Fluid Mechanics For Chemical Engineers
Fluid Mechanics forChemical EngineersSecond Editionwith Microfluidics and CFD
Prentice Hall International Series in thePhysical and Chemical Engineering SciencesVisit informit.com /ph /physandchemfor a complete list of available publications.The Prentice Hall International Series in the Physical andChemical Engineering Sciences had its auspicious beginning in1956 under the direction of Neal R. Amundsen. The series comprises themost widely adopted college textbooks and supplements for chemicalengineering education. Books in this series are written by the foremosteducators and researchers in the field of chemical engineering.
FLUID MECHANICS FORCHEMICAL ENGINEERSSecond Editionwith Microfluidics and CFDJAMES O. WILKESDepartment of Chemical EngineeringThe University of Michigan, Ann Arbor, MIwith contributions bySTACY G. BIRMINGHAM: Non-Newtonian FlowMechanical Engineering DepartmentGrove City College, PABRIAN J. KIRBY: MicrofluidicsSibley School of Mechanical and Aerospace EngineeringCornell University, Ithaca, NYCOMSOL (FEMLAB): Multiphysics ModelingCOMSOL, Inc., Burlington, MACHI-YANG CHENG: Computational Fluid Dynamics and FlowLabFluent, Inc., Lebanon, NHPrentice Hall Professional Technical ReferenceUpper Saddle River, NJ Boston Indianapolis San FranciscoNew York Toronto Montreal London Munich Paris MadridCapetown Sydney Tokyo Singapore Mexico City
Many of the designations used by manufacturers and sellers to distinguish their productsare claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed with initialcapital letters or in all capitals.The author and publisher have taken care in the preparation of this book, but makeno expressed or implied warranty of any kind and assume no responsibility for errors oromissions. No liability is assumed for incidental or consequential damages in connectionwith or arising out of the use of the information or programs contained herein.The publisher offers excellent discounts on this book when ordered in quantity for bulkpurchases or special sales, which may include electronic versions and/or custom coversand content particular to your business, training goals, marketing focus, and brandinginterests.For more information, please contact:U.S. Corporate and Government Sales(800) 382–3419corpsales@pearsontechgroup.comFor sales outside the U.S., please contact:International Salesinternational@pearsoned.comVisit us on the Web: www.phptr.comLibrary of Congress Cataloging-in-Publication DataWilkes, James O.Fluid mechanics for chemical engineers, 2nd ed., with microfluidicsand CFD/James O. Wilkes.p. cm.Includes bibliographical references and index.ISBN 0–13–148212–2 (alk. paper)1. Chemical processes. 2. Fluid dynamics. I. Title.TP155.7.W55 2006660’.29–dc222005017816c 2006 Pearson Education, Inc.Copyright All rights reserved. Printed in the United States of America. This publication is protectedby copyright, and permission must be obtained from the publisher prior to any prohibitedreproduction, storage in a retrieval system, or transmission in any form or by any means,electronic, mechanical, photocopying, recording, or likewise. For information regardingpermissions, write to:Pearson Education, Inc.Rights and Contracts DepartmentOne Lake StreetUpper Saddle River, NJ 07458ISBN 0-13-148212-2Text printed in the United States on recycled paper at Courier Westford in Westford, Massachusetts8th PrintingOctober 2012.
