# Fluid Mechanics for Chemical Engineers : With Microfluidics and CFD

, by Wilkes, James O.**Note:**Supplemental materials are not guaranteed with Rental or Used book purchases.

- ISBN: 9780131482128 | 0131482122
- Cover: Hardcover
- Copyright: 9/29/2005

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.

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

Preface | p. xv |

Macroscopic Fluid Mechanics | |

Introduction to Fluid Mechanics | |

Fluid Mechanics in Chemical Engineering | p. 3 |

General Concepts of a Fluid | p. 3 |

Stresses, Pressure, Velocity, and the Basic Laws | p. 5 |

Physical Properties-Density, Viscosity, and Surface Tension | p. 10 |

Units and Systems of Units | p. 21 |

Units Conversion | p. 24 |

Mass of Air in a Room | p. 25 |

Hydrostatics | p. 26 |

Pressure in an Oil Storage Tank | p. 29 |

Multiple Fluid Hydrostatics | p. 30 |

Pressure Variations in a Gas | p. 31 |

Hydrostatic Force on a Curved Surface | p. 35 |

Application of Archimedes' Law | p. 37 |

Pressure Change Caused by Rotation | p. 39 |

Overflow from a Spinning Container | p. 40 |

Problems for Chapter 1 | p. 42 |

Mass, Energy, and Momentum Balances | |

General Conservation Laws | p. 55 |

Mass Balances | p. 57 |

Mass Balance for Tank Evacuation | p. 58 |

Energy Balances | p. 61 |

Pumping n-Pentane | p. 65 |

Bernoulli's Equation | p. 67 |

Applications of Bernoulli's Equation | p. 70 |

Tank Filling | p. 76 |

Momentum Balances | p. 78 |

Impinging Jet of Water | p. 83 |

Velocity of Wave on Water | p. 84 |

Flow Measurement by a Rotameter | p. 89 |

Pressure, Velocity, and Flow Rate Measurement | p. 92 |

Problems for Chapter 2 | p. 96 |

Fluid Friction in Pipes | |

Introduction | p. 120 |

Laminar Flow | p. 123 |

Polymer Flow in a Pipeline | p. 128 |

Models for Shear Stress | p. 129 |

Piping and Pumping Problems | p. 133 |

Unloading Oil from a Tanker Specified Flow Rate and Diameter | p. 142 |

Unloading Oil from a Tanker Specified Diameter and Pressure Drop | p. 144 |

Unloading Oil from a Tanker Specified Flow Rate and Pressure Drop | p. 147 |

Unloading Oil from a Tanker Miscellaneous Additional Calculations | p. 147 |

Flow in Noncircular Ducts | p. 150 |

Flow in an Irrigation Ditch | p. 152 |

Compressible Gas Flow in Pipelines | p. 156 |

Compressible Flow in Nozzles | p. 159 |

Complex Piping Systems | p. 163 |

Solution of a Piping/Pumping Problem | p. 165 |

Problems for Chapter 3 | p. 168 |

Flow in Chemical Engineering Equipment | |

Introduction | p. 185 |

Pumps and Compressors | p. 188 |

Pumps in Series and Parallel | p. 193 |

Drag Force on Solid Particles in Fluids | p. 194 |

Manufacture of Lead Shot | p. 202 |

Flow Through Packed Beds | p. 204 |

Pressure Drop in a Packed-Bed Reactor | p. 208 |

Filtration | p. 210 |

Fluidization | p. 215 |

Dynamics of a Bubble-Cap Distillation Column | p. 216 |

Cyclone Separators | p. 219 |

Sedimentation | p. 222 |

Dimensional Analysis | p. 224 |

Thickness of the Laminar Sublayer | p. 229 |

Problems for Chapter 4 | p. 230 |

Microscopic Fluid Mechanics | |

Differential Equations of Fluid Mechanics | |

Introduction to Vector Analysis | p. 249 |

Vector Operations | p. 250 |

The Gradient of a Scalar | p. 253 |

The Divergence of a Vector | p. 257 |

An Alternative to the Differential Element | p. 257 |

The Curl of a Vector | p. 262 |

The Laplacian of a Scalar | p. 262 |

Other Coordinate Systems | p. 263 |

The Convective Derivative | p. 266 |

Differential Mass Balance | p. 267 |

Physical Interpretation of the Net Rate of Mass Outflow | p. 269 |

