Viscous Flows (eBook)

Front Cover 1
Viscous Flows: The Practical Use of Theory 4
Copyright Page 5
Table of Contents 8
Dedication 6
Invocation 14
Preface 16
Acknowledgments 22
PART I: ONE-DIMENSIONAL LAMINAR FLOWS 24
Chapter 1. Identification of Geometries and Dimensionless Variables 26
Flows that Produce One-Dimensional Velocity Fields 26
Dimensional Considerations 28
Dimensionless Groups Determining One-Dimensionality 35
Alternative Dimensionless Groups 37
Summary 38
Problems 38
References 39
Chapter 2. Momentum Transfer, Viscosity, and Shear Stress 40
Momentum Transfer by Molecular Diffusion 40
Non-Newtonian Fluids 43
Applications 51
Summary 51
Problems 51
References 57
Chapter 3. Newtonian Flow between Parallel Plates 60
Single-Phase Flow 60
Concurrent, Stratified, Horizontal Flow of Two Immiscible Fluids 66
Summary 71
Problems 72
References 73
Chapter 4. Newtonian Flow in Round Tubes and Circular Annuli 74
Single-Phase Flow in Round Tubes 74
Concurrent Annular Two-Phase Flow in a Round Tube 78
Flow through a Circular Annulus 81
Summary 92
Problems 92
References 94
Chapter 5. Non-Newtonian Flow through Channels 96
Pseudoplastics and Dilatants 96
Bingham Plastics 98
General Viscous Fluids 100
The Metzner-Reed Model 103
Other Forced Flows 107
Summary 107
Problems 108
References 111
Chapter 6. Thin Films and Other Open, Gravitational Flows 114
Newtonian Flow Down an Inclined Plane 115
Other Free Flows 123
Summary 125
Problems 125
References 127
Chapter 7. Couette Flows 130
Planar Couette Flow of a Newtonian Fluid 130
Planar Couette Flow of Non-Newtonian Fluids 132
Longitudinal Annular Couette Flow 135
Planar Rotational Couette Flow 137
Annular Rotational Couette Flow 139
Couette Flow in a Gap of Varying Depth 142
Planar Couette-Poiseuille Flow 145
Summary 148
Problems 149
References 152
PART II: THE GENERAL EQUATIONS OF MOTION 154
Chapter 8. Derivation of the General Mass and Force-Momentum Balances 156
The Mass Balance 156
The Force-Momentum Balance 162
Molecular Transfer of Momentum for Newtonian Fluids 164
The Force-Momentum Balance for Newtonian Fluids 165
Integral Formulations 171
The Energy Balance 173
Summary 173
Problems 174
References 176
Chapter 9. Modified Forms of the General Mass and Force-Momentum Balances 178
Special Formulations for General Conditions 178
Special Formulations for Creeping Flow 185
Special Formulations for Inviscid Flow 187
Summary 193
Problems 193
References 194
Chapter 10. Exact, Closed-Form Solutions of the Equations of Motion 196
Introduction 196
Exact Solutions for General Flows 199
Exact Solutions for Creeping Flow 216
Exact Solutions for Inviscid Flow 235
Summary 266
Problems 266
References 271
PART III: UNCONFINED, MULTIDIMENSIONAL, LAMINAR FLOWS 274
Chapter 11. The Blasius Solution for Laminar Flow along a Flat Plate 278
Differential Boundary-Layer Model 278
Stream-Function Model 279
Reduction of Model 280
Derivation of Asymptotic Solutions 285
Derivation of a Correlating Equation 287
Alternative Methods of Solution 288
Summary 289
Problems 289
References 290
Chapter 12. Integral Boundary-Layer Solution for Laminar Flow along a Flat Plate 294
Heuristic Derivation of the Model 294
Derivation from the Differential Model 296
Pohlhausen Method of Solution 296
Summary 300
Problems 300
References 301
Chapter 13. Experimental Results and Extended Solutions for Laminar Flow along a Flat Plate 302
Slightly Inertial (Tomotika–Aoi) Flow along a Flat Plate 302
Sub-Boundary-Layer (Imai) Flow along a Flat Plate 303
Effect of Finite Length of Plate 304
Numerical Solutions for Flow along a Flat Plate 304
Experimental Results for the Flat Plate 307
Flow along a Porous Flat Plate with Suction or Blowing 310
Power-Law (Acrivos) Flows 316
Boundary-Layer Thickness 318
Summary 319
Problems 319
References 321
Chapter 14. Laminar Flow over Wedges and Disks 324
Thin-Boundary-Layer Flow over a Wedge (Falkner–Skan Flow) 324
Thin-Boundary-Layer Flow Impinging on a Disk (Homann Flow) 331
Integral Boundary-Layer Method for a Wedge 334
Boundary-Layer Thicknesses 336
Summary 336
Problems 336
References 338
Chapter 15. Laminar Flow over a Circular Cylinder 340
Inviscid Flow 344
Creeping Flow 347
Slightly Inertial (Lamb) Flow 347
Boundary-Layer Flow 348
Numerical Solutions 353
Comparison of Solutions with Experimental Measurements 356
Summary 373
Problems 374
References 378
Chapter 16. Laminar Flow over a Solid Sphere 382
Inviscid Flow 382
Creeping (Stokes) Flow 390
Slightly Inertial (Oseen) Flow 391
Boundary-Layer Flow 393
Newton's Equation for Large ReD 399
Numerical Solutions 400
Comparison of Solutions with Experimental Measurements 402
Ejection and Suction 415
Moving Spheres 422
Summary 428
Problems 428
References 430
Chapter 17. The Motion of Bubbles and Droplets 434
Qualitative Characteristics of Bubble Motion 434
Qualitative Characteristics of Droplet Motion in Gases and Liquids 438
Comparative Behavior of Bubbles, Droplets, and Solids 438
Dimensional Analysis 439
Theoretical Expressions for Spheres 445
Numerical Solutions for Spheres 448
Theoretical Solutions for Deformed Bubbles and Droplets 453
Comparison of Theoretical and Numerical Solutions for Bubbles 459
Comparison of Predicted and Measured Values for Bubbles and Droplets 463
Generalized Correlations for Bubbles and Droplets 491
Summary 498
Problems 498
References 502
Chapter 18. Generalized Methods and Other Geometries 506
Other Geometries and Conditions 506
Generalized Methods 507
Summary 519
Problems 519
References 520
PART IV: FLOW RELATIVE TO DISPERSED SOLIDS 522
Chapter 19. Flow through Porous Media 524
Types of Porous Media 524
Quantitative Characterization of Porous Media 525
Models and Solutions for Creeping (Laminar) Flow 532
Completely Inertial Flow 541
Models and Solutions for the Complete Regime of Flow 542
Miscellaneous Effects 554
Summary 555
Problems 555
References 559
Chapter 20. The Relative Motion of Fluids and Dispersed Solids 562
Single Particles 562
Batch Sedimentation 574
Fluidization of Solid Particles 574
Particulate Fluidization 587
Aggregative Fluidization 594
Summary 599
Problems 600
References 604
Appendix 606
Credits 608
Author Index 611
Subject Index 617