Fluid Mechanics for Chemical Engineers : With Microfluidics and CFD

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2005-09-29
  • Publisher: Prentice Hall
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Since most chemical processing applications are conducted either partially or totally in the fluid phase, chemical engineers need a strong understanding of fluid mechanics. Such knowledge is especially valuable for solving problems in the biochemical, chemical, energy, fermentation, materials, mining, petroleum, pharmaceuticals, polymer, and waste-processing industries.

Author Biography

James O. Wilkes is Professor Emeritus of Chemical Engineering at the University of Michigan, and served as department chairman and assistant dean for admissions.

Table of Contents

Prefacep. xv
Macroscopic Fluid Mechanics
Introduction to Fluid Mechanics
Fluid Mechanics in Chemical Engineeringp. 3
General Concepts of a Fluidp. 3
Stresses, Pressure, Velocity, and the Basic Lawsp. 5
Physical Properties-Density, Viscosity, and Surface Tensionp. 10
Units and Systems of Unitsp. 21
Units Conversionp. 24
Mass of Air in a Roomp. 25
Hydrostaticsp. 26
Pressure in an Oil Storage Tankp. 29
Multiple Fluid Hydrostaticsp. 30
Pressure Variations in a Gasp. 31
Hydrostatic Force on a Curved Surfacep. 35
Application of Archimedes' Lawp. 37
Pressure Change Caused by Rotationp. 39
Overflow from a Spinning Containerp. 40
Problems for Chapter 1p. 42
Mass, Energy, and Momentum Balances
General Conservation Lawsp. 55
Mass Balancesp. 57
Mass Balance for Tank Evacuationp. 58
Energy Balancesp. 61
Pumping n-Pentanep. 65
Bernoulli's Equationp. 67
Applications of Bernoulli's Equationp. 70
Tank Fillingp. 76
Momentum Balancesp. 78
Impinging Jet of Waterp. 83
Velocity of Wave on Waterp. 84
Flow Measurement by a Rotameterp. 89
Pressure, Velocity, and Flow Rate Measurementp. 92
Problems for Chapter 2p. 96
Fluid Friction in Pipes
Introductionp. 120
Laminar Flowp. 123
Polymer Flow in a Pipelinep. 128
Models for Shear Stressp. 129
Piping and Pumping Problemsp. 133
Unloading Oil from a Tanker Specified Flow Rate and Diameterp. 142
Unloading Oil from a Tanker Specified Diameter and Pressure Dropp. 144
Unloading Oil from a Tanker Specified Flow Rate and Pressure Dropp. 147
Unloading Oil from a Tanker Miscellaneous Additional Calculationsp. 147
Flow in Noncircular Ductsp. 150
Flow in an Irrigation Ditchp. 152
Compressible Gas Flow in Pipelinesp. 156
Compressible Flow in Nozzlesp. 159
Complex Piping Systemsp. 163
Solution of a Piping/Pumping Problemp. 165
Problems for Chapter 3p. 168
Flow in Chemical Engineering Equipment
Introductionp. 185
Pumps and Compressorsp. 188
Pumps in Series and Parallelp. 193
Drag Force on Solid Particles in Fluidsp. 194
Manufacture of Lead Shotp. 202
Flow Through Packed Bedsp. 204
Pressure Drop in a Packed-Bed Reactorp. 208
Filtrationp. 210
Fluidizationp. 215
Dynamics of a Bubble-Cap Distillation Columnp. 216
Cyclone Separatorsp. 219
Sedimentationp. 222
Dimensional Analysisp. 224
Thickness of the Laminar Sublayerp. 229
Problems for Chapter 4p. 230
Microscopic Fluid Mechanics
Differential Equations of Fluid Mechanics
Introduction to Vector Analysisp. 249
Vector Operationsp. 250
The Gradient of a Scalarp. 253
The Divergence of a Vectorp. 257
An Alternative to the Differential Elementp. 257
The Curl of a Vectorp. 262