Dedicated to the memory ofTerence Robert Corelli FoxShell Professor of Chemical EngineeringUniversity of Cambridge, 1946–1959
This page intentionally left blank
CONTENTSPREFACExvPART I—MACROSCOPIC FLUID MECHANICSCHAPTER 1—INTRODUCTION TO FLUID MECHANICS1.11.21.31.41.51.61.7Fluid Mechanics in Chemical EngineeringGeneral Concepts of a FluidStresses, Pressure, Velocity, and the Basic LawsPhysical Properties—Density, Viscosity, and Surface TensionUnits and Systems of UnitsExample 1.1—Units ConversionExample 1.2—Mass of Air in a RoomHydrostaticsExample 1.3—Pressure in an Oil Storage TankExample 1.4—Multiple Fluid HydrostaticsExample 1.5—Pressure Variations in a GasExample 1.6—Hydrostatic Force on a Curved SurfaceExample 1.7—Application of Archimedes’ LawPressure Change Caused by RotationExample 1.8—Overflow from a Spinning ContainerProblems for Chapter 133510212425262930313537394042CHAPTER 2—MASS, ENERGY, AND MOMENTUM BALANCES2.12.22.32.42.52.6General Conservation LawsMass BalancesExample 2.1—Mass Balance for Tank EvacuationEnergy BalancesExample 2.2—Pumping n-PentaneBernoulli’s EquationApplications of Bernoulli’s EquationExample 2.3—Tank FillingMomentum BalancesExample 2.4—Impinging Jet of WaterExample 2.5—Velocity of Wave on WaterExample 2.6—Flow Measurement by a Rotametervii555758616567707678838489
Contentsviii2.7Pressure, Velocity, and Flow Rate MeasurementProblems for Chapter 29296CHAPTER 3—FLUID FRICTION IN PIPES3.13.23.33.43.53.63.73.8IntroductionLaminar FlowExample 3.1—Polymer Flow in a PipelineModels for Shear StressPiping and Pumping ProblemsExample 3.2—Unloading Oil from a TankerSpecified Flow Rate and DiameterExample 3.3—Unloading Oil from a TankerSpecified Diameter and Pressure DropExample 3.4—Unloading Oil from a TankerSpecified Flow Rate and Pressure DropExample 3.5—Unloading Oil from a TankerMiscellaneous Additional CalculationsFlow in Noncircular DuctsExample 3.6—Flow in an Irrigation DitchCompressible Gas Flow in PipelinesCompressible Flow in NozzlesComplex Piping SystemsExample 3.7—Solution of a Piping/Pumping ProblemProblems for Chapter HAPTER 4—FLOW IN CHEMICAL ENGINEERING onPumps and CompressorsExample 4.1—Pumps in Series and ParallelDrag Force on Solid Particles in FluidsExample 4.2—Manufacture of Lead ShotFlow Through Packed BedsExample 4.3—Pressure Drop in a Packed-Bed ReactorFiltrationFluidizationDynamics of a Bubble-Cap Distillation ColumnCyclone SeparatorsSedimentationDimensional AnalysisExample 4.4—Thickness of the Laminar SublayerProblems for Chapter 4185188193194202204208210215216219222224229230
ContentsixPART II—MICROSCOPIC FLUID MECHANICSCHAPTER 5—DIFFERENTIAL EQUATIONS OF FLUID MECHANICS5.15.25.35.45.55.65.7Introduction to Vector AnalysisVector OperationsExample 5.1—The Gradient of a ScalarExample 5.2—The Divergence of a VectorExample 5.3—An Alternative to the DifferentialElementExample 5.4—The Curl of a VectorExample 5.5—The Laplacian of a ScalarOther Coordinate SystemsThe Convective DerivativeDifferential Mass BalanceExample 5.6—Physical Interpretation of the Net Rateof Mass OutflowExample 5.7—Alternative Derivation of the ContinuityEquationDifferential Momentum BalancesNewtonian Stress Components in Cartesian CoordinatesExample 5.8—Constant-Viscosity Momentum Balancesin Terms of Velocity GradientsExample 5.9—Vector Form of Variable-ViscosityMomentum BalanceProblems for Chapter 85CHAPTER 6—SOLUTION OF VISCOUS-FLOW PROBLEMS6.16.26.36.4IntroductionSolution of the Equations of Motion in RectangularCoordinatesExample 6.1—Flow Between Parallel PlatesAlternative Solution Using a Shell BalanceExample 6.2—Shell Balance for Flow Between ParallelPlatesExample 6.3—Film Flow on a Moving SubstrateExample 6.4—Transient Viscous Diffusion ofMomentum (COMSOL)Poiseuille and Couette Flows in Polymer ProcessingExample 6.5—The Single-Screw ExtruderExample 6.6—Flow Patterns in a Screw Extruder(COMSOL)292294294301301303307312313318