Alternative Derivation of the Continuity Equation | p. 270 |

Differential Momentum Balances | p. 271 |

Newtonian Stress Components in Cartesian Coordinates | p. 274 |

Constant-Viscosity Momentum Balances in Terms of Velocity Gradients | p. 280 |

Vector Form of Variable-Viscosity Momentum Balance | p. 284 |

Problems for Chapter 5 | p. 285 |

Solution of Viscous-Flow Problems | |

Introduction | p. 292 |

Solution of the Equations of Motion in Rectangular Coordinates | p. 294 |

Flow Between Parallel Plates | p. 294 |

Alternative Solution Using a Shell Balance | p. 301 |

Shell Balance for Flow Between Parallel Plates | p. 301 |

Film Flow on a Moving Substrate | p. 303 |

Transient Viscous Diffusion of Momentum (COMSOL) | p. 307 |

Poiseuille and Couette Flows in Polymer Processing | p. 312 |

The Single-Screw Extruder | p. 313 |

Flow Patterns in a Screw Extruder (COMSOL) | p. 318 |

Solution of the Equations of Motion in Cylindrical Coordinates | p. 322 |

Flow Through an Annular Die | p. 322 |

Spinning a Polymeric Fiber | p. 325 |

Solution of the Equations of Motion in Spherical Coordinates | p. 327 |

Analysis of a Cone-and-Plate Rheometer | p. 328 |

Problems for Chapter 6 | p. 333 |

Laplace's Equation, Irrotational and Porous-Media Flows | |

Introduction | p. 354 |

Rotational and Irrotational Flows | p. 356 |

Forced and Free Vortices | p. 359 |

Steady Two-Dimensional Irrotational Flow | p. 361 |

Physical Interpretation of the Stream Function | p. 364 |

Examples of Planar Irrotational Flow | p. 366 |

Stagnation Flow | p. 369 |

Combination of a Uniform Stream and a Line Sink (C) | p. 371 |

Flow Patterns in a Lake (COMSOL) | p. 373 |

Axially Symmetric Irrotational Flow | p. 378 |

Uniform Streams and Point Sources | p. 380 |

Doublets and Flow Past a Sphere | p. 384 |

Single-Phase Flow in a Porous Medium | p. 387 |

Underground Flow of Water | p. 388 |

Two-Phase Flow in Porous Media | p. 390 |

Wave Motion in Deep Water | p. 396 |

Problems for Chapter 7 | p. 400 |

Boundary-Layer and Other Nearly Unidirectional Flows | |

Introduction | p. 414 |

Simplified Treatment of Laminar Flow Past a Flat Plate | p. 415 |

Flow in an Air Intake (C) | p. 420 |

Simplification of the Equations of Motion | p. 422 |

Blasius Solution for Boundary-Layer Flow | p. 425 |

Turbulent Boundary Layers | p. 428 |

Laminar and Turbulent Boundary Layers Compared | p. 429 |

Dimensional Analysis of the Boundary-Layer Problem | p. 430 |

Boundary-Layer Separation | p. 433 |

Boundary-Layer Flow Between Parallel Plates (COMSOL Library) | p. 435 |

Entrance Region for Laminar Flow Between Flat Plates | p. 440 |

The Lubrication Approximation | p. 442 |

Flow in a Lubricated Bearing (COMSOL) | p. 448 |

Polymer Processing by Calendering | p. 450 |

Pressure Distribution in a Calendered Sheet | p. 454 |

Thin Films and Surface Tension | p. 456 |

Problems for Chapter 8 | p. 459 |

Turbulent Flow | |

Introduction | p. 473 |

Numerical Illustration of a Reynolds Stress Term | p. 479 |

Physical Interpretation of the Reynolds Stresses | p. 480 |

Mixing-Length Theory | p. 481 |

Determination of Eddy Kinematic Viscosity and Mixing Length | p. 484 |

Velocity Profiles Based on Mixing-Length Theory | p. 486 |

Investigation of the von Karman Hypothesis | p. 487 |

The Universal Velocity Profile for Smooth Pipes | p. 488 |

Friction Factor in Terms of Reynolds Number for Smooth Pipes | p. 490 |

Expression for the Mean Velocity | p. 491 |

Thickness of the Laminar Sublayer | p. 492 |

Velocity Profiles and Friction Factor for Rough Pipe | p. 494 |

