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Preface | p. xv |
Macroscopic Fluid Mechanics | |
Introduction to Fluid Mechanics | |
Fluid Mechanics in Chemical Engineering | p. 3 |
General Concepts of a Fluid | p. 3 |
Stresses, Pressure, Velocity, and the Basic Laws | p. 5 |
Physical Properties-Density, Viscosity, and Surface Tension | p. 10 |
Units and Systems of Units | p. 21 |
Units Conversion | p. 24 |
Mass of Air in a Room | p. 25 |
Hydrostatics | p. 26 |
Pressure in an Oil Storage Tank | p. 29 |
Multiple Fluid Hydrostatics | p. 30 |
Pressure Variations in a Gas | p. 31 |
Hydrostatic Force on a Curved Surface | p. 35 |
Application of Archimedes' Law | p. 37 |
Pressure Change Caused by Rotation | p. 39 |
Overflow from a Spinning Container | p. 40 |
Problems for Chapter 1 | p. 42 |
Mass, Energy, and Momentum Balances | |
General Conservation Laws | p. 55 |
Mass Balances | p. 57 |
Mass Balance for Tank Evacuation | p. 58 |
Energy Balances | p. 61 |
Pumping n-Pentane | p. 65 |
Bernoulli's Equation | p. 67 |
Applications of Bernoulli's Equation | p. 70 |
Tank Filling | p. 76 |
Momentum Balances | p. 78 |
Impinging Jet of Water | p. 83 |
Velocity of Wave on Water | p. 84 |
Flow Measurement by a Rotameter | p. 89 |
Pressure, Velocity, and Flow Rate Measurement | p. 92 |
Problems for Chapter 2 | p. 96 |
Fluid Friction in Pipes | |
Introduction | p. 120 |
Laminar Flow | p. 123 |
Polymer Flow in a Pipeline | p. 128 |
Models for Shear Stress | p. 129 |
Piping and Pumping Problems | p. 133 |
Unloading Oil from a Tanker Specified Flow Rate and Diameter | p. 142 |
Unloading Oil from a Tanker Specified Diameter and Pressure Drop | p. 144 |
Unloading Oil from a Tanker Specified Flow Rate and Pressure Drop | p. 147 |
Unloading Oil from a Tanker Miscellaneous Additional Calculations | p. 147 |
Flow in Noncircular Ducts | p. 150 |
Flow in an Irrigation Ditch | p. 152 |
Compressible Gas Flow in Pipelines | p. 156 |
Compressible Flow in Nozzles | p. 159 |
Complex Piping Systems | p. 163 |
Solution of a Piping/Pumping Problem | p. 165 |
Problems for Chapter 3 | p. 168 |
Flow in Chemical Engineering Equipment | |
Introduction | p. 185 |
Pumps and Compressors | p. 188 |
Pumps in Series and Parallel | p. 193 |
Drag Force on Solid Particles in Fluids | p. 194 |
Manufacture of Lead Shot | p. 202 |
Flow Through Packed Beds | p. 204 |
Pressure Drop in a Packed-Bed Reactor | p. 208 |
Filtration | p. 210 |
Fluidization | p. 215 |
Dynamics of a Bubble-Cap Distillation Column | p. 216 |
Cyclone Separators | p. 219 |
Sedimentation | p. 222 |
Dimensional Analysis | p. 224 |
Thickness of the Laminar Sublayer | p. 229 |
Problems for Chapter 4 | p. 230 |
Microscopic Fluid Mechanics | |
Differential Equations of Fluid Mechanics | |
Introduction to Vector Analysis | p. 249 |
Vector Operations | p. 250 |
The Gradient of a Scalar | p. 253 |
The Divergence of a Vector | p. 257 |
An Alternative to the Differential Element | p. 257 |
The Curl of a Vector | p. 262 |
The Laplacian of a Scalar | p. 262 |
Other Coordinate Systems | p. 263 |
The Convective Derivative | p. 266 |
Differential Mass Balance | p. 267 |
Physical Interpretation of the Net Rate of Mass Outflow | p. 269 |
Alternative Derivation of the Continuity Equation | p. 270 |
Differential Momentum Balances | p. 271 |
Newtonian Stress Components in Cartesian Coordinates | p. 274 |
Constant-Viscosity Momentum Balances in Terms of Velocity Gradients | p. 280 |
