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Overview
The Chemical Engineer's Practical Guide to Contemporary Fluid Mechanics
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 wasteprocessing industries.
Fluid Mechanics for Chemical Engineers, Second Edition, with Microfluidics and CFD, systematically introduces fluid mechanics from the perspective of the chemical engineer who must understand actual physical behavior and solve realworld problems. Building on a first edition that earned Choice Magazine's Outstanding Academic Title award, this edition has been thoroughly updated to reflect the field's latest advances.
This second edition contains extensive new coverage of both microfluidics and computational fluid dynamics, systematically demonstrating CFD through detailed examples using FlowLab and COMSOL Multiphysics. The chapter on turbulence has been extensively revised to address more complex and realistic challenges, including turbulent mixing and recirculating flows.
Part I offers a clear, succinct, easytofollow introduction to macroscopic fluid mechanics, including physical properties; hydrostatics; basic rate laws for mass, energy, and momentum; and the fundamental principles of flow through pumps, pipes, and other equipment. Part II turns to microscopic fluid mechanics, which covers
Fluid Mechanics for Chemical Engineers, Second Edition, with Microfluidics and CFD, includes 83 completely worked practical examples, several of which involve FlowLab and COMSOL Multiphysics. There are also 330 endofchapter problems of varying complexity, including several from the University of Cambridge chemical engineering examinations. The author covers all the material needed for the fluid mechanics portion of the Professional Engineer's examination.
The author's Web site, www.engin.umich.edu/~fmche/, provides additional notes on individual chapters, problemsolving tips, errata, and more.
Editorial Reviews
Booknews
A text for undergraduates and firstyear graduate students, offering four chapters on macroscopic or relatively largescale phenomena, followed by eight chapters on microscopic or relatively smallscale phenomena. Provides numerous realworld examples and chapter problems of increasing complexity, including several from the University of Cambridge chemical engineering exams, and covers all the material necessary to pass the fluid mechanics portion of the Professional Engineer's exam. Annotation c. by Book News, Inc., Portland, Or.Product Details
Related Subjects
Meet the Author
James O. Wilkes is Professor Emeritus of Chemical Engineering at the University of Michigan, where he served as department chairman and assistant dean for admissions. From 1989 to 1992, he was an Arthur F. Thurnau Professor. Wilkes coauthored Applied Numerical Methods (Wiley, 1969) and Digital Computing and Numerical Methods (Wiley, 1973). He received his bachelor s degree from the University of Cambridge and his M.S. and Ph.D. in chemical engineering from the University of Michigan. His research interests involve numerical methods for solving a wide variety of engineering problems.
Read an Excerpt
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.^{1} The 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 endofchapter 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 website http://www.engin.umich.edu/~fmche is 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 is wilkes@umich.edu. The text was composed on a Power Macintosh G4 computer using the TEXtures "typesetting" program. Elevenpoint 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 appreciation^{2} of 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 résumé 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. 5355, February28, 1983.
Table of Contents
Preface.
