| |

| |

Preface | |

| |

| |

| |

Macroscopic Fluid Mechanics | |

| |

| |

| |

Introduction to Fluid Mechanics | |

| |

| |

| |

Fluid Mechanics in Chemical Engineering | |

| |

| |

| |

General Concepts of a Fluid | |

| |

| |

| |

Stresses, Pressure, Velocity, and the Basic Laws | |

| |

| |

| |

Physical Properties-Density, Viscosity, and Surface Tension | |

| |

| |

| |

Units and Systems of Units | |

| |

| |

| |

Units Conversion | |

| |

| |

| |

Mass of Air in a Room | |

| |

| |

| |

Hydrostatics | |

| |

| |

| |

Pressure in an Oil Storage Tank | |

| |

| |

| |

Multiple Fluid Hydrostatics | |

| |

| |

| |

Pressure Variations in a Gas | |

| |

| |

| |

Hydrostatic Force on a Curved Surface | |

| |

| |

| |

Application of Archimedes' Law | |

| |

| |

| |

Pressure Change Caused by Rotation | |

| |

| |

| |

Overflow from a Spinning Container | |

| |

| |

Problems for Chapter 1 | |

| |

| |

| |

Mass, Energy, and Momentum Balances | |

| |

| |

| |

General Conservation Laws | |

| |

| |

| |

Mass Balances | |

| |

| |

| |

Mass Balance for Tank Evacuation | |

| |

| |

| |

Energy Balances | |

| |

| |

| |

Pumping n-Pentane | |

| |

| |

| |

Bernoulli's Equation | |

| |

| |

| |

Applications of Bernoulli's Equation | |

| |

| |

| |

Tank Filling | |

| |

| |

| |

Momentum Balances | |

| |

| |

| |

Impinging Jet of Water | |

| |

| |

| |

Velocity of Wave on Water | |

| |

| |

| |

Flow Measurement by a Rotameter | |

| |

| |

| |

Pressure, Velocity, and Flow Rate Measurement | |

| |

| |

Problems for Chapter 2 | |

| |

| |

| |

Fluid Friction in Pipes | |

| |

| |

| |

Introduction | |

| |

| |

| |

Laminar Flow | |

| |

| |

| |

Polymer Flow in a Pipeline | |

| |

| |

| |

Models for Shear Stress | |

| |

| |

| |

Piping and Pumping Problems | |

| |

| |

| |

Unloading Oil from a Tanker Specified Flow Rate and Diameter | |

| |

| |

| |

Unloading Oil from a Tanker Specified Diameter and Pressure Drop | |

| |

| |

| |

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

| |

| |

| |

Unloading Oil from a Tanker Miscellaneous Additional Calculations | |

| |

| |

| |

Flow in Noncircular Ducts | |

| |

| |

| |

Flow in an Irrigation Ditch | |

| |

| |

| |

Compressible Gas Flow in Pipelines | |

| |

| |

| |

Compressible Flow in Nozzles | |

| |

| |

| |

Complex Piping Systems | |

| |

| |

| |

Solution of a Piping/Pumping Problem | |

| |

| |

Problems for Chapter 3 | |

| |

| |

| |

Flow in Chemical Engineering Equipment | |

| |

| |

| |

Introduction | |

| |

| |

| |

Pumps and Compressors | |

| |

| |

| |

Pumps in Series and Parallel | |

| |

| |

| |

Drag Force on Solid Particles in Fluids | |

| |

| |

| |

Manufacture of Lead Shot | |

| |

| |

| |

Flow Through Packed Beds | |

| |

| |

| |

Pressure Drop in a Packed-Bed Reactor | |

| |

| |

| |

Filtration | |

| |

| |

| |

Fluidization | |

| |

| |

| |

Dynamics of a Bubble-Cap Distillation Column | |

| |

| |

| |

Cyclone Separators | |

| |

| |

| |

Sedimentation | |

| |

| |

| |

Dimensional Analysis | |

| |

| |

| |

Thickness of the Laminar Sublayer | |

| |

| |

Problems for Chapter 4 | |

| |

| |

| |

Microscopic Fluid Mechanics | |

| |

| |

| |

Differential Equations of Fluid Mechanics | |

| |

| |

| |

Introduction to Vector Analysis | |

| |

| |

| |

Vector Operations | |

| |

| |

| |

The Gradient of a Scalar | |

| |

| |

| |

The Divergence of a Vector | |

| |

| |

| |

An Alternative to the Differential Element | |

| |

| |

| |

The Curl of a Vector | |

| |

| |

| |

The Laplacian of a Scalar | |

| |

| |

| |

Other Coordinate Systems | |

| |

| |

| |

The Convective Derivative | |

| |

| |

| |

Differential Mass Balance | |

| |

| |

| |

Physical Interpretation of the Net Rate of Mass Outflow | |

| |

| |

| |

Alternative Derivation of the Continuity Equation | |

| |

| |

| |

Differential Momentum Balances | |

| |

| |

| |

Newtonian Stress Components in Cartesian Coordinates | |

| |

| |

| |