The Laplacian of a Scalarp. 262
Other Coordinate Systemsp. 263
The Convective Derivativep. 266
Differential Mass Balancep. 267
Physical Interpretation of the Net Rate of Mass Outflowp. 269
Alternative Derivation of the Continuity Equationp. 270
Differential Momentum Balancesp. 271
Newtonian Stress Components in Cartesian Coordinatesp. 274
Constant-Viscosity Momentum Balances in Terms of Velocity Gradientsp. 280
Vector Form of Variable-Viscosity Momentum Balancep. 284
Problems for Chapter 5p. 285
Solution of Viscous-Flow Problems
Introductionp. 292
Solution of the Equations of Motion in Rectangular Coordinatesp. 294
Flow Between Parallel Platesp. 294
Alternative Solution Using a Shell Balancep. 301
Shell Balance for Flow Between Parallel Platesp. 301
Film Flow on a Moving Substratep. 303
Transient Viscous Diffusion of Momentum (COMSOL)p. 307
Poiseuille and Couette Flows in Polymer Processingp. 312
The Single-Screw Extruderp. 313
Flow Patterns in a Screw Extruder (COMSOL)p. 318
Solution of the Equations of Motion in Cylindrical Coordinatesp. 322
Flow Through an Annular Diep. 322
Spinning a Polymeric Fiberp. 325
Solution of the Equations of Motion in Spherical Coordinatesp. 327
Analysis of a Cone-and-Plate Rheometerp. 328
Problems for Chapter 6p. 333
Laplace's Equation, Irrotational and Porous-Media Flows
Introductionp. 354
Rotational and Irrotational Flowsp. 356
Forced and Free Vorticesp. 359
Steady Two-Dimensional Irrotational Flowp. 361
Physical Interpretation of the Stream Functionp. 364
Examples of Planar Irrotational Flowp. 366
Stagnation Flowp. 369
Combination of a Uniform Stream and a Line Sink (C)p. 371
Flow Patterns in a Lake (COMSOL)p. 373
Axially Symmetric Irrotational Flowp. 378
Uniform Streams and Point Sourcesp. 380
Doublets and Flow Past a Spherep. 384
Single-Phase Flow in a Porous Mediump. 387
Underground Flow of Waterp. 388
Two-Phase Flow in Porous Mediap. 390
Wave Motion in Deep Waterp. 396
Problems for Chapter 7p. 400
Boundary-Layer and Other Nearly Unidirectional Flows
Introductionp. 414
Simplified Treatment of Laminar Flow Past a Flat Platep. 415
Flow in an Air Intake (C)p. 420
Simplification of the Equations of Motionp. 422
Blasius Solution for Boundary-Layer Flowp. 425
Turbulent Boundary Layersp. 428
Laminar and Turbulent Boundary Layers Comparedp. 429
Dimensional Analysis of the Boundary-Layer Problemp. 430
Boundary-Layer Separationp. 433
Boundary-Layer Flow Between Parallel Plates (COMSOL Library)p. 435
Entrance Region for Laminar Flow Between Flat Platesp. 440
The Lubrication Approximationp. 442
Flow in a Lubricated Bearing (COMSOL)p. 448
Polymer Processing by Calenderingp. 450
Pressure Distribution in a Calendered Sheetp. 454
Thin Films and Surface Tensionp. 456
Problems for Chapter 8p. 459
Turbulent Flow
Introductionp. 473
Numerical Illustration of a Reynolds Stress Termp. 479
Physical Interpretation of the Reynolds Stressesp. 480
Mixing-Length Theoryp. 481
Determination of Eddy Kinematic Viscosity and Mixing Lengthp. 484
Velocity Profiles Based on Mixing-Length Theoryp. 486
Investigation of the von Karman Hypothesisp. 487
The Universal Velocity Profile for Smooth Pipesp. 488
Friction Factor in Terms of Reynolds Number for Smooth Pipesp. 490
Expression for the Mean Velocityp. 491
Thickness of the Laminar Sublayerp. 492
Velocity Profiles and Friction Factor for Rough Pipep. 494
