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An Introduction to Fluid Dynamics Principles of Analysis and Design

by: Middleman, Stanley

An Introduction to Fluid Dynamics Principles of Analysis and Design

by: Middleman, Stanley

ISBN 13:
9780471182092
ISBN 10:
0471182095
Edition: 1st
Format: Paperback
Copyright: 10/15/1997
Publisher: Wiley

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Summary

This comprehensive text links abstract mathematics to engineering applications in order to provide a clear and thorough exploration of fluid dynamics. Focus is on the development of mathematical models of physical phenomena and the wide range of technologies available to students. Filled with examples and problems inspired by real engineering applications, this resource will not only teach, but motivate students to further emerge themselves in the field.

CHAPTER 1 WHAT IS FLUID DYNAMICS?

(29)

1.1 Thinking About Fluid Dynamics: Some Typical Problems

(10)

1.1.1 Drop Breakup in a Stirred Tank

(1)

Table 1.1.1 Important Physical Properties for the System Illustrated in Fig. 1.1.1

(3)

1.1.2 Removal of an Oil Film from a Surface

(1)

1.1.3 Flow Field in a CVD Reactor

(3)

1.1.4 Dry-Eye Syndrome

(1)

1.1.5 Absorption of an Ink Drop by Paper

(1)

1.2 Dimensional Analysis

(10)

Example 1.2.1 Coherent Length of a Wasp Spray

(3)

Example 1.2.2 Dispersion (Breakup) of an Oil Stream in an Aqueous Pipe Flow

(4)

1.3 Classification of Problems in Fluid Dynamics

(1)

Summary

(1)

Problems

(7)

CHAPTER 2 STATICS, DYNAMICS, AND SURFACE TENSION

(35)

2.1 Hydrostatics

(9)

2.1.1 Surface Tension

(2)

2.1.2 Test of the Model of Critical Drop Size

(2)

Example 2.1.1 Surface Tension by the "Drop Weight" Method

(1)

Example 2.1.2 Design of a Drop Dispenser

(1)

2.2 Capillary Hydrostatics: The Young-Laplace Equation

(8)

Example 2.2.1 Pressure Inside a Gas Bubble

(1)

Example 2.2.2 Liquid Rise in a Capillary

(2)

Table 2.2.1 Surface Tensions of Common Pairs of Fluids at 25 (Degree)C

(1)

Example 2.2.3 Pressure Inside a Growing Drop

(1)

2.3 Pressure in Response to External Forces

(4)

Example 2.3.1 Surface of a Rotating Liquid

(1)

Example 2.3.2 Design of a Parabolic Mirror

(1)

Example 2.3.3 Pressure in an Accelerating Liquid; Shape of the Free Surface

(2)

2.4 The Shape of Interfaces

(5)

Summary

(1)

Problems

(9)

CHAPTER 3 FORCES ON, AND WITHIN, A FLOWING MEDIUM

(65)

3.1 Concepts of Shear Stress and Momentum Flux

(2)

3.2 Problem Solving/Model Building

(16)

3.2.1 A Model of Laminar Flow Through a Tube

(6)

Example 3.2.1 Determination of Viscosity from a Poiseuille Flow Experiment

(1)

Example 3.2.2 Passage of a Viscous Drop Through a Long Tube

(4)

Example 3.2.3 A Model of Laminar Flow Through a Lubricated Tube

(4)

3.3 Engineering Design: The Role of Analysis

(14)

Example 3.3.1 Treatment of Data from a Capillary Viscometer

(1)

3.3.1 Classification of Simple Laminar Flows

(1)

3.3.2 Axial Annular Flow in a Closed Container

(3)

Example 3.3.2 Pressure in an Enclosure

(1)

3.3.3 Axial Annular Flow in an Open Tube

(1)

3.3.4 The Design of a Wire Coating Die and Analysis of Its Performance

(4)

Example 3.3.3 Conditions to Achieve a Specific Coating Thickness

(1)

Example 3.3.4 Maximum Shear Stress in a Wire Coating Die

(2)

3.4 The Viscosity of Fluids

(11)

3.4.1 The Viscosity of Liquids

(2)

Table 3.4.1 Pseudocritical Viscosity XXX(+) for Some Common Liquids

(1)

Table 3.4.2 Group Contributions to J

(1)

Example 3.4.1 Viscosity of Liquid Propane

100

(1)

3.4.2 The Viscosity of Gases

100

(1)

Table 3.4.3 Parameters for the Chapman-Enskog Equation (Eq. 3.4.8) and T(c) Values

101

(1)

Example 3.4.2 Viscosity of Gaseous Ammonia

102

(1)

