Introductory Fluid Mechanics

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 13
A Word to the Instructor......Page 15
1.2 A Brief History......Page 17
1.3 Dimensions and Units......Page 19
1.4.1 Continuum......Page 20
1.4.2 Laminar and Turbulent Flows......Page 21
1.4.3 Attached and Separated Flows......Page 22
1.5.1 Density......Page 23
1.5.3 Temperature......Page 24
1.5.4 Viscosity......Page 25
1.5.5 Specific Heat......Page 27
1.5.6 Heat Transfer Coefficient k......Page 28
1.5.7 Surface Tension sigma......Page 29
1.5.8 Modulus of Elasticity E......Page 32
1.5.9 Vapor Pressure......Page 33
1.6 Advanced Topics: Fluid Properties and the Kinetic Theory of Gases......Page 34
REFERENCE......Page 37
2.1 Introduction......Page 48
2.2 Description of Fluid Motion......Page 49
2.3 Choice of Coordinate System......Page 50
2.4 Pathlines, Streak Lines, and Streamlines......Page 52
2.5 Forces in a Fluid......Page 53
2.6 Integral Form of the Fluid Dynamic Equations......Page 55
2.7 Differential Form of the Fluid Dynamic Equations......Page 60
2.8 The Material Derivative......Page 66
2.9 Alternative Derivation of the Fluid Dynamic Equations......Page 68
2.10 Summary and Concluding Remarks......Page 71
REFERENCES......Page 72
3.2 Fluid Statics: The Governing Equations......Page 81
3.3 Pressure Due to Gravity......Page 82
3.4 Hydrostatic Pressure in a Compressible Fluid......Page 86
3.5 “Solid-Body” Acceleration of Liquids......Page 87
3.5.1 Linear Acceleration......Page 88
3.5.2 Solid-Body Rotation of a Fluid......Page 90
3.6 Hydrostatic Forces on Submerged Surfaces and Bodies......Page 93
3.6.1.1 Hydrostatic Force on a Submerged Surface......Page 94
3.6.1.2 The Center of Pressure......Page 95
3.6.2 Hydrostatic Forces on Submerged Curved Surfaces......Page 101
3.7 Buoyancy......Page 103
3.8 Stability of Floating Objects......Page 107
3.9 Summary and Conclusions......Page 109
4.1 Introduction......Page 127
4.2 The Bernoulli Equation......Page 128
4.3 Summary of the One-Dimensional Tools......Page 129
4.4.1 Free Jets......Page 130
4.4.2 Examples for Using the Bernoulli Equation......Page 134
4.4.3 Simple Models for Time-Dependent Changes in a Control Volume......Page 135
4.5.1 The Pitot Tube......Page 138
4.5.2 The Venturi Tube......Page 139
4.5.3 The Orifice......Page 141
4.5.4 The Sluice Gate......Page 142
4.6 Summary and Conclusions......Page 143
5.2 The Viscous Incompressible Flow Equations (Steady State)......Page 158
5.3 Laminar Flow between Two Infinite Parallel Plates – The Couette Flow......Page 159
5.3.1 Flow with a Moving Upper Surface......Page 160
5.3.2 Flow between Two Infinite Parallel Plates – The Results......Page 161
5.3.3 Flow between Two Infinite Parallel Plates — The Poiseuille Flow......Page 164
5.3.4 The Hydrodynamic Bearing (Reynolds Lubrication Theory)......Page 167
5.4 Laminar Flow in Circular Pipes (The Hagen–Poiseuille Flow)......Page 173
5.5 Fully Developed Laminar Flow between Two Concentric Circular Pipes......Page 177
5.6 Flow in Pipes: Darcy’s Formula......Page 179
5.7 The Reynolds Dye Experiment, Laminar–Turbulent Flow in Pipes......Page 180
5.8 Additional Losses in Pipe Flow......Page 182
5.9 Summary of One-Dimensional Pipe Flow......Page 183
5.9.2 Flow in Pipes with Noncircular Cross Sections......Page 186
5.9.3 Examples for One-Dimensional Pipe Flow......Page 188
5.9.4 Network of Pipes......Page 193
5.10.1 Simple Models for Open Channel Flows......Page 195
5.10.2 Uniform Open Channel Flows......Page 198
5.10.3 Hydraulic Jump......Page 204
5.10.4 Flow Discharge through Sharp-Crested Weirs......Page 208
5.11 Advanced Topics: Exact Solutions; Two-Dimensional Inviscid Incompressible Vortex Flow......Page 210
5.11.1 Angular Velocity, Vorticity, and Circulation......Page 213
REFERENCES......Page 215
6.2 Dimensional Analysis of the Fluid Dynamic Equations......Page 229
6.3 The Process of Simplifying the Governing Equations......Page 232
6.4 Similarity of Flows......Page 233
6.5 Flow with High Reynolds Number......Page 234
6.6 High-Reynolds-Number Flows and Turbulence......Page 236
6.7 Summary and Conclusions......Page 238
7.1 Introduction......Page 243
