Fluid Mechanics for Chemical Engineers

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 bachelors 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.

• Preface xv   Part I: Macroscopic Fluid Mechanics 1  Chapter 1: Introduction to Fluid Mechanics 3 1.1 Fluid Mechanics in Chemical Engineering 31.2 General Concepts of a Fluid 31.3 Stresses, Pressure, Velocity, and the Basic Laws 51.4 Physical Properties—Density, Viscosity, and Surface Tension 101.5 Units and Systems of Units 211.6 Hydrostatics 261.7 Pressure Change Caused by Rotation 39Problems for Chapter 1 42  Chapter 2: Mass, Energy, and Momentum Balances 552.1 General Conservation Laws 552.2 Mass Balances 572.3 Energy Balances 612.4 Bernoulli’s Equation 672.5 Applications of Bernoulli’s Equation 702.6 Momentum Balances 782.7 Pressure, Velocity, and Flow Rate Measurement 92Problems for Chapter 2 96  Chapter 3: Fluid Friction in Pipes 1203.1 Introduction 1203.2 Laminar Flow 1233.3 Models for Shear Stress 1293.4 Piping and Pumping Problems 1333.5 Flow in Noncircular Ducts 1503.6 Compressible Gas Flow in Pipelines 1563.7 Compressible Flow in Nozzles 1593.8 Complex Piping Systems 163Problems for Chapter 3 168  Chapter 4: Flow in Chemical Engineering Equipment 1854.1 Introduction 1854.2 Pumps and Compressors 1884.3 Drag Force on Solid Particles in Fluids 1944.4 Flow Through Packed Beds 2044.5 Filtration 2104.6 Fluidization 2154.7 Dynamics of a Bubble-Cap Distillation Column 2164.8 Cyclone Separators 2194.9 Sedimentation 2224.10 Dimensional Analysis 224Problems for Chapter 4 230   Part II: Microscopic Fluid Mechanics 247  Chapter 5: Differential Equations of Fluid Mechanics 249 5.1 Introduction to Vector Analysis 2495.2 Vector Operations 2505.3 Other Coordinate Systems 2635.4 The Convective Derivative 2665.5 Differential Mass Balance 2675.6 Differential Momentum Balances 2715.7 Newtonian Stress Components in Cartesian Coordinates 274Problems for Chapter 5 285  Chapter 6: Solution Of Viscous-Flow Problems 2926.1 Introduction 2926.2 Solution of the Equations of Motion in Rectangular Coordinates 2946.3 Alternative Solution Using a Shell Balance 3016.4 Poiseuille and Couette Flows in Polymer Processing 3136.5 Solution of the Equations of Motion in Cylindrical Coordinates 3256.6 Solution of the Equations of Motion in Spherical Coordinates 330Problems for Chapter 6 336  Chapter 7: Laplace’s Equation, Irrotational and Porous-Media Flows 3577.1 Introduction 3577.2 Rotational and Irrotational Flows 3597.3 Steady Two-Dimensional Irrotational Flow 3647.4 Physical Interpretation of the Stream Function 3677.5 Examples of Planar Irrotational Flow 3697.6 Axially Symmetric Irrotational Flow 3827.7 Uniform Streams and Point Sources 3847.8 Doublets and Flow Past a Sphere 3887.9 Single-Phase Flow in a Porous Medium 3917.10 Two-Phase Flow in Porous Media 3947.11 Wave Motion in Deep Water 400Problems for Chapter 7 404  Chapter 8: Boundary-Layer and Other Nearly Unidirectional Flows 4188.1 Introduction 4188.2 Simplified Treatment of Laminar Flow Past a Flat Plate 4198.3 Simplification of the Equations of Motion 4268.4 Blasius Solution for Boundary-Layer Flow 4298.5 Turbulent Boundary Layers 4328.6 Dimensional Analysis of the Boundary-Layer Problem 4348.7 Boundary-Layer Separation 4378.8 The Lubrication Approximation 4488.9 Polymer Processing by Calendering 4578.10 Thin Films and Surface Tension 463Problems for Chapter 8 466  Chapter 9: Turbulent Flow 4809.1 Introduction 4809.2 Physical Interpretation of the Reynolds Stresses 4879.3 Mixing-Length Theory 4889.4 Determination of Eddy Kinematic Viscosity and Mixing Length 4919.5 Velocity Profiles Based on Mixing-Length Theory 4939.6 The Universal Velocity Profile for Smooth Pipes 4959.7 Friction Factor in Terms of Reynolds Number for Smooth Pipes 4979.8 Thickness of the Laminar Sublayer 4999.9 Velocity Profiles and Friction Factor for Rough Pipe 5019.10 Blasius-Type Law and the Power-Law Velocity Profile 5029.11 A Correlation for the Reynolds Stresses 5039.12 Computation of Turbulence by the k–ε Method 5069.13 Analogies Between Momentum and Heat Transfer 5209.14 Turbulent Jets 524Problems for Chapter 9 532  Chapter 10: Bubble Motion, Two-Phase Flow, and Fluidization 54210.1 Introduction 54210.2 Rise of Bubbles in Unconfined Liquids 54210.3 Pressure Drop and Void Fraction in Horizontal Pipes 54710.4 Two-Phase Flow in Vertical Pipes 55410.5 Flooding 56610.6 Introduction to Fluidization 57010.7 Bubble Mechanics 57210.8 Bubbles in Aggregatively Fluidized Beds 577Problems for Chapter 10 586  Chapter 11: Non-Newtonian Fluids 60211.1 Introduction 60211.2 Classification of Non-Newtonian Fluids 60311.3 Constitutive Equations for Inelastic Viscous Fluids 60611.4 Constitutive Equations for Viscoelastic Fluids 62611.5 Response to Oscillatory Shear 63311.6 Characterization of the Rheological Properties of Fluids 636Problems for Chapter 11 644  Chapter 12: Microfluidics and Electrokinetic Flow Effects 65312.1 Introduction 65312.2 Physics of Microscale Fluid Mechanics 65412.3 Pressure-Driven Flow Through Microscale Tubes 65512.4 Mixing, Transport, and Dispersion 65612.5 Species, Energy, and Charge Transport 65812.6 The Electrical Double Layer and Electrokinetic Phenomena 66112.7 Measuring the Zeta Potential 67612.8 Electroviscosity 67812.9 Particle and Macromolecule Motion in Microfluidic Channels 678Problems for Chapter 12 683  Chapter 13: An Introduction to Computational Fluid Dynamics and ANSYS Fluent 68813.1 Introduction and Motivation 68813.2 Numerical Methods 69013.3 Learning CFD by Using ANSYS Fluent 69913.4 Practical CFD Examples 703References for Chapter 13 719  Chapter 14: COMSOL Multiphysics for Solving Fluid Mechanics Problems 72014.1 COMSOL Multiphysics—An Overview 72014.2 The Steps for Solving Problems in COMSOL 72314.3 How to Run COMSOL 72514.4 Variables, Constants, Expressions, and Units 74114.5 Boundary Conditions 74214.6 Variables Used by COMSOL 74314.7 Wall Functions in Turbulent-Flow Problems 74414.8 Streamline Plotting in COMSOL 74714.9 Special COMSOL Features Used in the Examples 74914.10 Drawing Tools 75414.11 Fluid Mechanics Problems Solvable by COMSOL 75614.12 Conclusion—Problems and Learning Tools 761   Appendix A: Useful Mathematical Relationships 762  Appendix B: Answers to the True/False Assertions 768  Appendix C: Some Vector and Tensor Operations 771   General Index 773Comsol Multiphysics Index 782The Authors 784