# Fluid Mechanics for Chemical Engineers: with Microfluidics, CFD, and COMSOL Multiphysics 5, 3rd edition

Published by Pearson (February 16, 2022) Â© 2018

**James O. Wilkes**University of Michigan

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*Preface xv*

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Part I: Macroscopic Fluid Mechanics 1

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Chapter 1: Introduction to Fluid Mechanics 3

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 Propertiesâ€”Density, Viscosity, and Surface Tension 10

1.5 Units and Systems of Units 21

1.6 Hydrostatics 26

1.7 Pressure Change Caused by Rotation 39

Problems for Chapter 1 42

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**Chapter 2: Mass, Energy, and Momentum Balances 55**

2.1 General Conservation Laws 55

2.2 Mass Balances 57

2.3 Energy Balances 61

2.4 Bernoulliâ€™s Equation 67

2.5 Applications of Bernoulliâ€™s Equation 70

2.6 Momentum Balances 78

2.7 Pressure, Velocity, and Flow Rate Measurement 92

Problems for Chapter 2 96

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**Chapter 3: Fluid Friction in Pipes 120**

3.1 Introduction 120

3.2 Laminar Flow 123

3.3 Models for Shear Stress 129

3.4 Piping and Pumping Problems 133

3.5 Flow in Noncircular Ducts 150

3.6 Compressible Gas Flow in Pipelines 156

3.7 Compressible Flow in Nozzles 159

3.8 Complex Piping Systems 163

Problems for Chapter 3 168

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**Chapter 4: Flow in Chemical Engineering Equipment 185**

4.1 Introduction 185

4.2 Pumps and Compressors 188

4.3 Drag Force on Solid Particles in Fluids 194

4.4 Flow Through Packed Beds 204

4.5 Filtration 210

4.6 Fluidization 215

4.7 Dynamics of a Bubble-Cap Distillation Column 216

4.8 Cyclone Separators 219

4.9 Sedimentation 222

4.10 Dimensional Analysis 224

Problems for Chapter 4 230

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Part II: Microscopic Fluid Mechanics 247

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Chapter 5: Differential Equations of Fluid Mechanics 249

5.1 Introduction to Vector Analysis 249

5.2 Vector Operations 250

5.3 Other Coordinate Systems 263

5.4 The Convective Derivative 266

5.5 Differential Mass Balance 267

5.6 Differential Momentum Balances 271

5.7 Newtonian Stress Components in Cartesian Coordinates 274

Problems for Chapter 5 285

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**Chapter 6: Solution Of Viscous-Flow Problems 292**

6.1 Introduction 292

6.2 Solution of the Equations of Motion in Rectangular Coordinates 294

6.3 Alternative Solution Using a Shell Balance 301

6.4 Poiseuille and Couette Flows in Polymer Processing 313

6.5 Solution of the Equations of Motion in Cylindrical Coordinates 325

6.6 Solution of the Equations of Motion in Spherical Coordinates 330

Problems for Chapter 6 336

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**Chapter 7: Laplaceâ€™s Equation, Irrotational and Porous-Media Flows 357**

7.1 Introduction 357

7.2 Rotational and Irrotational Flows 359

7.3 Steady Two-Dimensional Irrotational Flow 364

7.4 Physical Interpretation of the Stream Function 367

7.5 Examples of Planar Irrotational Flow 369

7.6 Axially Symmetric Irrotational Flow 382

7.7 Uniform Streams and Point Sources 384

7.8 Doublets and Flow Past a Sphere 388

7.9 Single-Phase Flow in a Porous Medium 391

7.10 Two-Phase Flow in Porous Media 394

7.11 Wave Motion in Deep Water 400

Problems for Chapter 7 404

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**Chapter 8: Boundary-Layer and Other Nearly Unidirectional Flows 418**

8.1 Introduction 418

8.2 Simplified Treatment of Laminar Flow Past a Flat Plate 419

8.3 Simplification of the Equations of Motion 426

8.4 Blasius Solution for Boundary-Layer Flow 429

8.5 Turbulent Boundary Layers 432

8.6 Dimensional Analysis of the Boundary-Layer Problem 434

8.7 Boundary-Layer Separation 437

8.8 The Lubrication Approximation 448

8.9 Polymer Processing by Calendering 457

8.10 Thin Films and Surface Tension 463

Problems for Chapter 8 466

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**Chapter 9: Turbulent Flow 480**