3.4.3 The Design of a System for Measurement of the Viscosity of Gases

103

(1)

Example 3.4.3 Design Specifications for a Capillary Viscometer for Gases

104

(4)

3.5 Hydrostatics and Body Forces: Another Look

108

(4)

Example 3.5.1 Motion of a Planar Sheet Through a Submerged Restriction

108

(3)

Example 3.5.2 Motion of a Wetted Planar Sheet Through a Restriction

111

(1)

3.6 Molecular Flow

112

(7)

Example 3.6.1 Characteristics of a Gas at Low Pressure

113

(2)

Example 3.6.2 Treatment of Some Data for a Gas Flow at Low Pressure

115

(2)

Example 3.6.3 A Vapor Delivery System

117

(2)

Summary

119

(1)

Problems

119

(11)

CHAPTER 4 CONSERVATION OF MASS AND MOMENTUM IN A CONTINUOUS FLUID

130

(84)

4.1 The Distribution of Mass in a Continuous Fluid (the Continuity Equation)

131

(3)

Table 4.1.1 Components of the Divergence Operator

134

(1)

4.2 Deformation in a Fluid

134

(4)

Table 4.2.1 Components of the Rate of Deformation Tensor

137

(1)

Example 4.2.1 The Deformation Rate Tensor in Poiseuille Flow

137

(1)

4.3 Stresses in a Fluid: Conservation of Momentum and the Equations of Motion

138

(8)

Table 4.3.1 The Navier-Stokes Equations for Newtonian Isothermal Incompressible Flow

144

(2)

4.4 Some Problems Solved Through Simplification of the Navier-Stokes Equations

146

(29)

4.4.1 Angular (Rotational) Drag Flow Between Long Concentric Cylinders

146

(3)

4.4.2 Liquid Film on a Vertical Surface

149

(3)

4.4.3 Growth of a Bubble in a Viscous Liquid

152

(3)

Example 4.4.1 Growth of a Bubble in a Very Viscous Liquid

155

(2)

4.4.4 Viscous Resistance to a Freely Falling Object: A Long Cylinder in a Coaxial, Fluid-Filled Tube

157

(8)

Example 4.4.2 Design of a Simple Falling Cylinder Viscometer

165

(1)

Example 4.4.3 Determination of Viscosity from a Falling Cylinder Experiment

165

(1)

4.4.5 Slow Flow Around a Solid Sphere: A Two-Dimensional Flow

166

(6)

Example 4.4.4 Gravitational Sedimentation of Small Particles

172

(1)

4.4.6 Flow Around a Deformable Particle

173

(1)

4.4.7 A Summary of the Modeling Procedure

174

(1)

4.5 Formulation of the Dynamic Equations for Some Complex But Interesting Problems: Engineering Approximations

175

(19)

Example 4.5.1 Steady Radial Flow Between Parallel Disks

175

(5)

Example 4.5.2 A Biomedical Flow Device

180

(5)

Example 4.5.3 Film Thickness on a Center-Fed Rotating Disk

185

(5)

Example 4.5.4 Film Thickness on a Center-Fed Rotating Disk: Evaluation of Approximations

190

(1)

Example 4.5.5 A Model of Torsional Flow Between Parallel Disks

191

(2)

Example 4.5.6 Evaluation of the Design of a Rotational Disk Viscometer

193

(1)

Summary

194

(1)

Problems

194

(20)

CHAPTER 5 DIMENSIONAL ANALYSIS AND DYNAMIC SIMILARITY

214

(38)

5.1 The Principle of Dynamic Similarity

215

(10)

Example 5.1.1 Design of an Experimental Study of Ink-Jet Printing

219

(4)

Example 5.1.2 Design of an Experimental Study of Oil Film Entrainment

223

(2)

5.2 Correlation of Data

225

(3)

5.3 Inspectional Analysis

228

(8)

5.3.1 Fully Developed Laminar Flow

229

(5)

Example 5.3.1 Laminar Flow Through a Semicircular Pipe

234

(1)

5.3.2 Entry Region Flow

235

(1)

5.4 Experimental Design

236

(4)

Example 5.4.1 A Model for the Flow Field in a CVD Reactor

239

(1)

Summary

240

(1)

Problems

241

(11)

CHAPTER 6 NEARLY PARALLEL FLOWS

252

(69)

6.1 The Slider Bearing

252

(9)

Example 6.1.1 Load Capacity of a Slider Bearing

258

(1)

6.1.1 Examination of the Nearly Parallel Assumption

258

(1)

6.1.2 Effect of Geometry on the Character of the Flow

259

(1)

