Fluid Mechanics for Chemical Engineers: with Microfluidics, CFD, and COMSOL Multiphysics 5 (International Series in the Physical and Chemical Engineering Sciences)

The Chemical Engineer's Practical Guide to Fluid Mechanics: Now Includes COMSOL Multiphysics 5 Since most chemical processing applications are conducted either partially or totally in the fluid phase, chemical engineers need mastery of fluid mechanics. Such knowledge is especially valuable in the biochemical, chemical, energy, fermentation, materials, mining, petroleum, pharmaceuticals, polymer, and waste-processing industries. Fluid Mechanics for Chemical Engineers: with Microfluidics, CFD, and COMSOL Multiphysics 5, Third Edition, systematically introduces fluid mechanics from the perspective of the chemical engineer who must understand actual physical behavior and solve real-world problems. Building on the book that earned Choice Magazine's Outstanding Academic Title award, this edition also gives a comprehensive introduction to the popular COMSOL Multiphysics 5 software. This third edition contains extensive coverage of both microfluidics and computational fluid dynamics, systematically demonstrating CFD through detailed examples using COMSOL Multiphysics 5 and ANSYS Fluent. The chapter on turbulence now presents valuable CFD techniques to investigate practical situations such as turbulent mixing and recirculating flows. Part I offers a clear, succinct, easy-to-follow introduction to macroscopic fluid mechanics, including physical properties; hydrostatics; basic rate laws; and fundamental principles of flow through equipment. Part II turns to microscopic fluid mechanics: Differential equations of fluid mechanics Viscous-flow problems, some including polymer processing Laplace's equation; irrotational and porous-media flows Nearly unidirectional flows, from boundary layers to lubrication, calendering, and thin-film applications Turbulent flows, showing how the k-ε method extends conventional mixing-length theory Bubble motion, two-phase flow, and fluidization Non-Newtonian fluids, including inelastic and viscoelastic fluids Microfluidics and electrokinetic flow effects, including electroosmosis, electrophoresis, streaming potentials, and electroosmotic switching Computational fluid mechanics with ANSYS Fluent and COMSOL Multiphysics Nearly 100 completely worked practical examples include 12 new COMSOL 5 examples: boundary layer flow, non-Newtonian flow, jet flow, die flow, lubrication, momentum diffusion, turbulent flow, and others. More than 300 end-of-chapter problems of varying complexity are presented, including several from University of Cambridge exams. The author covers all material needed for the fluid mechanics portion of the professional engineer's exam. The author's website (fmche.engin.umich.edu) provides additional notes, problem-solving tips, and errata. Register your book for convenient access to downloads, updates, and/or corrections as they become available. See inside book for details. 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 The Chemical Engineer's Practical Guide to Fluid Mechanics: Now Includes COMSOL Multiphysics 5 Since most chemical processing applications are conducted either partially or totally in the fluid phase, chemical engineers need mastery of fluid mechanics. Such knowledge is especially valuable in the biochemical, chemical, energy, fermentation, materials, mining, petroleum, pharmaceuticals, polymer, and waste-processing industries. Fluid Mechanics for Chemical Engineers: with Microfluidics, CFD, and COMSOL Multiphysics 5, Third Edition, systematically introduces fluid mechanics from the perspective of the chemical engineer who must understand actual physical behavior and solve real-world problems. Building on the book that earned Choice Magazine's Outstanding Academic Title award, this edition also thoroughly introduces the popular COMSOL Multiphysics 5 software. This third edition contains extensive coverage of both microfluidics and computational fluid dynamics, systematically demonstrating CFD through detailed examples using COMSOL Multiphysics 5 and ANSYS Fluent. The chapter on turbulence now presents valuable CFD techniques to investigate practical situations such as turbulent mixing and recirculating flows. Part I offers a clear, succinct, easy-to-follow introduction to macroscopic fluid mechanics, including physical properties; hydrostatics; basic rate laws; and fundamental principles of flow through equipment. Part II turns to microscopic fluid mechanics. Differential equations of fluid mechanics Viscous-flow problems, some including polymer processing Laplace's equation, irrotational, and porous-media flows Nearly unidirectional flows, from boundary layers to lubrication, calendering, and thin-film applications Turbulent flows, showing how the k/e method extends conventional mixing-length theory Bubble motion, two-phase flow, and fluidization Non-Newtonian fluids, including inelastic and viscoelastic fluids Microfluidics and electrokinetic flow effects including electroosmosis, electrophoresis, streaming potentials, and electroosmotic switching Computational fluid mechanics with ANSYS