Introduction to Fluid Mechanics

Cover......Page 1
Title Page
......Page 3
Copyright......Page 4
Preface......Page 5
Contents......Page 8
Chapter 1 Problems......Page 13
Chapter 1 Introduction......Page 15
Note to Students......Page 16
Definition of a Fluid......Page 17
1.2 Basic Equations......Page 18
1.3 Methods of Analysis......Page 19
System and Control Volume......Page 20
Methods of Description......Page 21
Systems of Dimensions......Page 23
Systems of Units......Page 24
Dimensional Consistency and “Engineering” Equations 
......Page 25
1.5 Analysis of Experimental Error......Page 27
References......Page 28
Chapter 2 Problems......Page 29
Chapter 2 Fundamental Concepts......Page 33
2.1 Fluid as a Continuum......Page 34
2.2 Velocity Field......Page 35
One-, Two-, and Three-Dimensional Flows......Page 36
Timelines, Pathlines, Streaklines, and Streamlines......Page 37
2.3 Stress Field......Page 41
2.4 Viscosity......Page 43
Newtonian Fluid......Page 44
Non-Newtonian Fluids......Page 46
2.5 Surface Tension......Page 47
2.6 Description and Classification of Fluid Motions......Page 48
Viscous and Inviscid Flows......Page 50
Compressible and Incompressible Flows......Page 52
Internal and External Flows......Page 53
2.7 Summary and Useful Equations......Page 54
References......Page 55
Chapter 3 Problems......Page 56
Chapter 3 Fluid Statics......Page 61
3.1 The Basic Equation of Fluid Statics......Page 62
3.2 The Standard Atmosphere......Page 65
Incompressible Liquids: Manometers......Page 66
Gases......Page 71
Hydrostatic Force on a Plane Submerged Surface......Page 73
Hydrostatic Force on a Curved Submerged Surface......Page 80
3.5 Buoyancy and Stability......Page 83
3.6 Fluids in Rigid-Body Motion......Page 86
3.7 Summary and Useful Equations......Page 91
References......Page 92
Chapter 4 Problems......Page 93
Chapter 4 Basic Equations in Integral Form for a Control Volume......Page 98
Conservation of Mass......Page 99
The First Law of Thermodynamics......Page 100
4.2 Relation of System Derivatives to the Control Volume Formulation......Page 101
Derivation......Page 102
Physical Interpretation......Page 104
4.3 Conservation of Mass......Page 105
Special Cases......Page 106
4.4 Momentum Equation for Inertial Control Volume......Page 110
Differential Control Volume Analysis......Page 121
Control Volume Moving with Constant Velocity......Page 125
4.5 Momentum Equation for Control Volume with Rectilinear Acceleration......Page 127
4.6 Momentum Equation for Control Volume with Arbitrary Acceleration......Page 133
Equation for Fixed Control Volume......Page 138
Equation for Rotating Control Volume......Page 142
4.8 The First and Second Laws of Thermodynamics......Page 146
Rate of Work Done by a Control Volume......Page 147
Control Volume Equation......Page 149
4.9 Summary and Useful Equations......Page 153
Chapter 5 Problems......Page 156
Chapter 5 Introduction to Differential Analysis of Fluid Motion......Page 158
Rectangular Coordinate System......Page 159
Cylindrical Coordinate System......Page 163
5.2 Stream Function for Two-Dimensional Incompressible Flow......Page 165
5.3 Motion of a Fluid Particle (Kinematics)......Page 167
Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field......Page 168
Fluid Rotation......Page 174
Fluid Deformation......Page 177
Forces Acting on a Fluid Particle......Page 181
Newtonian Fluid: Navier–Stokes Equations......Page 182
5.5 Summary and Useful Equations......Page 190
References......Page 191
Chapter 6 Problems......Page 192
Chapter 6 Incompressible Inviscid Flow......Page 196
6.1 Momentum Equation for Frictionless Flow: Euler’s Equation......Page 197
Derivation Using Streamline Coordinates......Page 201
Derivation Using Rectangular Coordinates......Page 202
Static, Stagnation, and Dynamic Pressures......Page 203
Applications......Page 205
Cautions on Use of the Bernoulli Equation......Page 210
6.3 The Bernoulli Equation Interpreted as an Energy Equation......Page 211
6.4 Energy Grade Line and Hydraulic Grade Line......Page 215
6.5 Unsteady Bernoulli Equation: Integration of Euler’s Equation Along a Streamline......Page 217
Bernoulli Equation Applied to Irrotational Flow......Page 219
Velocity Potential......Page 220
Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace’s Equation......Page 221
Elementary Plane Flows......Page 223
Superposition of Elementary Plane Flows......Page 225
6.7 Summary and Useful Equations......Page 234
References......Page 235
Chapter 7 Problems......Page 236
Chapter 7 Dimensional Analysis and Similitude......Page 239
7.1 Nondimensionalizing the Basic Differential Equations......Page 241
7.2 Buckingham Pi Theorem......Page 243
7.3 Significant Dimensionless Groups in Fluid Mechanics......Page 249
7.4 Flow Similarity and Model Studies......Page 251
Incomplete Similarity......Page 253
Scaling with Multiple Dependent Parameters......Page 258
Comments on Model Testing......Page 261
7.5 Summary and Useful Equations......Page 262
References......Page 263
Chapter 8 Problems......Page 264
Chapter 8 Internal Incompressible Viscous Flow......Page 268
Laminar versus Turbulent Flow......Page 269
The Entrance Region......Page 270
Both Plates Stationary......Page 271
Upper Plate Moving with Constant Speed, U
......Page 277
8.3 Fully Developed Laminar Flow in a Pipe......Page 282
Part B Flow in Pipes and Ducts......Page 286