Blasius-Type Law and the Power-Law Velocity Profile | p. 495 |

A Correlation for the Reynolds Stresses | p. 496 |

Computation of Turbulence by the [kappa]/[epsilon] Method | p. 499 |

Flow Through an Orifice Plate (COMSOL) | p. 501 |

Turbulent Jet Flow (COMSOL) | p. 505 |

Analogies Between Momentum and Heat Transfer | p. 509 |

Evaluation of the Momentum/Heat-Transfer Analogies | p. 511 |

Turbulent Jets | p. 513 |

Problems for Chapter 9 | p. 521 |

Bubble Motion, Two-Phase Flow, and Fluidization | |

Introduction | p. 531 |

Rise of Bubbles in Unconfined Liquids | p. 531 |

Rise Velocity of Single Bubbles | p. 536 |

Pressure Drop and Void Fraction in Horizontal Pipes | p. 536 |

Two-Phase Flow in a Horizontal Pipe | p. 541 |

Two-Phase Flow in Vertical Pipes | p. 543 |

Limits of Bubble Flow | p. 546 |

Performance of a Gas-Lift Pump | p. 550 |

Two-Phase Flow in a Vertical Pipe | p. 553 |

Flooding | p. 555 |

Introduction to Fluidization | p. 559 |

Bubble Mechanics | p. 561 |

Bubbles in Aggregatively Fluidized Beds | p. 566 |

Fluidized Bed with Reaction (C) | p. 572 |

Problems for Chapter 10 | p. 575 |

Non-Newtonian Fluids | |

Introduction | p. 591 |

Classification of Non-Newtonian Fluids | p. 592 |

Constitutive Equations for Inelastic Viscous Fluids | p. 595 |

Pipe Flow of a Power-Law Fluid | p. 600 |

Pipe Flow of a Bingham Plastic | p. 604 |

Non-Newtonian Flow in a Die (COMSOL Library) | p. 606 |

Constitutive Equations for Viscoelastic Fluids | p. 613 |

Response to Oscillatory Shear | p. 620 |

Characterization of the Rheological Properties of Fluids | p. 623 |

Proof of the Rabinowitsch Equation | p. 624 |

Working Equation for a Coaxial-Cylinder Rheometer: Newtonian Fluid | p. 628 |

Problems for Chapter 11 | p. 630 |

Microfluidics and Electrokinetic Flow Effects | |

Introduction | p. 639 |

Physics of Microscale Fluid Mechanics | p. 640 |

Pressure-Driven Flow Through Microscale Tubes | p. 641 |

Calculation of Reynolds Numbers | p. 641 |

Mixing, Transport, and Dispersion | p. 642 |

Species, Energy, and Charge Transport | p. 644 |

The Electrical Double Layer and Electrokinetic Phenomena | p. 647 |

Relative Magnitudes of Electroosmotic and Pressure-Driven Flows | p. 648 |

Electroosmotic Flow Around a Particle | p. 653 |

Electroosmosis in a Microchannel (COMSOL) | p. 653 |

Electroosmotic Switching in a Branched Microchannel (COMSOL) | p. 657 |

Measuring the Zeta Potential | p. 659 |

Magnitude of Typical Streaming Potentials | p. 660 |

Electroviscosity | p. 661 |

Particle and Macromolecule Motion in Microfluidic Channels | p. 661 |

Gravitational and Magnetic Settling of Assay Beads | p. 662 |

Problems for Chapter 12 | p. 666 |

An Introduction to Computational Fluid Dynamics and Flowlab | |

Introduction and Motivation | p. 671 |

Numerical Methods | p. 673 |

Learning CFD by Using FlowLab | p. 682 |

Practical CFD Examples | p. 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 13 | p. 702 |

Comsol (Femlab) Multiphysics for Solving Fluid Mechanics Problems | |

Introduction to COMSOL | p. 703 |

How to Run COMSOL | p. 705 |

Flow in a Porous Medium with an Obstruction (COMSOL) | p. 705 |

Draw Mode | p. 719 |

Solution and Related Modes | p. 724 |

Fluid Mechanics Problems Solvable by COMSOL | p. 725 |

Problems for Chapter 14 | p. 730 |

Useful Mathematical Relationships | p. 731 |

Answers to the True/False Assertions | p. 737 |

Some Vector and Tensor Operations | p. 740 |

Index | p. 743 |

The Authors | p. 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.