I. MACROSCOPIC FLUID MECHANICS.
1. Introduction to Fluid Mechanics.
1.1 Fluid Mechanics in Chemical Engineering
1.2 General Concepts of a Fluid
1.3 Stresses, Pressure, Velocity, and the Basic Laws
1.4 Physical Properties  Density, Viscosity, and Surface Tension
1.5 Units and Systems of Units
Example 1.1  Units Conversion
Example 1.2  Mass of Air in a Room
1.6 Hydrostatics
Example 1.3  Pressure in an Oil Storage Tank
Example 1.4  Multiple Fluid Hydrostatics
Example 1.5  Pressure Variations in a Gas
Example 1.6  Hydrostatic Force on a Curved Surface
Example 1.7  Application of Archimedes?f Law
1.7 Pressure Change Caused by Rotation
Example 1.8  Overflow from a Spinning Container
Problems for Chapter 1
2. Mass, Energy, and Momentum Balances.
2.1 General Conservation Laws
2.2 Mass Balances
Example 2.1  Mass Balance for Tank Evacuation
2.3 Energy Balances
Example 2.2  Pumping nPentane
2.4 Bernoulli’s Equation
2.5 Applications of Bernoulli?fs Equation
Example 2.3  Tank Filling
2.6 Momentum Balances
Example 2.4  Impinging Jet of Water
Example 2.5  Velocity of Wave on Water
Example 2.6  Flow Measurement by a Rotameter
2.7 Pressure, Velocity, and Flow Rate Measurement
Problems for Chapter
3. Fluid Friction in Pipes.
3.1 Introduction
3.2 Laminar Flow
Example 3.1  Polymer Flow in a Pipeline
3.3 Models for Shear Stress
3.4 Piping and Pumping Problems
Example 3.2  Unloading Oil from a Tanker
Specified Flow Rate and Diameter
Example 3.3  Unloading Oil from a Tanker
Specified Diameter and Pressure Drop
Example 3.4  Unloading Oil from a Tanker
Specified Flow Rate and Pressure Drop
Example 3.5  Unloading Oil from a Tanker
Miscellaneous Additional Calculations
3.5 Flow in Noncircular Ducts
Example 3.6  Flow in an Irrigation Ditch
3.6 Compressible Gas Flow in Pipelines
3.7 Compressible Flow in Nozzles
3.8 Complex Piping Systems
Example 3.7  Solution of a Piping/Pumping Problem
Problems for Chapter 3
4. Flow in Chemical Engineering Equipment.
4.1 Introduction
4.2 Pumps and Compressors
Example 4.1  Pumps in Series and Parallel
4.3 Drag Force on Solid Particles in Fluids
Example 4.2  Manufacture of Lead Shot
4.4 Flow Through Packed Beds
Example 4.3  Pressure Drop in a PackedBed Reactor
4.5 Filtration
4.6 Fluidization
4.7 Dynamics of a BubbleCap Distillation Column
4.8 Cyclone Separators
4.9 Sedimentation
4.10 Dimensional Analysis
Example 4.4  Thickness of the Laminar Sublayer
Problems for Chapter 4
II. MICROSCOPIC FLUID MECHANICS.
5. Differential Equations of Fluid Mechanics.
5.1 Introduction to Vector Analysis
5.2 Vector Operations
Example 5.1  The Gradient of a Scalar
Example 5.2  The Divergence of a Vector
Example 5.3  An Alternative to the Differential Element
Example 5.4  The Curl of a Vector
Example 5.5  The Laplacian of a Scalar
5.3 Other Coordinate Systems
5.4 The Convective Derivative
5.5 Differential Mass Balance
Example 5.6  Physical Interpretation of the Net Rate of Mass Outflow
Example 5.7  Alternative Derivation of the Continuity Equation
5.6 Differential Momentum Balances
5.7 Newtonian Stress Components in Cartesian Coordinates
Example 5.8  ConstantViscosity Momentum Balances in Terms of Velocity Gradients
Example 5.9  Vector Form of VariableViscosity Momentum Balance
Problems for Chapter 5
6. Solution of ViscousFlow Problems.
6.1 Introduction
6.2 Solution of the Equations of Motion in Rectangular Coordinates
Example 6.1  Flow Between Parallel Plates
6.3 Alternative Solution Using a Shell Balance
Example 6.2  Shell Balance for Flow Between Parallel Plates
Example 6.3  Film Flow on a Moving Substrate
Example 6.4  Transient Viscous Diffusion of Momentum (FEMLAB)
6.4 Poiseuille and Couette Flows in Polymer Processing
Example 6.5  The SingleScrew Extruder
Example 6.6  Flow Patterns in a Screw Extruder (FEMLAB)