xContents6.56.6Solution of the Equations of Motion in CylindricalCoordinatesExample 6.7—Flow Through an Annular DieExample 6.8—Spinning a Polymeric FiberSolution of the Equations of Motion in SphericalCoordinatesExample 6.9—Analysis of a Cone-and-Plate RheometerProblems for Chapter 6322322325327328333CHAPTER 7—LAPLACE’S EQUATION, IRROTATIONAL ANDPOROUS-MEDIA onRotational and Irrotational FlowsExample 7.1—Forced and Free VorticesSteady Two-Dimensional Irrotational FlowPhysical Interpretation of the Stream FunctionExamples of Planar Irrotational FlowExample 7.2—Stagnation FlowExample 7.3—Combination of a Uniform Stream anda Line Sink (C)Example 7.4—Flow Patterns in a Lake (COMSOL)Axially Symmetric Irrotational FlowUniform Streams and Point SourcesDoublets and Flow Past a SphereSingle-Phase Flow in a Porous MediumExample 7.5—Underground Flow of WaterTwo-Phase Flow in Porous MediaWave Motion in Deep WaterProblems for Chapter 00CHAPTER 8—BOUNDARY-LAYER AND OTHER NEARLYUNIDIRECTIONAL FLOWS8.18.28.38.48.58.6IntroductionSimplified Treatment of Laminar Flow Past a Flat PlateExample 8.1—Flow in an Air Intake (C)Simplification of the Equations of MotionBlasius Solution for Boundary-Layer FlowTurbulent Boundary LayersExample 8.2—Laminar and Turbulent BoundaryLayers ComparedDimensional Analysis of the Boundary-Layer Problem414415420422425428429430
Contents8.78.88.98.10Boundary-Layer SeparationExample 8.3—Boundary-Layer Flow Between ParallelPlates (COMSOL Library)Example 8.4—Entrance Region for Laminar FlowBetween Flat PlatesThe Lubrication ApproximationExample 8.5—Flow in a Lubricated Bearing (COMSOL)Polymer Processing by CalenderingExample 8.6—Pressure Distribution in a CalenderedSheetThin Films and Surface TensionProblems for Chapter 8xi433435440442448450454456459CHAPTER 9—TURBULENT 4IntroductionExample 9.1—Numerical Illustration of a ReynoldsStress TermPhysical Interpretation of the Reynolds StressesMixing-Length TheoryDetermination of Eddy Kinematic Viscosity andMixing LengthVelocity Profiles Based on Mixing-Length TheoryExample 9.2—Investigation of the von KármánHypothesisThe Universal Velocity Profile for Smooth PipesFriction Factor in Terms of Reynolds Number for SmoothPipesExample 9.3—Expression for the Mean VelocityThickness of the Laminar SublayerVelocity Profiles and Friction Factor for Rough PipeBlasius-Type Law and the Power-Law Velocity ProfileA Correlation for the Reynolds StressesComputation of Turbulence by the k/ε MethodExample 9.4—Flow Through an Orifice Plate (COMSOL)Example 9.5—Turbulent Jet Flow (COMSOL)Analogies Between Momentum and Heat TransferExample 9.6—Evaluation of the Momentum/HeatTransfer AnalogiesTurbulent JetsProblems for Chapter 05509511513521