8.4 Shear Stress Distribution in Fully Developed Pipe Flow......Page 287
8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow......Page 288
8.6 Energy Considerations in Pipe Flow......Page 292
Head Loss......Page 293
Major Losses: Friction Factor......Page 294
Minor Losses......Page 299
Noncircular Ducts......Page 303
8.8 Solution of Pipe Flow Problems......Page 304
Single-Path Systems......Page 305
Multiple-Path Systems......Page 317
8.9 Restriction Flow Meters for Internal Flows......Page 320
The Orifice Plate......Page 323
The Venturi......Page 327
The Laminar Flow Element......Page 328
Linear Flow Meters......Page 329
Traversing Methods......Page 330
8.10 Summary and Useful Equations......Page 331
References......Page 333
Chapter 9 Problems......Page 334
Chapter 9 External Incompressible Viscous Flow......Page 337
9.1 The Boundary Layer Concept......Page 339
9.2 Laminar Flat Plate Boundary Layer: Exact Solution......Page 343
9.3 Momentum Integral Equation......Page 346
9.4 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient......Page 350
Laminar Flow......Page 351
Turbulent Flow......Page 355
9.5 Pressure Gradients in Boundary Layer Flow......Page 358
9.6 Drag......Page 360
Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow......Page 361
Friction and Pressure Drag: Flow over a Sphere and Cylinder......Page 364
Streamlining......Page 370
9.7 Lift......Page 372
9.8 Summary and Useful Equations......Page 384
References......Page 386
Chapter 10 Problems......Page 387
Chapter 10 Fluid Machinery......Page 391
Machines for Doing Work on a Fluid......Page 392
Machines for Extracting Work (Power) from a Fluid......Page 394
The Angular-Momentum Principle: The Euler Turbomachine Equation......Page 396
Velocity Diagrams......Page 398
Performance—Hydraulic Power......Page 400
Dimensional Analysis and Specific Speed......Page 401
Application of Euler Turbomachine Equation to Centrifugal Pumps......Page 406
Application of the Euler Equation to Axial Flow Pumps and Fans......Page 407
Performance Characteristics......Page 410
Similarity Rules......Page 415
Cavitation and Net Positive Suction Head......Page 419
Pump Selection: Applications to Fluid Systems......Page 422
Blowers and Fans......Page 428
10.4 Positive Displacement Pumps......Page 432
Hydraulic Turbine Theory......Page 435
Performance Characteristics for Hydraulic Turbines......Page 437
Propellers......Page 443
Wind Turbines......Page 448
Application of the Energy Equation to a Compressible Flow Machine......Page 454
Compressors......Page 455
10.8 Summary and Useful Equations......Page 458
References......Page 460
Chapter 11 Problems......Page 462
Chapter 11 Flow in Open Channels......Page 464
Simplifying Assumptions......Page 466
Channel Geometry......Page 468
Speed of Surface Waves and the Froude Number......Page 469
11.2 Energy Equation for Open-Channel Flows......Page 473
Specific Energy......Page 475
Critical Depth: Minimum Specific Energy......Page 476
Flow over a Bump......Page 481
11.4 The Hydraulic Jump......Page 485
Depth Increase Across a Hydraulic Jump......Page 488
Head Loss Across a Hydraulic Jump......Page 489
11.5 Steady Uniform Flow......Page 491
The Manning Equation for Uniform Flow......Page 493
Energy Equation for Uniform Flow......Page 498
Optimum Channel Cross Section......Page 500
11.6 Flow with Gradually Varying Depth......Page 501
Calculation of Surface Profiles......Page 502
Suppressed Rectangular Weir......Page 505
Triangular Weir......Page 506
Broad-Crested Weir......Page 507
11.8 Summary and Useful Equations......Page 508
References......Page 509
Chapter 12 Problems......Page 510
Chapter 12 Introduction to Compressible Flow......Page 512
12.1 Review of Thermodynamics......Page 513
Speed of Sound......Page 519
Types of Flow—The Mach Cone......Page 523
12.3 Reference State: Local Isentropic Stagnation Properties......Page 525
Local Isentropic Stagnation Properties for the Flow of an Ideal Gas......Page 526
12.5 Basic Equations for One-Dimensional Compressible Flow......Page 532
First Law of Thermodynamics......Page 533
Second Law of Thermodynamics......Page 534
12.6 Isentropic Flow of an Ideal Gas: Area Variation......Page 535
Subsonic Flow, M< 1......Page 537
Sonic Flow, M=1......Page 538
Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas......Page 539
Isentropic Flow in a Converging Nozzle......Page 544
Isentropic Flow in a Converging-Diverging Nozzle......Page 548
Basic Equations for a Normal Shock......Page 553
Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas......Page 555
12.8 Supersonic Channel Flow with Shocks......Page 559
12.9 Summary and Useful Equations......Page 561
References......Page 563
A.1 Specific Gravity......Page 564
A.2 Surface Tension......Page 567
Effect of Temperature on Viscosity......Page 568
Effect of Pressure on Viscosity......Page 570
A.4 Lubricating Oils......Page 572
A.5 Properties of Common Gases, Air, and Water......Page 573
Appendix B Videos for Fluid Mechanics
......Page 576
C.2 Pump Selection......Page 578
C.3 Fan Selection......Page 579
D.1 Isentropic Flow......Page 589
D.2 Normal Shock......Page 590
E.3 Estimation of Uncertainty......Page 592
E.4 Applications to Data......Page 595
References......Page 597
The Need for CFD......Page 598
F.2 Finite Difference Approach to CFD......Page 599
Techniques of CFD......Page 602
References......Page 603
Index......Page 604
EULA......Page 610