Fluid mechanics for chemical engineers

Me M cG ra w -H ill’s

Sur C H E M IC A L E N G IN E E R IN G S E R I E S

Fluid Mechanics

for Chemical

Engineers

FLUID MECHANICS FOR

CHEMICAL ENGINEERS

Girr OF

T ' FOUNOAT' ° ” USA NOT FOR RESALE!

McGraw-Hill Chemical Engineering Series

E ditorial Advisory B oard

E du ard o D. G landt, Dean, School o f Engineering and Applied Science, University

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Thom as F. Edgar, Professor o f Chemical Engineering, University o f Texas

at Austin

Bailey and Ollis: Biochemical Engineering Fundamentals

Bennett and Myers: Momentum, Heat and Mass Transfer

Coughanowr and LeBlanc: Process Systems Analysis and Control

Davis and Davis: Fundamentals o f Chemical Reaction Engineering

de Nevers: Air Pollution Control Engineering

de Nevers: Fluid Mechanics fo r Chemical Engineers

Douglas: Conceptual Design o f Chemical Processes

Edgar, Himmelblau, and Lasdon: Optimization o f Chemical Processes

Gates, Katzer, and Schuit: Chemistry o f Catalytic Processes

King: Separation Processes

Luyben: Process Modeling, Simulation, and Control fo r Chemical Engineers

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McCabe, Smith, and Harriott: Unit Operations o f Chemical Engineering

Middleman and Hochberg: Process Engineering Analysis in Semiconductor Device

Fabrication

Perry and Green: Perry’s Chemical Engineers' Handbook

Peters, Timmerhaus, and West: Plant Design and Economics fo r Chemical

Engineers

Reid, Prausnitz, and Poling: Properties o f Gases and Liquids

Smith, Van Ness, and Abbott: Introduction to Chemical Engineering

Thermodynamics

Treybal: Mass Transfer Operations

T he Founding of a Discipline:

T he M cG raw -H ill C om panies, Inc. Series in C hem ical E ngineering

Over 80 years ago, fifteen prominent chemical engineers met in New York to plan a

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Textbooks such as McCabe et al, Unit Operations o f Chemical Engineering,

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years to come.

FLUID MECHANICS FOR

CHEMICAL ENGINEERS

THIRD EDITION

Noel de Nevers

Department of Chemical and Fuels Engineering

University o f Utah

Higher Education

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FLU ID M ECHANICS FOR CH EM ICA L ENG INEERS, TH IRD EDITION

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ABOUT THE AUTHOR

Noel de N evers received a B.S. from Stanford in 1954, and M.S. and Ph.D. degrees

from the University of M ichigan in 1956 and 1959, all in chemical engineering.

He worked for the research arms of the Chevron Oil Company from 1958 to

1963 in the areas of chemical process development, chemical and refinery process

design, and secondary recovery of petroleum. He has been on the faculty of the Uni￾versity o f Utah from 1963 to the present in the Department of Chemical and Fuels

Engineering, becom ing emeritus in 2002.

He has worked for the National Reactor Testing Site, Idaho Falls, Idaho, on

nuclear problems, for the U.S. Army Harry Diamond Laboratory, Washington DC, on

weapons, and for the Office of Air Programs of the U.S. EPA in Durham, NC, on air

pollution.

He was a Fulbright student of Chemical Engineering at the Technical Univer￾sity of Karlsruhe, Germany, in 1954-1955, a Fulbright lecturer on Air Pollution at the

Universidad del Valle, in Cali, Colombia, in the summer of 1974, and at the Univer￾sidad de la República, M ontevideo Uruguay and the Universidad Naciónal Mar del

Plata, Argentina in the Autumn of 1996.

His areas o f research and publication are in fluid mechanics, thermodynamics,

air pollution, technology and society, energy and energy policy, and explosions and

fires. He regularly consults on air pollution problems, explosions, fires and toxic

exposures.

In 1993 he received the Corcoran Award from the Chemical Engineering Divi￾sion of the American Society for Engineering Education for the best paper (‘“ Prod￾uct in the W ay’ Processes”) that year in Chemical Engineering Education.