xiiContentsCHAPTER 10—BUBBLE MOTION, TWO-PHASE FLOW, roductionRise of Bubbles in Unconfined LiquidsExample 10.1—Rise Velocity of Single BubblesPressure Drop and Void Fraction in Horizontal PipesExample 10.2—Two-Phase Flow in a Horizontal PipeTwo-Phase Flow in Vertical PipesExample 10.3—Limits of Bubble FlowExample 10.4—Performance of a Gas-Lift PumpExample 10.5—Two-Phase Flow in a Vertical PipeFloodingIntroduction to FluidizationBubble MechanicsBubbles in Aggregatively Fluidized BedsExample 10.6—Fluidized Bed with Reaction (C)Problems for Chapter PTER 11—NON-NEWTONIAN �cation of Non-Newtonian FluidsConstitutive Equations for Inelastic Viscous FluidsExample 11.1—Pipe Flow of a Power-Law FluidExample 11.2—Pipe Flow of a Bingham PlasticExample 11.3—Non-Newtonian Flow in a Die(COMSOL Library)Constitutive Equations for Viscoelastic FluidsResponse to Oscillatory ShearCharacterization of the Rheological Properties of FluidsExample 11.4—Proof of the Rabinowitsch EquationExample 11.5—Working Equation for a CoaxialCylinder Rheometer: Newtonian FluidProblems for Chapter 11591592595600604606613620623624628630CHAPTER 12—MICROFLUIDICS AND ELECTROKINETICFLOW EFFECTS12.112.212.312.4IntroductionPhysics of Microscale Fluid MechanicsPressure-Driven Flow Through Microscale TubesExample 12.1—Calculation of Reynolds NumbersMixing, Transport, and Dispersion639640641641642
Contents12.512.612.712.812.9Species, Energy, and Charge TransportThe Electrical Double Layer and Electrokinetic PhenomenaExample 12.2—Relative Magnitudes of Electroosmoticand Pressure-Driven FlowsExample 12.3—Electroosmotic Flow Around a ParticleExample 12.4—Electroosmosis in a Microchannel(COMSOL)Example 12.5—Electroosmotic Switching in aBranched Microchannel (COMSOL)Measuring the Zeta PotentialExample 12.6—Magnitude of Typical StreamingPotentialsElectroviscosityParticle and Macromolecule Motion in Microfluidic ChannelsExample 12.7—Gravitational and Magnetic Settlingof Assay BeadsProblems for Chapter 12xiii644647648653653657659660661661662666CHAPTER 13—AN INTRODUCTION TO COMPUTATIONALFLUID DYNAMICS AND FLOWLAB13.113.213.313.4Introduction and MotivationNumerical MethodsLearning CFD by Using FlowLabPractical CFD ExamplesExample 13.1—Developing Flow in a PipeEntrance Region (FlowLab)Example 13.2—Pipe Flow Through a SuddenExpansion (FlowLab)Example 13.3—A Two-Dimensional Mixing Junction(FlowLab)Example 13.4—Flow Over a Cylinder (FlowLab)References for Chapter 13671673682686687690692696702CHAPTER 14—COMSOL (FEMLAB) MULTIPHYSICS FORSOLVING FLUID MECHANICS PROBLEMS14.114.214.314.4Introduction to COMSOLHow to Run COMSOLExample 14.1—Flow in a Porous Medium with anObstruction (COMSOL)Draw ModeSolution and Related Modes703705705719724
Contentsxiv14.5Fluid Mechanics Problems Solvable by COMSOLProblems for Chapter 14725730APPENDIX A:USEFUL MATHEMATICAL RELATIONSHIPS731APPENDIX B:ANSWERS TO THE TRUE/FALSE ASSERTIONS737APPENDIX C:SOME VECTOR AND TENSOR OPERATIONS740INDEX743THE AUTHORS753
PREFACETHIS text has evolved from a need for a single volume that embraces a widerange of topics in fluid mechanics. The material consists of two parts—fourchapters on macroscopic or relatively large-scale phenomena, followed by ten chapters on microscopic or relatively small-scale phenomena. Throughout, I have triedto keep in mind topics of industrial importance to the chemical engineer. Thescheme is summarized in the following list of chapters.Part I—Macroscopic Fluid Mechanics1. Introduction to Fluid Mechanics2. Mass, Energy, and MomentumBalances3. Fluid Friction in Pipes4. Flow in ChemicalEngineering EquipmentPart II—Microscopic Fluid Mechanics5. Differential Equations of FluidMechanics6. Solution of Viscous-Flow Problems7. Laplace’s Equation, Irrotationaland Porous-Media Flows8. Boundary-Layer and OtherNearly Unidirectional Flows9. Turbulent Flow10. Bubble Motion, Two-Phase Flow,and Fluidization11. Non-Newtonian Fluids12. Microfluidics andElectrokinetic Flow Effects13. An Introduction toComputational FluidDynamics and FlowLab14. COMSOL (FEMLAB) Multiphysics for