Example 6.1.2 Floating Position of a Slider Bearing

259

(2)

6.2 Laminar Flow Through a Leaky Tube

261

(5)

Example 6.2.1 A Hollow Fiber Water Purifier

264

(2)

6.3 A Device for the Treatment of Hydrocephalus

266

(6)

Example 6.3.1 In Vitro Test of a Hydrocephalus Shunt

270

(2)

6.4 Spreading of a Very Viscous Drop

272

(3)

6.5 The Hydrodynamic Entry Length for a Film Flowing Along a Surface: An Example of an Integral Analysis

275

(7)

6.6 Recovery from an Oil Spill: The Rotating Disk Skimmer

282

(5)

Example 6.6.1 Yield from a Rotating Disk Oil Skimmer

286

(1)

Example 6.6.2 Dependence of the Recovery Rate on R

286

(1)

6.7 Floating a Disk on an Air Table

287

(4)

Example 6.7.1 Design of a Coating Thickness Monitor

290

(1)

6.8 Flow Through a Converging Planar Region

291

(11)

Example 6.8.1 Reynolds Numbers for Flow Toward and Through a Converging Planar Duct

296

(5)

Example 6.8.2 Pressure Requirement for Flow Through a Nonuniform Planar Duct

301

(1)

6.9 Laminar Flow Through a Leaky Tube: The Perturbation Method of Approximation

302

(4)

6.10 Roll Coating

306

(4)

Summary

310

(1)

Problems

311

(10)

CHAPTER 7 UNSTEADY FLOWS

321

(45)

7.1 A Transient Pressure Flow

321

(4)

Example 7.7.1 Start-Up of a Capillary Viscometer

324

(1)

7.2 Stability of a Laminar Liquid Jet

325

(11)

7.2.1 Stability of an Inviscid Jet

327

(5)

Example 7.2.1 Design of a Liquid Electrical Contact

332

(3)

7.2.2 Assessment of Some Assumptions of the Stability Analysis

335

(1)

7.3 Quasi-Steady Flows

336

(13)

Example 7.3.1 Model of Draining of a Tank Through a Capillary

336

(3)

Example 7.3.2 A Quasi-Steady Model of a Viscous Squeezing Flow

339

(4)

7.3.1 Intertial Effects in the Absence of Viscosity

343

(1)

Example 7.3.3 Design of a Viscous Damper

344

(1)

Example 7.3.4 Squeeze-Film Lubrication in the Knee

345

(1)

Example 7.3.5 Draining of a Film of Liquid from a Vertical Plate

346

(3)

7.4 Transient Flow in the Microcirculation

349

(5)

7.5 The Leveling of a Surface Disturbance on a Thin Film

354

(6)

Example 7.5.1 Decay Rate of a Small Surface Disturbance

357

(1)

Example 7.5.2 Retention of a Lubricant Film on a Spinning Disk

358

(2)

Example 7.5.3 Rate of Loss of Lubricant

360

(1)

Summary

360

(1)

Problems

360

(6)

CHAPTER 8 THE STREAM FUNCTION

366

(16)

8.1 Definition of the Stream Function

366

(5)

Example 8.1.1 The Stream Function Analysis for Poiseuille Flow in a Tube

369

(2)

8.2 Streamlines for Other Axisymmetric Flows

371

(5)

8.2.1 Flow Around a Sphere

371

(1)

8.2.2 Flow in a CVD Reactor

372

(1)

8.2.3 Flow in an Occluded Blood Vessel

373

(2)

8.2.4 Radial Flow Between Parallel Disks

375

(1)

8.3 Streamline Analysis for a Wiping Flow

376

(3)

Summary

379

(1)

Problems

379

(3)

CHAPTER 9 TURBULENT FLOW AND THE LAMINAR BOUNDARY LAYER

382

(29)

9.1 Turbulent Flow

382

(12)

9.1.1 Time-Averaging and the Reynolds Stresses

384

(1)

9.1.2 Reynolds Stress Models

385

(1)

Example 9.1.1 Time-Averaged Velocity Profile in a Pipe

386

(4)

Example 9.1.2 The Turbulent Friction Factor

390

(1)

9.1.3 The Friction Factor for Pipe Flow: Laminar and Turbulent

391

(2)

Example 9.1.3 Predicting the Flowrate for a Turbulent Pipe Flow

393

(1)

9.2 The Developing Laminar Boundary Layer

394

(7)

Example 9.2.1 Thickness of the Laminar Boundary Layer

399

(1)

Example 9.2.2 The Mechanics of Water Beasts

400

(1)

9.3 The Integral Boundary Layer Analysis

401

(4)