Fluent and COMSOL Multiphysics Nearly 100 completely worked practical examples include ten new COMSOL 5 examples: boundary layer flow, non-Newtonian flow, jet flow, lathe flow, lubrication, momentum diffusion, turbulent flow, and others. More than 300 end-of-chapter problems of varying complexity are presented, including several from University of Cambridge exams. The author covers all material needed for the fluid mechanics portion of the professional engineer's exam The Chemical Engineer's Practical Guide to Fluid Now Includes COMSOL Multiphysics 5 Since most chemical processing applications are conducted either partially or totally in the fluid phase, chemical engineers need mastery of fluid mechanics. Such knowledge is especially valuable in the biochemical, chemical, energy, fermentation, materials, mining, petroleum, pharmaceuticals, polymer, and waste-processing industries. Fluid Mechanics for Chemical with Microfluidics, CFD, and COMSOL Multiphysics 5, Third Edition, systematically introduces fluid mechanics from the perspective of the chemical engineer who must understand actual physical behavior and solve real-world problems. Building on the book that earned Choice Magazine 's Outstanding Academic Title award, this edition also gives a comprehensive introduction to the popular COMSOL Multiphysics 5 software. This third edition contains extensive coverage of both microfluidics and computational fluid dynamics, systematically demonstrating CFD through detailed examples using COMSOL Multiphysics 5 and ANSYS Fluent. The chapter on turbulence now presents valuable CFD techniques to investigate practical situations such as turbulent mixing and recirculating flows. Part I offers a clear, succinct, easy-to-follow introduction to macroscopic fluid mechanics, including physical properties; hydrostatics; basic rate laws; and fundamental principles of flow through equipment. Part II turns to microscopic fluid Nearly 100 completely worked practical examples include 12 new COMSOL 5 boundary layer flow, non-Newtonian flow, jet flow, die flow, lubrication, momentum diffusion, turbulent flow, and others. More than 300 end-of-chapter problems of varying complexity are presented, including several from University of Cambridge exams. The author covers all material needed for the fluid mechanics portion of the professional engineer's exam. The author's website ( ) provides additional notes, problem-solving tips, and errata. Register your book for convenient access to downloads, updates, and/or corrections as they become available. See inside book for details. James O. Wilkes Has Updated His Expert Hands-on Fluid Mechanics Tutorial With A Complete Introduction To The Popular Comsol Multiphysics 5.2 Software Package, And Ten New Comsol 5.2 Examples. Building On The Text That Earned Choice Magazine's Prestigious Outstanding Academic Titles Award, Wilkes Offers Masterful Coverage Of Key Fluid Mechanics Topics Including Computing Turbulent Flows, Bubble Motion, Two-phase Flow, Fluidization, Microfluidics, Electro-kinetic Flow Effects, And Computational Fluid Dynamics. Throughout, He Presents More Than 300 Problems Of Incrementally Greater Difficulty, Helping Students Build Mastery Through Realistic Practice. Wilkes Starts With A Macroscopic Approach, Providing A Solid Foundation For Sizing Pumps And Operating Laboratory And Field Scale Equipment. The First Four Chapters Derive Equations Needed To Size Chemical Plant Equipment, Including Pipes In Packed Beds, Pumping Installation, Fluid Flow Measurement, Filtration, And Cyclone Separation. Next, He Moves To A Microscopic Approach, Introducing Key Principles For Modeling More Advanced Systems And Solving Industry Or Graduate-level Problems. These Chapters Start With A Simple Derivation Of The Navier-stokes Equation (nse), And Then Introduce Assumptions For Various Flow Geometries, Helping Students Reduce Equations For Easy Solution -- Analytically, Or Numerically With Comsol. Updated Comsol Examples Include Boundary Layer Flow, Non-newtonian Flow, Jet Flow, Lathe Flow, Lubrication, Momentum Diffusion, Flow Through An Orifice Plate Parallel Plate Flow, Turbulent Flow, And More. An understanding of fluid mechanics is essential for the chemical engineer because the majority of chemical-processing operations are conducted either partially or totally in the fluid phase. Such knowledge is needed in the biochemical, chemical, energy, fermentation, materials, mining, petroleum, pharmaceuticals, polymer, and waste-processing industries. Written from a chemical engineering perspective, this comprehensive text covers fluid mechanics first from a macroscopic then a microscopic perspective. Fluid Mechanics for Chemical Engineers gives the undergraduate and first-year graduate student a comprehensive overview of this essential topic. Bridging the gap between the physicist and the practitioner, the book provides numerous real-world examples and problems of increasing detail and complexity, including several from the University of Cambridge chemical engineering examinations. It also covers all the material necessary to pass the fluid mechanics portion of the Professional Engineer's exam.