Solving FluidMechanics ProblemsIn our experience, an undergraduate fluid mechanics course can be based onPart I plus selected parts of Part II, and a graduate course can be based onmuch of Part II, supplemented perhaps by additional material on topics such asapproximate 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 presenteda difficulty; for various reasons, I selected FlowLab and COMSOL Multiphysics,but there was no intention of “promoting” these in favor of other excellent CFDprograms.1 The use of CFD examples in the classroom really makes the subject1The software name “FEMLAB” was changed to “COMSOL Multiphysics” in September 2005, the firstrelease under the new name being COMSOL 3.2.xv
xviPrefacecome “alive,” because the previous restrictive necessities of “nice” geometries andconstant physical properties, etc., can now be lifted. Chapter 9, on turbulence, hasalso been extensively rewritten; here again, CFD allows us to venture beyond theusual flow in a pipe or between parallel plates and to investigate further practicalsituations 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 throughoutPart II) and FlowLab (all in Chapter 13). The end of each example is marked by asmall, hollow square: . All the COMSOL examples have been run on a MacintoshG4 computer using FEMLAB 3.1, but have also been checked on a PC; those usinga 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 anddiscussion (however, item (b) can easily be skipped for those interested only in theresults).The numerous end-of-chapter problems have been classified roughly as easy(E), moderate (M), or difficult/lengthy (D). The University of Cambridge has givenpermission—kindly endorsed by Professor J.F. Davidson, F.R.S.—for several oftheir chemical engineering examination problems to be reproduced in original ormodified form, and these have been given the additional designation of “(C)”.Acknowledgments.I gratefully acknowledge the written contributions ofmy former Michigan colleague Stacy Birmingham (non-Newtonian fluids), BrianKirby of Cornell University (microfluidics), and Chi-Yang Cheng of Fluent, Inc.(FlowLab). Although I wrote most of the COMSOL examples, I have had great helpand cooperation from COMSOL Inc. and the following personnel in particular—Philip Byrne, Bjorn Sjodin, Ed Fontes, Peter Georen, Olof Hernell, Johan Linde,and Rémi Magnard. At Fluent, Inc., Shane Moeykens was instrumental in identifying Chi-Yang Cheng as the person best suited to write the FlowLab chapter.Courtney Esposito and Jordan Schmidt of The MathWorks kindly helped me withMATLAB, needed for the earlier 2.3 version of FEMLAB.I appreciate the assistance of several other friends and colleagues, includingNitin Anturkar, Stuart Churchill, John Ellis, Kevin Ellwood, Scott Fogler, Leenaporn Jongpaiboonkit, Lisa Keyser, Kartic Khilar, Ronald Larson, Susan Montgomery, Donald Nicklin, the late Margaret Sansom, Michael Solomon, SandraSwisher, Rasin Tek, Robert Ziff, and my wife Mary Ann Gibson Wilkes. Also veryhelpful were Bernard Goodwin, Elizabeth Ryan, and Michelle Housley at Prentice Hall PTR, and my many students and friends at the University of Michiganand Chulalongkorn University in Bangkok. Others are acknowledged in specificliterature citations.Further information. The website http://www.engin.umich.edu/ fmcheis maintained as a “bulletin board” for giving additional information about the
