Fluid mechanics for chemical engineers

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
CONTENTS......Page 8
PREFACE......Page 16
PART I—MACROSCOPIC FLUID MECHANICS......Page 20
  1.2 General Concepts of a Fluid......Page 22
  1.3 Stresses, Pressure, Velocity, and the Basic Laws......Page 24
  1.4 Physical Properties—Density, Viscosity, and Surface Tension......Page 29
  1.5 Units and Systems of Units......Page 40
   Example 1.1—Units Conversion......Page 43
   Example 1.2—Mass of Air in a Room......Page 44
  1.6 Hydrostatics......Page 45
   Example 1.3—Pressure in an Oil Storage Tank......Page 48
   Example 1.4—Multiple Fluid Hydrostatics......Page 49
   Example 1.5—Pressure Variations in a Gas......Page 50
   Example 1.6—Hydrostatic Force on a Curved Surface......Page 54
   Example 1.7—Application of Archimedes’ Law......Page 56
  1.7 Pressure Change Caused by Rotation......Page 58
   Example 1.8—Overflow from a Spinning Container......Page 59
  Problems for Chapter 1......Page 61
  2.1 General Conservation Laws......Page 74
  2.2 Mass Balances......Page 76
   Example 2.1—Mass Balance for Tank Evacuation......Page 77
  2.3 Energy Balances......Page 80
   Example 2.2—Pumping n-Pentane......Page 84
  2.4 Bernoulli’s Equation......Page 86
  2.5 Applications of Bernoulli’s Equation......Page 89
   Example 2.3—Tank Filling......Page 95
  2.6 Momentum Balances......Page 97
   Example 2.4—Impinging Jet of Water......Page 102
   Example 2.5—Velocity of Wave on Water......Page 103
   Example 2.6—Flow Measurement by a Rotameter......Page 108
  2.7 Pressure, Velocity, and Flow Rate Measurement......Page 111
  Problems for Chapter 2......Page 115
  3.1 Introduction......Page 139
  3.2 Laminar Flow......Page 142
   Example 3.1—Polymer Flow in a Pipeline......Page 147
  3.3 Models for Shear Stress......Page 148
  3.4 Piping and Pumping Problems......Page 152
   Example 3.2—Unloading Oil from a Tanker Specified Flow Rate and Diameter......Page 161
   Example 3.3—Unloading Oil from a Tanker Specified Diameter and Pressure Drop......Page 163
   Example 3.5—Unloading Oil from a Tanker Miscellaneous Additional Calculations......Page 166
  3.5 Flow in Noncircular Ducts......Page 169
   Example 3.6—Flow in an Irrigation Ditch......Page 171
  3.6 Compressible Gas Flow in Pipelines......Page 175
  3.7 Compressible Flow in Nozzles......Page 178
  3.8 Complex Piping Systems......Page 182
   Example 3.7—Solution of a Piping/Pumping Problem......Page 184
  Problems for Chapter 3......Page 187
  4.1 Introduction......Page 204
  4.2 Pumps and Compressors......Page 207
   Example 4.1—Pumps in Series and Parallel......Page 212
  4.3 Drag Force on Solid Particles in Fluids......Page 213
   Example 4.2—Manufacture of Lead Shot......Page 221
  4.4 Flow Through Packed Beds......Page 223
   Example 4.3—Pressure Drop in a Packed-Bed Reactor......Page 227
  4.5 Filtration......Page 229
  4.6 Fluidization......Page 234
  4.7 Dynamics of a Bubble-Cap Distillation Column......Page 235
  4.8 Cyclone Separators......Page 238
  4.9 Sedimentation......Page 241
  4.10 Dimensional Analysis......Page 243
   Example 4.4—Thickness of the Laminar Sublayer......Page 248
  Problems for Chapter 4......Page 249
PART II—MICROSCOPIC FLUID MECHANICS......Page 266
  5.1 Introduction to Vector Analysis......Page 268
  5.2 Vector Operations......Page 269
   Example 5.1—The Gradient of a Scalar......Page 272
   Example 5.3—An Alternative to the Differential Element......Page 276
   Example 5.5—The Laplacian of a Scalar......Page 281
  5.3 Other Coordinate Systems......Page 282
  5.4 The Convective Derivative......Page 285
  5.5 Differential Mass Balance......Page 286
   Example 5.6—Physical Interpretation of the Net Rate of Mass Outflow......Page 288
   Example 5.7—Alternative Derivation of the Continuity Equation......Page 289
  5.6 Differential Momentum Balances......Page 290
  5.7 Newtonian Stress Components in Cartesian Coordinates......Page 293
   Example 5.8—Constant-Viscosity Momentum Balances in Terms of Velocity Gradients......Page 299
   Example 5.9—Vector Form of Variable-Viscosity Momentum Balance......Page 303