6.5 Solution of the Equations of Motion in Cylindrical x Table of Contents Coordinates
Example 6.7  Flow Through an Annular Die
Example 6.8  Spinning a Polymeric Fiber
6.6 Solution of the Equations of Motion in Spherical Coordinates
Example 6.9  Analysis of a ConeandPlate Rheometer
Problems for Chapter 6
7. Laplace’s Equation, Irrotational and PorousMedia Flows.
7.1 Introduction
7.2 Rotational and Irrotational Flows
Example 7.1  Forced and Free Vortices
7.3 Steady TwoDimensional Irrotational Flow
7.4 Physical Interpretation of the Stream Function
7.5 Examples of Planar Irrotational Flow
Example 7.2  Stagnation Flow
Example 7.3  Combination of a Uniform Stream and a Line Sink (C)
Example 7.4  Flow Patterns in a Lake (FEMLAB)
7.6 Axially Symmetric Irrotational Flow
7.7 Uniform Streams and Point Sources
7.8 Doublets and Flow Past a Sphere
7.9 SinglePhase Flow in a Porous Medium
Example 7.5  Underground Flow of Water
7.10 TwoPhase Flow in Porous Media
7.11 Wave Motion in Deep Water
Problems for Chapter 7
8. BoundaryLayer Aand Other Nearly Unidirectional Flows.
8.1 Introduction
8.2 Simplified Treatment of Laminar Flow Past a Flat Plate
Example 8.1  Flow in an Air Intake
8.3 Simplification of the Equations of Motion
8.4 Blasius Solution for BoundaryLayer Flow
8.5 Turbulent Boundary Layers
Example 8.2  Laminar and Turbulent Boundary Layers Compared
8.6 Dimensional Analysis of the BoundaryLayer Problem
8.7 BoundaryLayer Separation
Example 8.3  BoundaryLayer Flow Between Parallel Plates (FEMLAB Library)
Example 8.4  Entrance Region for Laminar Flow Between Flat Plates
8.8 The Lubrication Approximation
Example 8.5  Flow in a Lubricated Bearing (FEMLAB)
8.9 Polymer Processing by Calendering
Example 8.6  Pressure Distribution in a Calendered Sheet
8.10 Thin Films and Surface Tension
Problems for Chapter 8
9. Turbulent Flow.
9.1 Introduction
Example 9.1  Numerical Illustration of a Reynolds Stress Term
9.2 Physical Interpretation of the Reynolds Stresse
9.3 MixingLength Theory
9.4 Determination of Eddy Kinematic Viscosity and Mixing Length
9.5 Velocity Profiles Based on Mixing Length Theory 486
Example 9.2  Investigation of the von K?Larm?Lan Hypothesis
9.6 The Universal Velocity Profile for Smooth Pipes
9.7 Friction Factor in Terms of Reynolds Number for Smooth Pipes
Example 9.3  Expression for the Mean Velocity
9.8 Thickness of the Laminar Sublayer
9.9 Velocity Profiles and Friction Factor for Rough Pipe
9.10 BlasiusType Law and the PowerLaw Velocity Profile
9.11 A Correlation for the Reynolds Stresses
9.12 Computation of Turbulence by the k/? Method
Example 9.4  Flow Through an Orifice Plate (FEMLAB)
Example 9.5  Turbulent Jet Flow (FEMLAB)
9.13 Analogies Between Momentum and Heat Transfer
Example 9.6  Evaluation of the Momentum/HeatTransfer Analogies
9.14 Turbulent Jets
Problems for Chapter 9
10. Bubble Motion, TwoPhase Flow, and Fluidization.
10.1 Introduction
10.2 Rise of Bubbles in Unconfined Liquids
Example 10.1  Rise Velocity of Single Bubbles
10.3 Pressure Drop and Void Fraction in Horizontal Pipes
Example 10.2  TwoPhase Flow in a Horizontal Pipe
10.4 TwoPhase Flow in Vertical Pipes
Example 10.3  Limits of Bubble Flow
Example 10.4  Performance of a GasLift Pump
Example 10.5  TwoPhase Flow in a Vertical Pipe
10.5 Flooding
10.6 Introduction to Fluidization
10.7 Bubble Mechanics
10.8 Bubbles in Aggregatively Fluidized Beds
Example 10.6  Fluidized Bed with Reaction (C)