Constant-Viscosity Momentum Balances in Terms of Velocity Gradients | |

| |

| |

| |

Vector Form of Variable-Viscosity Momentum Balance | |

| |

| |

Problems for Chapter 5 | |

| |

| |

| |

Solution of Viscous-Flow Problems | |

| |

| |

| |

Introduction | |

| |

| |

| |

Solution of the Equations of Motion in Rectangular Coordinates | |

| |

| |

| |

Flow Between Parallel Plates | |

| |

| |

| |

Alternative Solution Using a Shell Balance | |

| |

| |

| |

Shell Balance for Flow Between Parallel Plates | |

| |

| |

| |

Film Flow on a Moving Substrate | |

| |

| |

| |

Transient Viscous Diffusion of Momentum (COMSOL) | |

| |

| |

| |

Poiseuille and Couette Flows in Polymer Processing | |

| |

| |

| |

The Single-Screw Extruder | |

| |

| |

| |

Flow Patterns in a Screw Extruder (COMSOL) | |

| |

| |

| |

Solution of the Equations of Motion in Cylindrical Coordinates | |

| |

| |

| |

Flow Through an Annular Die | |

| |

| |

| |

Spinning a Polymeric Fiber | |

| |

| |

| |

Solution of the Equations of Motion in Spherical Coordinates | |

| |

| |

| |

Analysis of a Cone-and-Plate Rheometer | |

| |

| |

Problems for Chapter 6 | |

| |

| |

| |

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

| |

| |

| |

Introduction | |

| |

| |

| |

Rotational and Irrotational Flows | |

| |

| |

| |

Forced and Free Vortices | |

| |

| |

| |

Steady Two-Dimensional Irrotational Flow | |

| |

| |

| |

Physical Interpretation of the Stream Function | |

| |

| |

| |

Examples of Planar Irrotational Flow | |

| |

| |

| |

Stagnation Flow | |

| |

| |

| |

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

| |

| |

| |

Flow Patterns in a Lake (COMSOL) | |

| |

| |

| |

Axially Symmetric Irrotational Flow | |

| |

| |

| |

Uniform Streams and Point Sources | |

| |

| |

| |

Doublets and Flow Past a Sphere | |

| |

| |

| |

Single-Phase Flow in a Porous Medium | |

| |

| |

| |

Underground Flow of Water | |

| |

| |

| |

Two-Phase Flow in Porous Media | |

| |

| |

| |

Wave Motion in Deep Water | |

| |

| |

Problems for Chapter 7 | |

| |

| |

| |

Boundary-Layer and Other Nearly Unidirectional Flows | |

| |

| |

| |

Introduction | |

| |

| |

| |

Simplified Treatment of Laminar Flow Past a Flat Plate | |

| |

| |

| |

Flow in an Air Intake (C) | |

| |

| |

| |

Simplification of the Equations of Motion | |

| |

| |

| |

Blasius Solution for Boundary-Layer Flow | |

| |

| |

| |

Turbulent Boundary Layers | |

| |

| |

| |

Laminar and Turbulent Boundary Layers Compared | |

| |

| |

| |

Dimensional Analysis of the Boundary-Layer Problem | |

| |

| |

| |

Boundary-Layer Separation | |

| |

| |

| |

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

| |

| |

| |

Entrance Region for Laminar Flow Between Flat Plates | |

| |

| |

| |

The Lubrication Approximation | |

| |

| |

| |

Flow in a Lubricated Bearing (COMSOL) | |

| |

| |

| |

Polymer Processing by Calendering | |

| |

| |

| |

Pressure Distribution in a Calendered Sheet | |

| |

| |

| |

Thin Films and Surface Tension | |

| |

| |

Problems for Chapter 8 | |

| |

| |

| |

Turbulent Flow | |

| |

| |

| |

Introduction | |

| |

| |

| |

Numerical Illustration of a Reynolds Stress Term | |

| |

| |

| |

Physical Interpretation of the Reynolds Stresses | |

| |

| |

| |

Mixing-Length Theory | |

| |

| |

| |

Determination of Eddy Kinematic Viscosity and Mixing Length | |

| |

| |

| |

Velocity Profiles Based on Mixing-Length Theory | |

| |

| |

| |

Investigation of the von Karman Hypothesis | |

| |

| |

| |

The Universal Velocity Profile for Smooth Pipes | |

| |

| |

| |

Friction Factor in Terms of Reynolds Number for Smooth Pipes | |

| |

| |

| |

Expression for the Mean Velocity | |

| |

| |

| |

Thickness of the Laminar Sublayer | |

| |

| |

| |

Velocity Profiles and Friction Factor for Rough Pipe | |

| |

| |

| |

Blasius-Type Law and the Power-Law Velocity Profile | |

| |

| |

| |

A Correlation for the Reynolds Stresses | |

| |

| |

| |

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