Blasius-Type Law and the Power-Law Velocity Profilep. 495
A Correlation for the Reynolds Stressesp. 496
Computation of Turbulence by the [kappa]/[epsilon] Methodp. 499
Flow Through an Orifice Plate (COMSOL)p. 501
Turbulent Jet Flow (COMSOL)p. 505
Analogies Between Momentum and Heat Transferp. 509
Evaluation of the Momentum/Heat-Transfer Analogiesp. 511
Turbulent Jetsp. 513
Problems for Chapter 9p. 521
Bubble Motion, Two-Phase Flow, and Fluidization
Introductionp. 531
Rise of Bubbles in Unconfined Liquidsp. 531
Rise Velocity of Single Bubblesp. 536
Pressure Drop and Void Fraction in Horizontal Pipesp. 536
Two-Phase Flow in a Horizontal Pipep. 541
Two-Phase Flow in Vertical Pipesp. 543
Limits of Bubble Flowp. 546
Performance of a Gas-Lift Pumpp. 550
Two-Phase Flow in a Vertical Pipep. 553
Floodingp. 555
Introduction to Fluidizationp. 559
Bubble Mechanicsp. 561
Bubbles in Aggregatively Fluidized Bedsp. 566
Fluidized Bed with Reaction (C)p. 572
Problems for Chapter 10p. 575
Non-Newtonian Fluids
Introductionp. 591
Classification of Non-Newtonian Fluidsp. 592
Constitutive Equations for Inelastic Viscous Fluidsp. 595
Pipe Flow of a Power-Law Fluidp. 600
Pipe Flow of a Bingham Plasticp. 604
Non-Newtonian Flow in a Die (COMSOL Library)p. 606
Constitutive Equations for Viscoelastic Fluidsp. 613
Response to Oscillatory Shearp. 620
Characterization of the Rheological Properties of Fluidsp. 623
Proof of the Rabinowitsch Equationp. 624
Working Equation for a Coaxial-Cylinder Rheometer: Newtonian Fluidp. 628
Problems for Chapter 11p. 630
Microfluidics and Electrokinetic Flow Effects
Introductionp. 639
Physics of Microscale Fluid Mechanicsp. 640
Pressure-Driven Flow Through Microscale Tubesp. 641
Calculation of Reynolds Numbersp. 641
Mixing, Transport, and Dispersionp. 642
Species, Energy, and Charge Transportp. 644
The Electrical Double Layer and Electrokinetic Phenomenap. 647
Relative Magnitudes of Electroosmotic and Pressure-Driven Flowsp. 648
Electroosmotic Flow Around a Particlep. 653
Electroosmosis in a Microchannel (COMSOL)p. 653
Electroosmotic Switching in a Branched Microchannel (COMSOL)p. 657
Measuring the Zeta Potentialp. 659
Magnitude of Typical Streaming Potentialsp. 660
Electroviscosityp. 661
Particle and Macromolecule Motion in Microfluidic Channelsp. 661
Gravitational and Magnetic Settling of Assay Beadsp. 662
Problems for Chapter 12p. 666
An Introduction to Computational Fluid Dynamics and Flowlab
Introduction and Motivationp. 671
Numerical Methodsp. 673
Learning CFD by Using FlowLabp. 682
Practical CFD Examplesp. 686
Developing Flow in a Pipe Entrance Region (FlowLab)p. 687
Pipe Flow Through a Sudden Expansion (FlowLab)p. 690
A Two-Dimensional Mixing Junction (FlowLab)p. 692
Flow Over a Cylinder (FlowLab)p. 696
References for Chapter 13p. 702
Comsol (Femlab) Multiphysics for Solving Fluid Mechanics Problems
Introduction to COMSOLp. 703
How to Run COMSOLp. 705
Flow in a Porous Medium with an Obstruction (COMSOL)p. 705
Draw Modep. 719
Solution and Related Modesp. 724
Fluid Mechanics Problems Solvable by COMSOLp. 725
Problems for Chapter 14p. 730
Useful Mathematical Relationshipsp. 731
Answers to the True/False Assertionsp. 737
Some Vector and Tensor Operationsp. 740
Indexp. 743
The Authorsp. 753
Table of Contents provided by Ingram. All Rights Reserved.