Vector Form of Variable-Viscosity Momentum Balance | p. 284 |
Problems for Chapter 5 | p. 285 |
Solution of Viscous-Flow Problems | |
Introduction | p. 292 |
Solution of the Equations of Motion in Rectangular Coordinates | p. 294 |
Flow Between Parallel Plates | p. 294 |
Alternative Solution Using a Shell Balance | p. 301 |
Shell Balance for Flow Between Parallel Plates | p. 301 |
Film Flow on a Moving Substrate | p. 303 |
Transient Viscous Diffusion of Momentum (COMSOL) | p. 307 |
Poiseuille and Couette Flows in Polymer Processing | p. 312 |
The Single-Screw Extruder | p. 313 |
Flow Patterns in a Screw Extruder (COMSOL) | p. 318 |
Solution of the Equations of Motion in Cylindrical Coordinates | p. 322 |
Flow Through an Annular Die | p. 322 |
Spinning a Polymeric Fiber | p. 325 |
Solution of the Equations of Motion in Spherical Coordinates | p. 327 |
Analysis of a Cone-and-Plate Rheometer | p. 328 |
Problems for Chapter 6 | p. 333 |
Laplace's Equation, Irrotational and Porous-Media Flows | |
Introduction | p. 354 |
Rotational and Irrotational Flows | p. 356 |
Forced and Free Vortices | p. 359 |
Steady Two-Dimensional Irrotational Flow | p. 361 |
Physical Interpretation of the Stream Function | p. 364 |
Examples of Planar Irrotational Flow | p. 366 |
Stagnation Flow | p. 369 |
Combination of a Uniform Stream and a Line Sink (C) | p. 371 |
Flow Patterns in a Lake (COMSOL) | p. 373 |
Axially Symmetric Irrotational Flow | p. 378 |
Uniform Streams and Point Sources | p. 380 |
Doublets and Flow Past a Sphere | p. 384 |
Single-Phase Flow in a Porous Medium | p. 387 |
Underground Flow of Water | p. 388 |
Two-Phase Flow in Porous Media | p. 390 |
Wave Motion in Deep Water | p. 396 |
Problems for Chapter 7 | p. 400 |
Boundary-Layer and Other Nearly Unidirectional Flows | |
Introduction | p. 414 |
Simplified Treatment of Laminar Flow Past a Flat Plate | p. 415 |
Flow in an Air Intake (C) | p. 420 |
Simplification of the Equations of Motion | p. 422 |
Blasius Solution for Boundary-Layer Flow | p. 425 |
Turbulent Boundary Layers | p. 428 |
Laminar and Turbulent Boundary Layers Compared | p. 429 |
Dimensional Analysis of the Boundary-Layer Problem | p. 430 |
Boundary-Layer Separation | p. 433 |
Boundary-Layer Flow Between Parallel Plates (COMSOL Library) | p. 435 |
Entrance Region for Laminar Flow Between Flat Plates | p. 440 |
The Lubrication Approximation | p. 442 |
Flow in a Lubricated Bearing (COMSOL) | p. 448 |
Polymer Processing by Calendering | p. 450 |
Pressure Distribution in a Calendered Sheet | p. 454 |
Thin Films and Surface Tension | p. 456 |
Problems for Chapter 8 | p. 459 |
Turbulent Flow | |
Introduction | p. 473 |
Numerical Illustration of a Reynolds Stress Term | p. 479 |
Physical Interpretation of the Reynolds Stresses | p. 480 |
Mixing-Length Theory | p. 481 |
Determination of Eddy Kinematic Viscosity and Mixing Length | p. 484 |
Velocity Profiles Based on Mixing-Length Theory | p. 486 |
Investigation of the von Karman Hypothesis | p. 487 |
The Universal Velocity Profile for Smooth Pipes | p. 488 |
Friction Factor in Terms of Reynolds Number for Smooth Pipes | p. 490 |
Expression for the Mean Velocity | p. 491 |
Thickness of the Laminar Sublayer | p. 492 |
Velocity Profiles and Friction Factor for Rough Pipe | p. 494 |
Blasius-Type Law and the Power-Law Velocity Profile | p. 495 |
A Correlation for the Reynolds Stresses | p. 496 |
Computation of Turbulence by the [kappa]/[epsilon] Method | p. 499 |
Flow Through an Orifice Plate (COMSOL) | p. 501 |