| |

| |

| |

Flow Through an Orifice Plate (COMSOL) | |

| |

| |

| |

Turbulent Jet Flow (COMSOL) | |

| |

| |

| |

Analogies Between Momentum and Heat Transfer | |

| |

| |

| |

Evaluation of the Momentum/Heat-Transfer Analogies | |

| |

| |

| |

Turbulent Jets | |

| |

| |

Problems for Chapter 9 | |

| |

| |

| |

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

| |

| |

| |

Introduction | |

| |

| |

| |

Rise of Bubbles in Unconfined Liquids | |

| |

| |

| |

Rise Velocity of Single Bubbles | |

| |

| |

| |

Pressure Drop and Void Fraction in Horizontal Pipes | |

| |

| |

| |

Two-Phase Flow in a Horizontal Pipe | |

| |

| |

| |

Two-Phase Flow in Vertical Pipes | |

| |

| |

| |

Limits of Bubble Flow | |

| |

| |

| |

Performance of a Gas-Lift Pump | |

| |

| |

| |

Two-Phase Flow in a Vertical Pipe | |

| |

| |

| |

Flooding | |

| |

| |

| |

Introduction to Fluidization | |

| |

| |

| |

Bubble Mechanics | |

| |

| |

| |

Bubbles in Aggregatively Fluidized Beds | |

| |

| |

| |

Fluidized Bed with Reaction (C) | |

| |

| |

Problems for Chapter 10 | |

| |

| |

| |

Non-Newtonian Fluids | |

| |

| |

| |

Introduction | |

| |

| |

| |

Classification of Non-Newtonian Fluids | |

| |

| |

| |

Constitutive Equations for Inelastic Viscous Fluids | |

| |

| |

| |

Pipe Flow of a Power-Law Fluid | |

| |

| |

| |

Pipe Flow of a Bingham Plastic | |

| |

| |

| |

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

| |

| |

| |

Constitutive Equations for Viscoelastic Fluids | |

| |

| |

| |

Response to Oscillatory Shear | |

| |

| |

| |

Characterization of the Rheological Properties of Fluids | |

| |

| |

| |

Proof of the Rabinowitsch Equation | |

| |

| |

| |

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

| |

| |

Problems for Chapter 11 | |

| |

| |

| |

Microfluidics and Electrokinetic Flow Effects | |

| |

| |

| |

Introduction | |

| |

| |

| |

Physics of Microscale Fluid Mechanics | |

| |

| |

| |

Pressure-Driven Flow Through Microscale Tubes | |

| |

| |

| |

Calculation of Reynolds Numbers | |

| |

| |

| |

Mixing, Transport, and Dispersion | |

| |

| |

| |

Species, Energy, and Charge Transport | |

| |

| |

| |

The Electrical Double Layer and Electrokinetic Phenomena | |

| |

| |

| |

Relative Magnitudes of Electroosmotic and Pressure-Driven Flows | |

| |

| |

| |

Electroosmotic Flow Around a Particle | |

| |

| |

| |

Electroosmosis in a Microchannel (COMSOL) | |

| |

| |

| |

Electroosmotic Switching in a Branched Microchannel (COMSOL) | |

| |

| |

| |

Measuring the Zeta Potential | |

| |

| |

| |

Magnitude of Typical Streaming Potentials | |

| |

| |

| |

Electroviscosity | |

| |

| |

| |

Particle and Macromolecule Motion in Microfluidic Channels | |

| |

| |

| |

Gravitational and Magnetic Settling of Assay Beads | |

| |

| |

Problems for Chapter 12 | |

| |

| |

| |

An Introduction to Computational Fluid Dynamics and Flowlab | |

| |

| |

| |

Introduction and Motivation | |

| |

| |

| |

Numerical Methods | |

| |

| |

| |

Learning CFD by Using FlowLab | |

| |

| |

| |

Practical CFD Examples | |

| |

| |

| |

Developing Flow in a Pipe Entrance Region (FlowLab) | |

| |

| |

| |

Pipe Flow Through a Sudden Expansion (FlowLab) | |

| |

| |

| |

A Two-Dimensional Mixing Junction (FlowLab) | |

| |

| |

| |

Flow Over a Cylinder (FlowLab) | |

| |

| |

References for Chapter 13 | |

| |

| |

| |

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

| |

| |

| |

Introduction to COMSOL | |

| |

| |

| |

How to Run COMSOL | |

| |

| |

| |

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

| |

| |

| |

Draw Mode | |

| |

| |

| |

Solution and Related Modes | |

| |

| |

| |

Fluid Mechanics Problems Solvable by COMSOL | |

| |

| |

Problems for Chapter 14 | |

| |

| |

| |

Useful Mathematical Relationships | |

| |

| |

| |

Answers to the True/False Assertions | |

| |

| |

| |

Some Vector and Tensor Operations | |

| |

| |

Index | |

| |

| |

The Authors | |