Flow of an Ideal Gas: Area Variation......Page 716
Supersonic Flow, M > 1......Page 719
Sonic Flow, M = 1......Page 720
Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas......Page 721
Isentropic Flow in a Converging Nozzle......Page 726
Isentropic Flow in a Converging-Diverging Nozzle......Page 731
13.3 Normal Shocks......Page 737
Basic Equations for a Normal Shock......Page 738
Fanno and Rayleigh Interpretation of Normal Shock......Page 740
Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas......Page 741
Flow in a Converging-Diverging Nozzle......Page 746
Supersonic Flow with Heat Addition in a Constant-Area Channel (on the Web)......Page 748
Basic Equations for Adiabatic Flow......Page 749
Adiabatic Flow: The Fanno Line......Page 750
Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas......Page 754
Basic Equations for Flow with Heat Exchange......Page 762
The Rayleigh Line......Page 763
Rayleigh-Line Flow Functions for One-Dimensional Flow of an Ideal Gas......Page 768
Oblique Shocks......Page 772
Isentropic Expansion Waves......Page 781
13.8 Summary and Useful Equations......Page 790
References......Page 793
Problems......Page 794
APPENDIX A: FLUID PROPERTY DATA......Page 807
APPENDIX B: EQUATIONS OF MOTION IN CYLINDRICAL COORDINATES......Page 820
APPENDIX C: VIDEOS FOR FLUID MECHANICS......Page 822
APPENDIX D: SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS......Page 825
APPENDIX E: FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW......Page 840
APPENDIX F: ANALYSIS OF EXPERIMENTAL UNCERTAINTY......Page 851
APPENDIX G: SI UNITS, PREFIXES, AND CONVERSION FACTORS......Page 858
Answers to Selected Problems......Page 860
Index......Page 889