9.4 Turbulent Drag for Flows Relative to Blunt Bodies

405

(2)

Example 9.4.1 Wind Force on a Sphere

406

(1)

Summary

407

(1)

Problems

408

(3)

CHAPTER 10 FLOW THROUGH POROUS MEDIA

411

(30)

10.1 Flow Through a Packed Bed of Spheres

411

(7)

10.1.1 The Equivalent Capillary Model of a Porous Medium

411

(2)

10.1.2 The Laminar Flow Regime

413

(2)

10.1.3 The Turbulent Flow Regime

415

(1)

10.1.4 Pressure Drop Across a Fibrous Filter

416

(1)

Example 10.1.1 Finding the Solidity of a Filter

417

(1)

10.2 Flow Through Porous (Consolidated) Materials

418

(8)

10.2.1 Fluid Transport in a Tumor

419

(2)

Example 10.2.1 Pressure and Flow in a Tumor

421

(1)

10.2.2 Leakage from a Pressurized Porous Pipe

422

(2)

Example 10.2.2 Determination of Permeability from Transient Leakage Data

424

(1)

Example 10.2.3 Determination of Permeability from Steady Leakage Data

425

(1)

10.3 The Dynamics of Printing on a Porous Surface

426

(6)

10.3.1 Wicking of a Drop into a Porous Surface

429

(3)

10.4 Airflow Through Soil: A Problem in Environmental Decontamination

432

(3)

Summary

435

(1)

Problems

436

(5)

CHAPTER 11 MACROSCOPIC BALANCES

441

(66)

11.1 The Macroscopic Mass Balance

441

(4)

Example 11.1.1 The Egyptian Water Clock

441

(2)

Example 11.1.2 Pumping Rate Required for a Cleaning Jet

443

(1)

Example 11.1.3 Effect of Temperature and Pressure on the Flowrate of a Gas

444

(1)

11.2 The Macroscopic Momentum Balance

445

(9)

Example 11.2.1 Axial Force Exerted on the Walls of a Straight Pipe

447

(2)

Example 11.2.2 Force Exerted on a U-Bend in a Pipe

449

(1)

Example 11.2.3 Flow of Water Through a U-Bend in a Pipe

449

(1)

Example 11.2.4 Force on Converging Nozzle

450

(3)

Example 11.2.5 Forces on a Reversing Bucket

453

(1)

11.3 The Macroscopic Energy Balance

454

(19)

11.3.1 Application to Steady State Processes

456

(2)

Example 11.3.1 Turbulent Incompressible Steady Flow Through a Long Straight Pipe

458

(2)

Example 11.3.2 An Elevated Reservoir as a Power Source

460

(2)

Example 11.3.3 Pump Requirements for a Water Supply System

462

(2)

Example 11.3.4 Derivation and Application of Torricelli's Law

464

(3)

11.3.2 Energy Losses Through Bends and Fittings

467

(3)

11.3.3 Optimal Pipe Diameter to Minimize Power Costs

470

(1)

11.3.4 Mammalian Circulation and Optimal Design

471

(2)

11.4 Flowrate Measuring Devices

473

(4)

11.4.1 The Orifice Meter

473

(2)

11.4.2 The Venturi Meter

475

(2)

11.5 Compressible Flow in a Pipe with Friction

477

(15)

11.5.1 Adiabatic Compressible Flow in a Pipe with Friction

478

(3)

Example 11.5.1 Pipe Length to Achieve Sonic Flow

481

(1)

Example 11.5.2 Pipe Length to Achieve a Specified Mach Number

482

(1)

Example 11.5.3 Outlet Pressure to Achieve Sonic Flow

483

(1)

Example 11.5.4 Inlet Pressure to Achieve Sonic Flow

484

(1)

11.5.2 Isothermal Compressible Flow in a Pipe with Friction

485

(1)

Example 11.5.5 Inlet Pressure to Achieve Maximum Speed: Isothermal Flow

486

(1)

Example 11.5.6 The Design of a Mass Flow Controller

486

(2)

Example 11.5.7 Effect of Downstream Pressure on Flow into a Tube (Isothermal Flow)

488

(4)

11.6 Adiabatic Fictionless Compressible Flow

492

(3)

Example 11.6.1 Prediction of Compressible Flow Through a Tube

494

(1)

Summary

495

(1)

Problems

496

(11)

Appendix Unit Conversions

507

(3)

Index

510

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An Introduction to Fluid Dynamics Principles of Analysis and Design

An Introduction to Fluid Dynamics Principles of Analysis and Design

9780471182092

0471182095

Summary

Author Biography

Table of Contents

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