Fluid mechanics for chemical engineers

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Cover Title Page Copyright Page CONTENTS PREFACE PART I—MACROSCOPIC FLUID MECHANICS CHAPTER 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’ Law 1.7 Pressure Change Caused by Rotation Example 1.8—Overflow from a Spinning Container Problems for Chapter 1 CHAPTER 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 n-Pentane 2.4 Bernoulli’s Equation 2.5 Applications of Bernoulli’s 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 2 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 CHAPTER 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 Packed-Bed Reactor 4.5 Filtration 4.6 Fluidization 4.7 Dynamics of a Bubble-Cap 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 PART II—MICROSCOPIC FLUID MECHANICS CHAPTER 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—Constant-Viscosity Momentum Balances in Terms of Velocity Gradients Example 5.9—Vector Form of Variable-Viscosity Momentum Balance Problems for Chapter 5 CHAPTER 6—SOLUTION OF VISCOUS-FLOW 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 (COMSOL) 6.4 Poiseuille and Couette Flows in Polymer Processing Example 6.5—The Single-Screw Extruder Example 6.6—Flow Patterns in a Screw Extruder (COMSOL) 6.5 Solution of the Equations of Motion in Cylindrical 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 Cone-and-Plate Rheometer Problems for Chapter 6 CHAPTER 7—LAPLACE’S EQUATION, IRROTATIONAL AND POROUS-MEDIA FLOWS 7.1 Introduction 7.2 Rotational and Irrotational Flows Example 7.1—Forced and Free Vortices 7.3 Steady Two-Dimensional 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 (COMSOL) 7.6 Axially Symmetric Irrotational Flow 7.7 Uniform Streams and Point Sources 7.8 Doublets and Flow Past a Sphere 7.9 Single-Phase Flow in a Porous Medium Example 7.5—Underground Flow of Water 7.10 Two-Phase Flow in Porous Media 7.11 Wave Motion in Deep Water Problems for Chapter 7 CHAPTER 8—BOUNDARY-LAYER AND 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 (C) 8.3 Simplification of the Equations of Motion 8.4 Blasius Solution for Boundary-Layer Flow 8.5 Turbulent Boundary Layers Example 8.2—Laminar and Turbulent Boundary Layers Compared 8.6 Dimensional Analysis of the Boundary-Layer Problem 8.7 Boundary-Layer Separation Example 8.3—Boundary-Layer Flow Between Parallel Plates (COMSOL) Example 8.4—Entrance Region for Laminar Flow Between Flat Plates 8.8 The Lubrication Approximation Example 8.5—Flow in a Lubricated Bearing (COMSOL) 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 CHAPTER 9—TURBULENT FLOW 9.1 Introduction Example 9.1—Numerical Illustration of a Reynolds Stress Term 9.2 Physical Interpretation of the Reynolds Stresses 9.3 Mixing-Length Theory 9.4 Determination of Eddy Kinematic Viscosity and Mixing Length 9.5 Velocity Profiles Based on Mixing-Length Theory Example 9.2—Investigation of the von Kármán 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 Blasius-Type Law and the Power-Law Velocity Profile 9.11 A Correlation for the Reynolds Stresses 9.12 Computation of Turbulence by the κ–ɛ Method Example 9.4—Flow Through an Orifice Plate (COMSOL) Example 9.5—Turbulent Flow in an Obstructed U-Duct (COMSOL) 9.13 Analogies Between Momentum and Heat Transfer Example 9.6—Evaluation of the Momentum/Heat- Transfer Analogies 9.14 Turbulent Jets Problems for Chapter 9 CHAPTER 10—BUBBLE MOTION, TWO-PHASE 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—Two-Phase Flow in a Horizontal Pipe 10.4 Two-Phase Flow in Vertical Pipes Example 10.3—Limits of Bubble Flow Example 10.4—Performance of a Gas-Lift Pump Example 10.5—Two-Phase 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 CHAPTER 11—NON-NEWTONIAN FLUIDS 11.1 Introduction 11.2 Classification of Non-Newtonian Fluids 11.3 Constitutive Equations for Inelastic Viscous Fluids Example 11.1—Pipe Flow of a Power-Law Fluid Example 11.2—Pipe Flow of a Bingham Plastic Example 11.3—Non-Newtonian Flow in a Die (COMSOL) 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 CHAPTER 12—MICROFLUIDICS AND ELECTROKINETIC FLOW EFFECTS 12.1 Introduction 12.2 Physics of Microscale Fluid Mechanics 12.3 Pressure-Driven 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 Pressure-Driven Flows Example 12.3—Electroosmotic Flow Around a Particle Example 12.4—Electroosmosis in a Microchannel (COMSOL) Example 12.5—Electroosmotic Switching in a Branched Microchannel (COMSOL) 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 CHAPTER 13—AN INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS AND ANSYS FLUENT 13.1 Introduction and Motivation 13.2 Numerical Methods 13.3 Learning CFD by Using ANSYS Fluent 13.4 Practical CFD Examples Example 13.1—Fluent: Developing Flow in a Pipe Entrance Region Example 13.2—Fluent: Pipe Flow Through a Sudden Expansion Example 13.3—Fluent: A Two-Dimensional Mixing Junction Example 13.4—Fluent: Flow over a Cylinder References for Chapter 13 CHAPTER 14—COMSOL MULTIPHYSICS FOR SOLVING FLUID MECHANICS PROBLEMS 14.1 COMSOL Multiphysics—An Overview 14.2 The Steps for Solving Problems in COMSOL 14.3 How to Run COMSOL Example 14.1—Flow in a Porous Medium with an Impervious Hole (COMSOL) Example 14.2—Drawing a Complex Shape (COMSOL) 14.4 Variables, Constants, Expressions, and Units 14.5 Boundary Conditions 14.6 Variables Used by COMSOL 14.7 Wall Functions in Turbulent-Flow Problems 14.8 Streamline Plotting in COMSOL 14.9 Special COMSOL Features Used in the Examples 14.10 Drawing Tools 14.11 Fluid Mechanics Problems Solvable by COMSOL 14.12 Conclusion—Problems and Learning Tools APPENDIX A: USEFUL MATHEMATICAL RELATIONSHIPS APPENDIX B: ANSWERS TO THE TRUE/FALSE ASSERTIONS APPENDIX C: SOME VECTOR AND TENSOR OPERATIONS GENERAL INDEX A B C D E F G H I J K L M N O P R S T U V W Y Z COMSOL MULTIPHYSICS INDEX THE AUTHORS