In 2000 his textbook, Air Pollution Control Engineering, Second Edition, was

issued by McGraw-Hill.

In 2002 his textbook, Physical and Chemical Equilibrium fo r Chemical Engi￾neers was issued by John Wiley.

In addition to his serious work he has three “de Nevers’s Laws” in the latest

“M urphy’s Laws” compilation, and won the title “Poet Laureate of Jell-0 Salad” at

the Last Annual Jell-0 Salad Festival in Salt Lake City in 1983. He is the official

discoverer of Private Arch in Arches National Park.

CONTENTS

Notation xvii

Preface xxiii

Chapter 1 Introduction 1

1.1 What Is Fluid Mechanics? 1

1.2 What Good Is Fluid Mechanics? 2

13 Basic Ideas in Fluid Mechanics 3

1.4 Liquids and Gases 4

1.5 Properties of Fluids 5

1.5.1 Density / 1.5.2 Specific Gravity / 1.5.3 Viscosity /

1.5.4 Kinematic Viscosity / 1.5.5 Surface Tension

1.6 Pressure 16

1.7 Force, Mass, and Weight 19

1.8 Units and Conversion Factors 19

1.9 Principles and Techniques 25

1.10 Engineering Problems 26

1.11 Why This Book Is Different from Other Fluid Mechanics Books 28

1.12 Summary 30

PART I PRELIMINARIES 35

Chapter 2 Fluid Statics 37

2.1 The Basic Equation of Fluid Statics 38

2.2 Pressure-Depth Relationships 40

2.2.1 Constant-Density Fluids / 2.2.2 Ideal Gases

2.3 Pressure Forces on Surfaces 44

2.4 Pressure Vessels and Piping 47

2.5 Buoyancy 52

2.6 Pressure Measurement 54

2.7 Manometer-like Situations 59

2.8 Variable Gravity 63

viii

CONTENTS

2.9 Pressure in Accelerated Rigid-Body Motions 63

2.10 More Problems in Fluid Statics 68

2.11 Summary 69

Chapter 3 The Balance Equation and the Mass Balance 81

3.1 The General Balance Equation 81

3.2 The Mass Balance 84

3.3 Steady-State Balances 86

3.4 The Steady-State Flow, One-Dimensional Mass Balance 87

3.4.1 Average Velocity / 3.4.2 Velocity Distributions

3.5 Unsteady-State Mass Balances 91

3.6 Mass Balances for Mixtures 95

3.7 Summary 98

Chapter 4 The First Law of Thermodynamics 103

4.1 Energy 103

4.2 Forms of Energy 104

4.2.1 Internal Energy / 4.2.2 Kinetic Energy / 4.2.3 Potential

Energy / 4.2.4 Electrostatic Energy / 4.2.5 Magnetic Energy /

4.2.6 Surface Energy / 4.2.7 Nuclear Energy

4.3 Energy Transfer 107

4.4 The Energy Balance 108

4.4.1 The Sign Convention for Work

4.5 Kinetic and Potential Energies 110

4.6 Internal Energy 113

4.7 The Work Term 115

4.8 Injection Work 116

4.9 Enthalpy 118

4.10 Restricted Forms 119

4.11 Other Forms of Work and Energy 122

4.12 Limitations of the First Law 125

4.13 Summary 126

PART II FLOWS OF FLUIDS THAT ARE

ONE-DIMENSIONAL, OR THAT CAN

BE TREATED AS IF THEY WERE 131

Chapter 5 Bernoulli’s Equation 133

5.1 The Energy Balance for a Steady, Incompressible Flow 133

5.2 The Friction-Heating Term 134

5.3 Zero Flow 137

5.4 The Head Form of B.E. 138

5.5 Diffusers and Sudden Expansions 138

5.6 B.E. for Gases 141

X CONTENTS

5.7 Torricelli’S'Equation and Its Variants 143

5.8 B.E. for Fluid-Flow Measurements 146

5.8.1 Pitot Tube / 5.8.2 Pitot-Static Tube / 5.8.3 Venturi

Meter / 5.8.4 Orifice Meter / 5.8.5 Rotameters

5.9 Negative Absolute Pressures: Cavitation 155

5.10 B.E. for Unsteady Flows 158

5.11 Nonuniform Flows 160

5.12 Summary 162

Chapter 6 Fluid Friction in Steady, One-Dimensional Flow 173

6.1 The Pressure-Drop Experiment 174

6.2 Reynolds’ Experiment 175

6.3 Laminar Flow 177

6.4 Turbulent Flow 183

6.5 The Three !Friction Factor Problems 188

6.6 Some Comments about the Friction Factor Method and

Turbulent flow 193

6.7 More Convenient Methods 194

6.8 Enlargements and Contractions 200

6.9 Fitting Losses 202

6.10 Fluid Friction in One-Dimensional Flow in Noncircular Channels 204

6.10.1 Laminar Flow in Noncircular Channels / 6.10.2 Seal

Leaks / 6.10.3 Turbulent Flow in Noncircular Channels

6.11 More Complex Problems Involving B.E. 211

6.12 Economic Pipe Diameter, Economic Velocity 214

6.13 Flow around Submerged Objects 220

6.14 Summary 228

Chapter 7 The Momentum Balance 243

7.1 Momentum 244

7.2 The Momentum Balance 245

7.3 Some Steady-Flow Applications of the Momentum Balance 250

7.3.1 Jet-Surface Interactions / 7.3.2 Forces in Pipes /

7.3.3 Rockets and Jets / 7.3.4 Sudden Expansion /

7.3.5 Eductors, Ejectors, Aspirating Burners, Jet Mixers,

and Jet Pumps

7.4 Relative Velocities 266

7.5 Starting and Stopping Flows 271

7.5.1 Starting Flow in a Pipe / 7.5.2 Stopping Flow in a Pipe;

Water Hammer / 7.5.3 Stopping Flow in an Open Channel;