  Problems for Chapter 5......Page 304
  6.1 Introduction......Page 311
   Example 6.1—Flow Between Parallel Plates......Page 313
   Example 6.2—Shell Balance for Flow Between Parallel Plates......Page 320
   Example 6.3—Film Flow on a Moving Substrate......Page 322
   Example 6.4—Transient Viscous Diffusion of Momentum (COMSOL)......Page 326
  6.4 Poiseuille and Couette Flows in Polymer Processing......Page 332
   Example 6.5—The Single-Screw Extruder......Page 333
   Example 6.6—Flow Patterns in a Screw Extruder (COMSOL)......Page 338
   Example 6.7—Flow Through an Annular Die......Page 344
   Example 6.8—Spinning a Polymeric Fiber......Page 347
  6.6 Solution of the Equations of Motion in Spherical Coordinates......Page 349
   Example 6.9—Analysis of a Cone-and-Plate Rheometer......Page 350
  Problems for Chapter 6......Page 355
  7.1 Introduction......Page 376
  7.2 Rotational and Irrotational Flows......Page 378
   Example 7.1—Forced and Free Vortices......Page 381
  7.3 Steady Two-Dimensional Irrotational Flow......Page 383
  7.4 Physical Interpretation of the Stream Function......Page 386
  7.5 Examples of Planar Irrotational Flow......Page 388
   Example 7.2—Stagnation Flow......Page 391
   Example 7.3—Combination of a Uniform Stream and a Line Sink (C)......Page 393
   Example 7.4—Flow Patterns in a Lake (COMSOL)......Page 395
  7.6 Axially Symmetric Irrotational Flow......Page 401
  7.7 Uniform Streams and Point Sources......Page 403
  7.8 Doublets and Flow Past a Sphere......Page 407
  7.9 Single-Phase Flow in a Porous Medium......Page 410
   Example 7.5—Underground Flow of Water......Page 411
  7.10 Two-Phase Flow in Porous Media......Page 413
  7.11 Wave Motion in Deep Water......Page 419
  Problems for Chapter 7......Page 423
  8.1 Introduction......Page 437
  8.2 Simplified Treatment of Laminar Flow Past a Flat Plate......Page 438
   Example 8.1—Flow in an Air Intake (C)......Page 443
  8.3 Simplification of the Equations of Motion......Page 445
  8.4 Blasius Solution for Boundary-Layer Flow......Page 448
  8.5 Turbulent Boundary Layers......Page 451
   Example 8.2—Laminar and Turbulent Boundary Layers Compared......Page 452
  8.6 Dimensional Analysis of the Boundary-Layer Problem......Page 453
  8.7 Boundary-Layer Separation......Page 456
   Example 8.3—Boundary-Layer Flow Between Parallel Plates (COMSOL)......Page 458
   Example 8.4—Entrance Region for Laminar Flow Between Flat Plates......Page 465
  8.8 The Lubrication Approximation......Page 467
   Example 8.5—Flow in a Lubricated Bearing (COMSOL)......Page 473
  8.9 Polymer Processing by Calendering......Page 476
   Example 8.6—Pressure Distribution in a Calendered Sheet......Page 480
  8.10 Thin Films and Surface Tension......Page 482
  Problems for Chapter 8......Page 485
  9.1 Introduction......Page 499
   Example 9.1—Numerical Illustration of a Reynolds Stress Term......Page 505
  9.2 Physical Interpretation of the Reynolds Stresses......Page 506
  9.3 Mixing-Length Theory......Page 507
  9.4 Determination of Eddy Kinematic Viscosity and Mixing Length......Page 510
  9.5 Velocity Profiles Based on Mixing-Length Theory......Page 512
   Example 9.2—Investigation of the von Kármán Hypothesis......Page 513
  9.6 The Universal Velocity Profile for Smooth Pipes......Page 514
  9.7 Friction Factor in Terms of Reynolds Number for Smooth Pipes......Page 516
   Example 9.3—Expression for the Mean Velocity......Page 517
  9.8 Thickness of the Laminar Sublayer......Page 518
  9.9 Velocity Profiles and Friction Factor for Rough Pipe......Page 520
  9.10 Blasius-Type Law and the Power-Law Velocity Profile......Page 521
  9.11 A Correlation for the Reynolds Stresses......Page 522
  9.12 Computation of Turbulence by the κ–ɛ Method......Page 525
   Example 9.4—Flow Through an Orifice Plate (COMSOL)......Page 527
   Example 9.5—Turbulent Flow in an Obstructed U-Duct (COMSOL)......Page 533
  9.13 Analogies Between Momentum and Heat Transfer......Page 539
   Example 9.6—Evaluation of the Momentum/Heat- Transfer Analogies......Page 541
  9.14 Turbulent Jets......Page 543