7.2 Two-Dimensional Laminar Boundary-Layer Flow over a Flat Plate – (The Integral Approach)......Page 244
7.3 Solutions Based on the von Karman Integral Equation......Page 247
7.4 Summary and Practical Conclusions......Page 254
7.5 Effect of Pressure Gradient......Page 257
7.6 Advanced Topics: The Two-Dimensional Laminar Boundary-Layer Equations......Page 260
7.6.1 Summary of the Blasius Exact Solution for the Laminar Boundary Layer......Page 262
7.7 Concluding Remarks......Page 264
8.1 Introduction......Page 270
8.2 The Inviscid Irrotational Flow (and Some Math)......Page 271
8.3 Advanced Topics: A More Detailed Evaluation of the Bernoulli Equation......Page 274
8.4 The Potential Flow Model......Page 275
8.4.2 The Principle of Superposition......Page 276
8.5.1 Polynomial Solutions......Page 277
8.5.2 Two-Dimensional Source (or Sink)......Page 279
8.5.3 Two-Dimensional Doublet......Page 281
8.5.4 Two-Dimensional Vortex......Page 284
8.5.5 Advanced Topics: Solutions Based on the Green’s Identity......Page 286
8.6 Superposition of a Doublet and a Free Stream: Flow over a Cylinder......Page 289
8.7 Fluid Mechanic Drag......Page 293
8.7.1 The Drag of Simple Shapes......Page 294
8.7.2 The Drag of More Complex Shapes......Page 299
8.8 Periodic Vortex Shedding......Page 303
8.9.1 A Cylinder with Circulation in a Free Stream......Page 305
8.9.2 Two-Dimensional Flat Plate at a Small Angle of Attack (in a Free Stream)......Page 309
8.9.3 Note about the Center of Pressure......Page 310
8.10 Lifting Surfaces: Wings and Airfoils......Page 311
8.10.1 The Two-Dimensional Airfoil......Page 312
8.10.2 An Airfoil’s Lift......Page 314
8.10.3 An Airfoil’s Drag......Page 316
8.10.5 The Effect of Reynolds Number......Page 317
8.10.6 Three-Dimensional Wings......Page 319
8.11 Summary and Concluding Remarks......Page 329
REFERENCES......Page 330
9.1 Introduction......Page 340
9.2 The Finite-Difference Formulation......Page 341
9.3 Discretization and Grid Generation......Page 343
9.4 The Finite-Difference Equation......Page 344
9.5 The Solution: Convergence and Stability......Page 347
9.6 The Finite-Volume Method......Page 348
9.7 Example: Viscous Flow over a Cylinder......Page 350
9.8 Potential Flow Solvers: Panel Methods......Page 353
9.9 Summary......Page 356
REFERENCES......Page 357
10.1 Introduction......Page 359
10.2 Propagation of a Weak Compression Wave (the Speed of Sound)......Page 360
10.3 One-Dimensional Isentropic Compressible Flow......Page 363
10.3.1 Critical Conditions......Page 366
10.3.2 Practical Examples for One-Dimensional Compressible Flow......Page 368
10.4 Normal Shock Waves......Page 371
10.5.1 Normal Shock Wave ahead of a Circular Inlet......Page 376
10.5.2 The Converging–Diverging Nozzle (de Laval Nozzle)......Page 377
10.5.3 The Supersonic Wind Tunnel......Page 380
10.6 Effect of Compressibility on External Flows......Page 383
10.7 Concluding Remarks......Page 386
REFERENCE......Page 387
11.1 Introduction......Page 393
11.2 Work of a Continuous-Flow Machine......Page 396
11.3 Axial Compressors and Pumps (The Mean-Radius Model)......Page 398
11.3.1 Velocity Triangles......Page 401
11.3.2 Power and Compression-Ratio Calculations......Page 403
11.3.3 Radial Variations......Page 406
11.3.4 Pressure-Rise Limitations......Page 408
11.3.5 Performance Envelope of Compressors and Pumps......Page 410
11.3.6 Degree of Reaction......Page 415
11.4 The Centrifugal Compressor (or Pump)......Page 418
11.4.1 Torque, Power, and Pressure Rise......Page 419
11.4.2 Impeller Geometry......Page 421
11.4.3 The Diffuser......Page 424
11.4.4 Concluding Remarks: Axial versus Centrifugal Design......Page 426
11.5 Axial Turbines......Page 427
11.5.1 Torque, Power, and Pressure Drop......Page 428
11.5.2 Axial Turbine Geometry and Velocity Triangles......Page 430
11.5.3 Turbine Degree of Reaction......Page 431
11.5.4 Remarks on Exposed Tip Rotors (Wind Turbines and Propellers)......Page 439
REFERENCE......Page 442
APPENDIX A Conversion Factors......Page 449
APPENDIX B Properties of Compressible Isentropic Flow......Page 451
APPENDIX C Properties of Normal Shock Flow......Page 453
Index......Page 455