Hydraulic Jump

7.6 A Very Brief Introduction to Aeronautical Engineering 279

7.7 The Angular-Momentum Balance; Rotating Systems 283

7.8 Summary 285

CONTENTS xi

Chapter 8 One-Dimensional, High-Velocỉty Gas Flow 296

8.1 The Speed of Sound 297

8.2 Steady, Frictionless, Adiabatic, One-Dimensional Row of an

Ideal Gas 301

8.3 Nozzle-Choking 311

8.4 High-Velocity Gas Flow with Friction, Heating, or Both 313

8.4.1 Adiabatic Flow with Friction / 8.4.2 Isothermal Flow

with Friction

8.5 Normal Shock Waves 321

8.6 Relative Velocities, Changing Reservoir Conditions 324

8.7 Nozzles and Diffusers 326

8.8 Summary 331

PART m SOME OTHER TOPICS THAT CAN BE

VIEWED BY THE METHODS OF ONE￾DIMENSIONAL FLUID MECHANICS 341

Chapter 9 Models, Dimensional Analysis,

and Dimensionless Numbers 343

9.1 Models 343

9.2 Dimensionless Numbers 345

9.3 Finding the Dimensionless Numbers 346

9.3.1 The Method of Governing Equations / 9.3.2 The Method

o f Force Ratios / 9.3.3 Buckingham's 7T Method

9.4 Dimensionless Numbers and Physical Insight 356

9.5 Judgment, Guesswork, and Caution 357

9.6 Summary 358

Chapter 10 Pumps, Compressors, and Turbines 360

10.1 General Relations for All Pumps, Compressors, and Turbines 361

10.2 Positive-Displacement Pumps and Compressors 363

10.2.1 P.D. Pumps / 10.2.2 P.D. Compressors

10.3 Centrifugal Pumps and Compressors 372

10.3.1 Centrifugal Pumps / 10.3.2 NPSH /

10.3.3 Centrifugal Compressors

10.4 Axial Flow Pumps and Compressors 381

10.5 Compressor Efficiencies 382

10.6 Pump and Compressor Stability 384

10.7 Regenerative Pumps 386

10.8 Fluid Engines and Turbines 387

10.9 Fluid Engine and Turbine Efficiency 391

10.10 Summary 391

x ii CONTENTS

Chapter 11 Flow through Porous Media 397

11.1 Fluid Friction in Porous Media 398

11.2 Two-Fluid Cocurrent Flow in Porous Media 406

11.3 Countercurrent Flow in Porous Media 409

11.4 Simple Filter Theory 411

11.4.1 Surface Filters / 11.4.2 Depth Filters

11.5 Fluidization 414

11.6 Summary 415

Chapter 12 Gas-Liquid Flow 418

12.1 Vertical, Upward Gas-Liquid Flow 419

12.2 Horizontal Gas-Liquid Flow 423

12.3 Two-Phase Flow with Boiling 424

12.4 Summary 425

Chapter 13 Non-Newtonian Fluid Flow in Circular Pipes 428

13.1 The Role of Structure in Non-Newtonian Behavior 428

13.2 Measurement and Description of Non-Newtonian Fluids 429

13.3 Steady Laminar Row of Non-Newtonian Fluids in Horizontal

Circular Tubes 432

13.3.1 Power Law / 13.3.2 Bingham Plastic