  Problems for Chapter 9......Page 551
  10.2 Rise of Bubbles in Unconfined Liquids......Page 561
  10.3 Pressure Drop and Void Fraction in Horizontal Pipes......Page 566
   Example 10.2—Two-Phase Flow in a Horizontal Pipe......Page 571
  10.4 Two-Phase Flow in Vertical Pipes......Page 573
   Example 10.3—Limits of Bubble Flow......Page 576
   Example 10.4—Performance of a Gas-Lift Pump......Page 580
   Example 10.5—Two-Phase Flow in a Vertical Pipe......Page 583
  10.5 Flooding......Page 585
  10.6 Introduction to Fluidization......Page 589
  10.7 Bubble Mechanics......Page 591
  10.8 Bubbles in Aggregatively Fluidized Beds......Page 596
   Example 10.6—Fluidized Bed with Reaction (C)......Page 602
  Problems for Chapter 10......Page 605
  11.1 Introduction......Page 621
  11.2 Classification of Non-Newtonian Fluids......Page 622
  11.3 Constitutive Equations for Inelastic Viscous Fluids......Page 625
   Example 11.1—Pipe Flow of a Power-Law Fluid......Page 630
   Example 11.2—Pipe Flow of a Bingham Plastic......Page 634
   Example 11.3—Non-Newtonian Flow in a Die (COMSOL)......Page 636
  11.4 Constitutive Equations for Viscoelastic Fluids......Page 645
  11.5 Response to Oscillatory Shear......Page 652
  11.6 Characterization of the Rheological Properties of Fluids......Page 655
   Example 11.4—Proof of the Rabinowitsch Equation......Page 656
   Example 11.5—Working Equation for a Coaxial- Cylinder Rheometer: Newtonian Fluid......Page 661
  Problems for Chapter 11......Page 663
  12.1 Introduction......Page 672
  12.2 Physics of Microscale Fluid Mechanics......Page 673
   Example 12.1—Calculation of Reynolds Numbers......Page 674
  12.4 Mixing, Transport, and Dispersion......Page 675
  12.5 Species, Energy, and Charge Transport......Page 677
  12.6 The Electrical Double Layer and Electrokinetic Phenomena......Page 680
   Example 12.2—Relative Magnitudes of Electroosmotic and Pressure-Driven Flows......Page 681
   Example 12.4—Electroosmosis in a Microchannel (COMSOL)......Page 686
   Example 12.5—Electroosmotic Switching in a Branched Microchannel (COMSOL)......Page 692
  12.7 Measuring the Zeta Potential......Page 695
   Example 12.6—Magnitude of Typical Streaming Potentials......Page 696
  12.9 Particle and Macromolecule Motion in Microfluidic Channels......Page 697
   Example 12.7—Gravitational and Magnetic Settling of Assay Beads......Page 698
  Problems for Chapter 12......Page 702
  13.1 Introduction and Motivation......Page 707
  13.2 Numerical Methods......Page 709
  13.3 Learning CFD by Using ANSYS Fluent......Page 718
  13.4 Practical CFD Examples......Page 722
   Example 13.1—Fluent: Developing Flow in a Pipe Entrance Region......Page 723
   Example 13.2—Fluent: Pipe Flow Through a Sudden Expansion......Page 726
   Example 13.3—Fluent: A Two-Dimensional Mixing Junction......Page 728
   Example 13.4—Fluent: Flow over a Cylinder......Page 732
  References for Chapter 13......Page 738
  14.1 COMSOL Multiphysics—An Overview......Page 739
  14.2 The Steps for Solving Problems in COMSOL......Page 742
  14.3 How to Run COMSOL......Page 744
   Example 14.1—Flow in a Porous Medium with an Impervious Hole (COMSOL)......Page 745
   Example 14.2—Drawing a Complex Shape (COMSOL)......Page 757
  14.4 Variables, Constants, Expressions, and Units......Page 760
  14.5 Boundary Conditions......Page 761
  14.6 Variables Used by COMSOL......Page 762
  14.7 Wall Functions in Turbulent-Flow Problems......Page 763
  14.8 Streamline Plotting in COMSOL......Page 766
  14.9 Special COMSOL Features Used in the Examples......Page 768
  14.10 Drawing Tools......Page 773
  14.11 Fluid Mechanics Problems Solvable by COMSOL......Page 775
  14.12 Conclusion—Problems and Learning Tools......Page 780
APPENDIX A: USEFUL MATHEMATICAL RELATIONSHIPS......Page 781
APPENDIX B: ANSWERS TO THE TRUE/FALSE ASSERTIONS......Page 787
APPENDIX C: SOME VECTOR AND TENSOR OPERATIONS......Page 790
 C......Page 792
 D......Page 793
 F......Page 794
 J......Page 795
 N......Page 796
 P......Page 797
 S......Page 798
 V......Page 799
 Z......Page 800
COMSOL MULTIPHYSICS INDEX......Page 801
THE AUTHORS......Page 803