Prefacexviibook—hints for problem solutions, errata, how to contact the authors, etc.—asproves desirable. My own Internet address is wilkes@umich.edu. The text wascomposed on a Power Macintosh G4 computer using the TEXtures “typesetting”program. Eleven-point type was used for the majority of the text. Most of thefigures were constructed using MacDraw Pro, Excel, and KaleidaGraph.Professor Terence Fox , to whom this book is dedicated, was a Cambridgeengineering graduate who worked from 1933 to 1937 at Imperial Chemical Industries Ltd., Billingham, Yorkshire. Returning to Cambridge, he taught engineeringfrom 1937 to 1946 before being selected to lead the Department of Chemical Engineering at the University of Cambridge during its formative years after the endof World War II. As a scholar and a gentleman, Fox was a shy but exceptionallybrilliant person who had great insight into what was important and who quicklybrought the department to a preeminent position. He succeeded in combining anindustrial perspective with intellectual rigor. Fox relinquished the leadership ofthe 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 memb
1.1 Fluid Mechanics in Chemical Engineering 3 1.2 General Concepts of a Fluid 3 1.3 Stresses, Pressure, Velocity, and the Basic Laws 5 1.4 Physical Properties—Density, Viscosity, and Surface Tension 10 1.5 Units and Systems of Units 21 Example 1.1—Units Conversion 24 Example 1.2—Mass of Air in a Room 25 1.6 Hydrostatics 26 Example 1.3 .
Fluid Mechanics Fluid Engineers basic tools Experimental testing Computational Fluid Theoretical estimates Dynamics Fluid Mechanics, SG2214 Fluid Mechanics Definition of fluid F solid F fluid A fluid deforms continuously under the action of a s
Bruksanvisning för bilstereo . Bruksanvisning for bilstereo . Instrukcja obsługi samochodowego odtwarzacza stereo . Operating Instructions for Car Stereo . 610-104 . SV . Bruksanvisning i original
Fluid Mechanics 63 Chapter 6 Fluid Mechanics _ 6.0 Introduction Fluid mechanics is a branch of applied mechanics concerned with the static and dynamics of fluid - both liquids and gases. . Solution The relative density of fluid is defined as the rate of its density to the density of water. Thus, the relative density of oil is 850/1000 0.85.
Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and Bernoulli's Equation 7. General Energy Equation 8. Reynolds Number, Laminar Flow, Turbulent Flow and Energy Losses Due to Friction
Fundamentals of Fluid Mechanics. 1 F. UNDAMENTALS OF . F. LUID . M. ECHANICS . 1.1 A. SSUMPTIONS . 1. Fluid is a continuum 2. Fluid is inviscid 3. Fluid is adiabatic 4. Fluid is a perfect gas 5. Fluid is a constant-density fluid 6. Discontinuities (shocks, waves, vortex sheets) are treated as separate and serve as boundaries for continuous .
L M A B CVT Revision: December 2006 2007 Sentra CVT FLUID PFP:KLE50 Checking CVT Fluid UCS005XN FLUID LEVEL CHECK Fluid level should be checked with the fluid warmed up to 50 to 80 C (122 to 176 F). 1. Check for fluid leakage. 2. With the engine warmed up, drive the vehicle to warm up the CVT fluid. When ambient temperature is 20 C (68 F .
10 tips och tricks för att lyckas med ert sap-projekt 20 SAPSANYTT 2/2015 De flesta projektledare känner säkert till Cobb’s paradox. Martin Cobb verkade som CIO för sekretariatet för Treasury Board of Canada 1995 då han ställde frågan
service i Norge och Finland drivs inom ramen för ett enskilt företag (NRK. 1 och Yleisradio), fin ns det i Sverige tre: Ett för tv (Sveriges Television , SVT ), ett för radio (Sveriges Radio , SR ) och ett för utbildnings program (Sveriges Utbildningsradio, UR, vilket till följd av sin begränsade storlek inte återfinns bland de 25 största