Problems for Chapter 10
11. NonNewtonian Fluids.
11.1 Introduction
11.2 Classification of NonNewtonian Fluids
11.3 Constitutive Equations for Inelastic Viscous Fluids
Example 11.1  Pipe Flow of a PowerLaw Fluid
Example 11.2  Pipe Flow of a Bingham Plastic
Example 11.3  NonNewtonian Flow in a Die (FEMLAB Library)
11.4 Constitutive Equations for Viscoelastic Fluids
11.5 Response to Oscillatory Shear
11.6 Characterization of the Rheological Properties of Fluids
Example 11.4  Proof of the Rabinowitsch Equation
Example 11.5  Working Equation for a Coaxial Cylinder Rheometer: Newtonian Fluid
Problems for Chapter 11
12. Microfluidics and Electrokinetic Flow Effects.
12.1 Introduction
12.2 Physics of Microscale Fluid Mechanics
12.3 Pressuredriven Flow Through Microscale Tubes
Example 12.1  Calculation of Reynolds Numbers
12.4 Mixing, Transport, and Dispersion
12.5 Species, Energy, and Charge Transport
12.6 The Electrical Double Layer and Electrokinetic Phenomena
Example 12.2  Relative Magnitudes of Electroosmotic and Pressuredriven Flow
Example 12.3  Electroosmotic Flow Around a Particle
Example 12.4  Electroosmosis in a Microchannel (FEMLAB)
Example 12.5  Electroosmotic Switching in a Branched Microchannel (FEMLAB)
12.7 Measuring the Zeta Potential
Example 12.6  Magnitude of Typical Streaming Potentials
12.8 Electroviscosity
12.9 Particle and Macromolecule Motion in Microfluidic Channels
Example 12.7  Gravitational and Magnetic Settling of Assay Beads
Problems for Chapter 12
13. An Introduction to Computational Fluid Dynamics and Flowlab.
13.1 Introduction and Motivation
13.2 Numerical Methods
13.3 Learning CFD by Using FlowLab
13.4 Practical CFD Examples
Example 13.1  Developing Flow in a Pipe Entrance Region (FlowLab)
Example 13.2  Pipe Flow Through a Sudden Expansion (FlowLab)
Example 13.3  A TwoDimensional Mixing Junction (FlowLab)
Example 13.4  Flow Over a Cylinder (FlowLab)
References for Chapter 13
14. Femlab for Solving Fluid Mechanics Problems.
14.1 Introduction to FEMLAB
14.2 How to Run FEMLAB
Example 14.1  Flow in a Porous Medium with an Obstruction (FEMLAB)
14.3 Draw Mode
14.4 Solution and Related Modes
14.5 Fluid Mechanics Problems Solvable by FEMLAB
Problems for Chapter 14
Appendix A: Useful Mathematical Relationships.
Appendix B: Answers to the True/False Assertions.
Appendix C: Some Vector and Tensor Operations.
Index.
Preface
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 partsfour chapters on macroscopic or relatively largescale phenomena, followed by ten chapters on microscopic or relatively smallscale 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.
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 14one 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. ^{1} The 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 endofchapter problems have been classified roughly as easy (E), moderate (M), or difficult/lengthy (D). The University of Cambridge has given permissionkindly 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 website http://www.engin.umich.edu/~fmche is maintained as a "bulletin board" for giving additional information about the bookhints for problem solutions, errata, how to contact the authors, etc.as proves desirable. My own Internet address is wilkes@umich.edu. The text was composed on a Power Macintosh G4 computer using the TEXtures "typesetting" program. Elevenpoint 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 appreciation ^{2} of Fox's talents, saying, with almost complete accuracy: "Fox instigated no research and published nothing." How times have changedtoday, unless he were known personally, his résumé 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. 5355, February28, 1983.