9.1 Introduction 480

9.2 Physical Interpretation of the Reynolds Stresses 487

9.3 Mixing-Length Theory 488

9.4 Determination of Eddy Kinematic Viscosity and Mixing Length 491

9.5 Velocity Profiles Based on Mixing-Length Theory 493

9.6 The Universal Velocity Profile for Smooth Pipes 495

9.7 Friction Factor in Terms of Reynolds Number for Smooth Pipes 497

9.8 Thickness of the Laminar Sublayer 499

9.9 Velocity Profiles and Friction Factor for Rough Pipe 501

9.10 Blasius-Type Law and the Power-Law Velocity Profile 502

9.11 A Correlation for the Reynolds Stresses 503

9.12 Computation of Turbulence by the kâ€“Îµ Method 506

9.13 Analogies Between Momentum and Heat Transfer 520

9.14 Turbulent Jets 524

Problems for Chapter 9 532

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**Chapter 10: Bubble Motion, Two-Phase Flow, and Fluidization 542**

10.1 Introduction 542

10.2 Rise of Bubbles in Unconfined Liquids 542

10.3 Pressure Drop and Void Fraction in Horizontal Pipes 547

10.4 Two-Phase Flow in Vertical Pipes 554

10.5 Flooding 566

10.6 Introduction to Fluidization 570

10.7 Bubble Mechanics 572

10.8 Bubbles in Aggregatively Fluidized Beds 577

Problems for Chapter 10 586

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**Chapter 11: Non-Newtonian Fluids 602**

11.1 Introduction 602

11.2 Classification of Non-Newtonian Fluids 603

11.3 Constitutive Equations for Inelastic Viscous Fluids 606

11.4 Constitutive Equations for Viscoelastic Fluids 626

11.5 Response to Oscillatory Shear 633

11.6 Characterization of the Rheological Properties of Fluids 636

Problems for Chapter 11 644

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**Chapter 12: Microfluidics and Electrokinetic Flow Effects 653**

12.1 Introduction 653

12.2 Physics of Microscale Fluid Mechanics 654

12.3 Pressure-Driven Flow Through Microscale Tubes 655

12.4 Mixing, Transport, and Dispersion 656

12.5 Species, Energy, and Charge Transport 658

12.6 The Electrical Double Layer and Electrokinetic Phenomena 661

12.7 Measuring the Zeta Potential 676

12.8 Electroviscosity 678

12.9 Particle and Macromolecule Motion in Microfluidic Channels 678

Problems for Chapter 12 683

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**Chapter 13: An Introduction to Computational Fluid Dynamics and ANSYS Fluent 688**

13.1 Introduction and Motivation 688

13.2 Numerical Methods 690

13.3 Learning CFD by Using ANSYS Fluent 699

13.4 Practical CFD Examples 703

References for Chapter 13 719

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**Chapter 14: COMSOL Multiphysics for Solving Fluid Mechanics Problems 720**

14.1 COMSOL Multiphysicsâ€”An Overview 720

14.2 The Steps for Solving Problems in COMSOL 723

14.3 How to Run COMSOL 725

14.4 Variables, Constants, Expressions, and Units 741

14.5 Boundary Conditions 742

14.6 Variables Used by COMSOL 743

14.7 Wall Functions in Turbulent-Flow Problems 744

14.8 Streamline Plotting in COMSOL 747

14.9 Special COMSOL Features Used in the Examples 749

14.10 Drawing Tools 754

14.11 Fluid Mechanics Problems Solvable by COMSOL 756

14.12 Conclusionâ€”Problems and Learning Tools 761

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Appendix A: Useful Mathematical Relationships 762

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Appendix B: Answers to the True/False Assertions 768

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Appendix C: Some Vector and Tensor Operations 771

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General Index 773

Comsol Multiphysics Index 782

The Authors 784

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