## Table of Contents

**Preface.**

**I. MACROSCOPIC FLUID MECHANICS.**

**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?f Law

1.7 Pressure Change Caused by Rotation

Example 1.8 - Overflow from a Spinning Container

Problems for Chapter 1

**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?fs 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

**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

**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

**II. MICROSCOPIC FLUID MECHANICS.**

**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

**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 (FEMLAB)

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 (FEMLAB)

6.5 Solution of the Equations of Motion in Cylindrical x Table of Contents 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

**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 (FEMLAB)

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

**8. Boundary-Layer Aand 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

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 (FEMLAB Library)

Example 8.4 - Entrance Region for Laminar Flow Between Flat Plates

8.8 The Lubrication Approximation

Example 8.5 - Flow in a Lubricated Bearing (FEMLAB)

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

**9. Turbulent Flow.**

9.1 Introduction

Example 9.1 - Numerical Illustration of a Reynolds Stress Term

9.2 Physical Interpretation of the Reynolds Stresse

9.3 Mixing-Length Theory

9.4 Determination of Eddy Kinematic Viscosity and Mixing Length

9.5 Velocity Profiles Based on Mixing Length Theory 486

Example 9.2 - Investigation of the von K?Larm?Lan 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 k/? Method

Example 9.4 - Flow Through an Orifice Plate (FEMLAB)

Example 9.5 - Turbulent Jet Flow (FEMLAB)

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

**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

**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 (FEMLAB Library)

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

**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 Flow

Example 12.3 - Electroosmotic Flow Around a Particle

Example 12.4 - Electroosmosis in a Microchannel (FEMLAB)

Example 12.5 - Electroosmotic Switching in a Branched Microchannel (FEMLAB)

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

**13. An Introduction to Computational Fluid Dynamics and Flowlab.**

13.1 Introduction and Motivation

13.2 Numerical Methods

13.3 Learning CFD by Using FlowLab

13.4 Practical CFD Examples

Example 13.1 - Developing Flow in a Pipe Entrance Region (FlowLab)

Example 13.2 - Pipe Flow Through a Sudden Expansion (FlowLab)

Example 13.3 - A Two-Dimensional Mixing Junction (FlowLab)

Example 13.4 - Flow Over a Cylinder (FlowLab)

References for Chapter 13

**14. Femlab for Solving Fluid Mechanics Problems.**

14.1 Introduction to FEMLAB

14.2 How to Run FEMLAB

Example 14.1 - Flow in a Porous Medium with an Obstruction (FEMLAB)

14.3 Draw Mode

14.4 Solution and Related Modes

14.5 Fluid Mechanics Problems Solvable by FEMLAB

Problems for Chapter 14

**Appendix A: Useful Mathematical Relationships.**

**Appendix B: Answers to the True/False Assertions.**

**Appendix C: Some Vector and Tensor Operations.**

**Index.**