Turbulent Jet Flow (COMSOL) | p. 505 |
Analogies Between Momentum and Heat Transfer | p. 509 |
Evaluation of the Momentum/Heat-Transfer Analogies | p. 511 |
Turbulent Jets | p. 513 |
Problems for Chapter 9 | p. 521 |
Bubble Motion, Two-Phase Flow, and Fluidization | |
Introduction | p. 531 |
Rise of Bubbles in Unconfined Liquids | p. 531 |
Rise Velocity of Single Bubbles | p. 536 |
Pressure Drop and Void Fraction in Horizontal Pipes | p. 536 |
Two-Phase Flow in a Horizontal Pipe | p. 541 |
Two-Phase Flow in Vertical Pipes | p. 543 |
Limits of Bubble Flow | p. 546 |
Performance of a Gas-Lift Pump | p. 550 |
Two-Phase Flow in a Vertical Pipe | p. 553 |
Flooding | p. 555 |
Introduction to Fluidization | p. 559 |
Bubble Mechanics | p. 561 |
Bubbles in Aggregatively Fluidized Beds | p. 566 |
Fluidized Bed with Reaction (C) | p. 572 |
Problems for Chapter 10 | p. 575 |
Non-Newtonian Fluids | |
Introduction | p. 591 |
Classification of Non-Newtonian Fluids | p. 592 |
Constitutive Equations for Inelastic Viscous Fluids | p. 595 |
Pipe Flow of a Power-Law Fluid | p. 600 |
Pipe Flow of a Bingham Plastic | p. 604 |
Non-Newtonian Flow in a Die (COMSOL Library) | p. 606 |
Constitutive Equations for Viscoelastic Fluids | p. 613 |
Response to Oscillatory Shear | p. 620 |
Characterization of the Rheological Properties of Fluids | p. 623 |
Proof of the Rabinowitsch Equation | p. 624 |
Working Equation for a Coaxial-Cylinder Rheometer: Newtonian Fluid | p. 628 |
Problems for Chapter 11 | p. 630 |
Microfluidics and Electrokinetic Flow Effects | |
Introduction | p. 639 |
Physics of Microscale Fluid Mechanics | p. 640 |
Pressure-Driven Flow Through Microscale Tubes | p. 641 |
Calculation of Reynolds Numbers | p. 641 |
Mixing, Transport, and Dispersion | p. 642 |
Species, Energy, and Charge Transport | p. 644 |
The Electrical Double Layer and Electrokinetic Phenomena | p. 647 |
Relative Magnitudes of Electroosmotic and Pressure-Driven Flows | p. 648 |
Electroosmotic Flow Around a Particle | p. 653 |
Electroosmosis in a Microchannel (COMSOL) | p. 653 |
Electroosmotic Switching in a Branched Microchannel (COMSOL) | p. 657 |
Measuring the Zeta Potential | p. 659 |
Magnitude of Typical Streaming Potentials | p. 660 |
Electroviscosity | p. 661 |
Particle and Macromolecule Motion in Microfluidic Channels | p. 661 |
Gravitational and Magnetic Settling of Assay Beads | p. 662 |
Problems for Chapter 12 | p. 666 |
An Introduction to Computational Fluid Dynamics and Flowlab | |
Introduction and Motivation | p. 671 |
Numerical Methods | p. 673 |
Learning CFD by Using FlowLab | p. 682 |
Practical CFD Examples | p. 686 |
Developing Flow in a Pipe Entrance Region (FlowLab) | p. 687 |
Pipe Flow Through a Sudden Expansion (FlowLab) | p. 690 |
A Two-Dimensional Mixing Junction (FlowLab) | p. 692 |
Flow Over a Cylinder (FlowLab) | p. 696 |
References for Chapter 13 | p. 702 |
Comsol (Femlab) Multiphysics for Solving Fluid Mechanics Problems | |
Introduction to COMSOL | p. 703 |
How to Run COMSOL | p. 705 |
Flow in a Porous Medium with an Obstruction (COMSOL) | p. 705 |
Draw Mode | p. 719 |
Solution and Related Modes | p. 724 |
Fluid Mechanics Problems Solvable by COMSOL | p. 725 |
Problems for Chapter 14 | p. 730 |
Useful Mathematical Relationships | p. 731 |
Answers to the True/False Assertions | p. 737 |
Some Vector and Tensor Operations | p. 740 |
Index | p. 743 |
The Authors | p. 753 |
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