This text has evolved from a need for a single volume that embraces a wide range of topics in fluid mechanics. The material consists of two parts--four chapters on macroscopicor relatively large-scale phenomena, followed by ten chapters on microscopicor relatively small-scale phenomena. Throughout, I have tried to keep in mind topics of industrial importance to the chemical engineer. The scheme is summarized in the following list of chapters. Part I--Macroscopic Fluid Mechanics1. Introduction to Fluid Mechanics2. Mass, Energy, and Momentum Balances3. Fluid Friction in Pipes4. Flow in Chemical Engineering Equipment Part II--Microscopic Fluid Mechanics5. Differential Equations of Fluid Mechanics6. Solution of Viscous-Flow Problems7. Laplace''s Equation, Irrotational and Porous-Media Flows8. Boundary-Layer and Other Nearly Unidirectional Flows9. Turbulent Flow10. Bubble Motion, Two-Phase Flow, and Fluidization11. Non-Newtonian Fluids12. Microfluidics and Electrokinetic Flow Effects13. An Introduction to Computational Fluid Dynamics and FlowLab14. COMSOL (FEMLAB) Multi-physics for Solving Fluid Mechanics Problems In our experience, an undergraduate fluid mechanics course can be based on Part I plus selected parts of Part II, and a graduate course can be based on much of Part II, supplemented perhaps by additional material on topics such as approximate methods and stability. Second edition.I have attempted to bring the book up to date by the major addition of Chapters 12, 13, and 14--one on microfluidics and two on CFD (computational fluid dynamics). The choice of software for the CFD presented a difficulty; for various reasons, I selected FlowLab and COMSOL Multiphysics, but there was no intention of "promoting" these in favor of other excellent CFD programs.1The use of CFD examples in the classroom really makes the subject come "alive," because the previous restrictive necessities of "nice" geometries and constant physical properties, etc., can now be lifted. Chapter 9, on turbulence, has also been extensively rewritten; here again, CFD allows us to venture beyond the usual flow in a pipe or between parallel plates and to investigate further practical situations such as turbulent mixing and recirculating flows. Example problems.There is an average of about six completely worked examples in each chapter, including several involving COMSOL (dispersed throughout Part II) and FlowLab (all in Chapter 13). The end of each example is marked by a small, hollow square. All the COMSOL examples have been run on a Macintosh G4 computer using FEMLAB 3.1, but have also been checked on a PC; those using a PC or other releases of COMSOL/FEMLAB may encounter slightly different windows than those reproduced here. The format for each COMSOL example is: (a) problem statement, (b) details of COMSOL implementation, and (c) results and discussion (however, item (b) can easily be skipped for those interested only in the results). The numerous end-of-chapter problems have been classified roughly as easy (E), moderate (M), or difficult/lengthy (D). The University of Cambridge has given permission--kindly endorsed by Professor J.F. Davidson, F.R.S.--for several of their chemical engineering examination problems to be reproduced in original or modified form, and these have been given the additional designation of "(C)". Further information.The websitehttp://www.engin.umich.edu/~fmcheis maintained as a "bulletin board" for giving additional information about the book--hints for problem solutions, errata, how to contact the authors, etc.--as proves desirable. My own Internet address iswilkes@umich.edu. The text was composed on a Power Macintosh G4 computer using the TEXtures "typesetting" program. Eleven-point type was used for the majority of the text. Most of the figures were constructed using MacDraw Pro, Excel, and KaleidaGraph. Professor Terence Fox,to whom this book is dedicated, was a Cambridge engineering graduate who worked from 1933 to 1937 at Imperial Chemical Industries Ltd., Billingham, Yorkshire. Returning to Cambridge, he taught engineering from 1937 to 1946 before being selected to lead the Department of Chemical Engineering at the University of Cambridge during its formative years after the end of World War II. As a scholar and a gentleman, Fox was a shy but exceptionally brilliant person who had great insight into what was important and who quickly brought the department to a preeminent position. He succeeded in combining an industrial perspective with intellectual rigor. Fox relinquished the leadership of the department in 1959, after he had secured a permanent new building for it (carefully designed in part by himself). Fox was instrumental in bringing Peter Danckwerts, Kenneth Denbigh, John Davidson, and others into the department. He also accepted me in 1956 as a junior faculty member, and I spent four good years in the CambridgeUniversity Department of Chemical Engineering. Danckwerts subsequently wrote an appreciation2of Fox''s talents, saying, with almost complete accuracy: "Fox instigated no research and published nothing." How times have changed--today, unless he were known personally, his resume would probably be cast aside and he would stand little chance of being hired, let alone of receiving tenure! However, his lectures, meticulously written handouts, enthusiasm, genius, and friendship were a great inspiration to me, and I have much pleasure in acknowledging his positive impact on my career. James O. Wilkes August 18, 2005 1. The software name "FEMLAB" was changed to "COMSOL Multiphysics" in September 2005, the first release under the new name being COMSOL 3.2. 2. P.V. Danckwerts, "Chemical engineering comes to Cambridge," The Cambridge Review, pp. 53-55, February28, 1983.

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