13.4 Turbulent Steady Pipe Flow of Non-Newtonian Fluids, and

the Transition from Laminar to Turbulent Flow 436

13.4.1 Power Law / 13.4.2 Bingham Plastic

13.5 Summary 441

Chapter 14 Surface Forces 444

14.1 Surface Tension and Surface Energy 445

14.2 Wetting and Contact Angle 446

14.3 The Measurement of Surface Tension 447

14.4 Interfacial Tension 448

14.5 Forces Due to Curved Surfaces 449

14.6 Some Example of Surface-Force Effects 451

14.7 Summary 455

PART IV TWO- AND THREE-DIMENSIONAL

FLUID MECHANICS 461

Chapter 15 Two- and Three-Dimensional Fluid Mechanics 463

15.1 Notation for Multidimensional Flows 464

15.2 Mass Balances for Multidimensional Flows 464

15.3 Momentum Balances for Multidimensional Flows 466

CONTENTS XÎii

15.4 The Navier-Stokes Equations 469

15.4.1 Three Examples of Laminar Flow in a Circular Tube

15.5 What Good Is All of This? 477

15.6 Euler’s Equation, Bernoulli’s Equation Again 478

15.7 Transport Equations 479

15.8 Summary 480

Chapter 16 Potential Flow 485

16.1 The History of Potential Flow and Boundary Layer 485

16.2 Streamlines 487

16.3 Potential Flow 488

16.4 Irrotational Flow 496

16.5 Stream Function 500

16.6 Bernoulli’s Equation for Two-Dimensional, Perfect-Fluid,

Irrotational Rows 504

16.7 Row around a Cylinder 505

16.8 Separation 508

16.9 Summary 510

Chapter 17 The Boundary Layer 514

17.1 Prandtl’s Boundary-Layer Equations 514

17.2 The Steady-Row, Laminar Boundary Layer on a Rat Plate

Parallel to the Row 515

17.2.1 Boundary Layer Thickness / 17.2.2 Boundary Layer

Drag / 17.2.3 Displacement Thickness / 17.2.4 Momentum

Thickness

17.3 Turbulent Boundary Layers 524

17.4 Turbulent Flow in Pipes 525

17.5 The Steady, Turbulent Boundary Layer on a Rat Plate 529

17.6 The Successes of Boundary-Layer Theory 531

17.7 Summary 533

Chapter 18 IXirbulence 539

18.1 Nonmathematical Observations and Descriptions of Turbulence 539

18.1.1 Decay o f Turbulence / 18.1.2 Production o f Turbulence /

18.1.3 Free and Confined Turbulent Flows / 18.1.4 Turbulence

in the Atmosphere and the Oceans / 18.1.5 Three-Dimensional

Turbulence / 18.1.6 The Size of Eddies

18.2 Why Study Turbulence? 543

18.3 Turbulence Measurements and Definitions 544

18.4 The Experimental and Mathematical Descriptions of Turbulent Rows 546

18.4.1 Turbulent Intensity / 18.4.2 Turbulent ke /

18.4.3 Scale of Turbulence / 18.4.4 Correlation Coefficient /

18.4.5 Spectrum of Turbulence