Mass Transfer Operations for the Practicing Engineer

Mass Transfer Operations

for the Practicing

Engineer

Louis Theodore

Francesco Ricci

Mass Transfer Operations

for the Practicing

Engineer

Mass Transfer Operations

for the Practicing

Engineer

Louis Theodore

Francesco Ricci

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Theodore, Louis.

Mass transfer operations for the practicing engineer / Louis Theodore, Francesco Ricci.

p. cm.

Includes Index.

ISBN 978-0-470-57758-5 (hardback)

1. Engineering mathematics. 2. Mass transfer. I. Ricci, Francesco. II. Title.

TA331.T476 2010

530.4

7501512—dc22 2010013924

Printed in the United States of America

10987654321

To Ann Cadigan and Meg Norris:

for putting up with me (LT)

and

To my mother Laura, my father Joseph,

and my brother Joseph Jr:

for reasons which need not be spoken (FR)

Contents

Preface xv

Part One Introduction

1. History of Chemical Engineering and Mass Transfer Operations

References 5

2. Transport Phenomena vs Unit Operations Approach 7

References 10

3. Basic Calculations 11

Introduction 11

Units and Dimensions 11

Conversion of Units 15

The Gravitational Constant g

Signiﬁcant Figures and Scientiﬁc Notation 17

References 18

4. Process Variables 19

Introduction 19

Temperature 20

Pressure 22

Moles and Molecular Weight 23

Mass, Volume, and Density 25

Viscosity 25

Reynolds Number 28

pH 29

Vapor Pressure 31

Ideal Gas Law 31

References 35

vii

5. Equilibrium vs Rate Considerations 37

Introduction 37

Equilibrium 37

Rate 38

Chemical Reactions 39

References 40

6. Phase Equilibrium Principles 41

Introduction 41

Gibb’s Phase Rule 44

Raoult’s Law 45

Henry’s Law 53

Raoult’s Law vs Henry’s Law 59

Vapor–Liquid Equilibrium in Nonideal Solutions 61

Vapor–Solid Equilibrium 64

Liquid– Solid Equilibrium 68

References 69

7. Rate Principles 71

Introduction 71

The Operating Line 72

Fick’s Law 73

Diffusion in Gases 75

Diffusion in Liquids 79

Mass Transfer Coefﬁcients 80

Individual Mass Transfer Coefﬁcients 81

Equimolar Counterdiffusion 83

Diffusion of Component A Through Non-diffusing Component B 84

Overall Mass Transfer Coefﬁcients 87

Equimolar Counterdiffusion and/or Diffusion in Dilute Solutions 88

Gas Phase Resistance Controlling 89

Liquid Phase Resistance Controlling 89

Experimental Mass Transfer Coefﬁcients 90

References 93

Part Two Applications: Component and Phase Separation Processes

8. Introduction to Mass Transfe r Operations

Introduction 97

viii Contents

Classiﬁcation of Mass Transfer Operations 97

Contact of Immiscible Phases 98

Miscible Phases Separated by a Membrane 101

Direct Contact of Miscible Phases 102

Mass Transfer Equipment 102

Distillation 103

Absorption 104

Adsorption 104

Extraction 104

Humidiﬁcation and Drying 105

Other Mass Transfer Unit Operations 105

The Selection Decision 106

Characteristics of Mass Transfer Operations 107

Unsteady-State vs Steady-State Operation 108

Flow Pattern 109

Stagewise vs Continuous Operation 116

References 117

9. Distillation 119

Introduction 119

Flash Distillation 120

Batch Distillation 127

Continuous Distillation with Reﬂux 133

Equipment and Operation 133

Equilibrium Considerations 140

Binary Distillation Design: McCabe–Thiele Graphical Method 142

Multicomponent Distillation: Fenske–Underwood –Gilliland (FUG)

Method 161

Packed Column Distillation 184

References 185

10. Absorption and Stripping 187

Introduction 187

Description of Equipment 189

Packed Columns 189

Plate Columns 196

Design and Performance Equations—Packed Columns 200

Liquid Rate 200

Column Diameter 207

Column Height 210

Pressure Drop 224

Contents

Design and Performance Equations—Plate Columns 227

Stripping 235

Packed vs Plate Tower Comparison 241

Summary of Key Equations 242

References 243

11. Adsorption 245

Introduction 245

Adsorption Classiﬁcation 247

Activated Carbon 248

Activated Alumina 248

Silica Gel 249

Molecular Sieves 249

Adsorption Equilibria 250

Freundlich Equation 253

Langmuir Isotherms 253

Description of Equipment 257

Design and Performance Equations 264

Regeneration 283

References 291

12. Liquid– Liquid and Solid– Liquid Extraction 293

Introduction 293

Liquid– Liquid Extraction 294

The Extraction Process 294

Equipment 295

Solvent Selection 298

Equilibrium 300

Graphical Procedures 301

Analytical Procedures 304

Solid– Liquid Extraction (Leaching) 312

Process Variables 313

Equipment and Operation 315

Design and Predictive Equations 317

References 325

13. Humidiﬁcation and Drying 327

Introduction 327

Psychrometry and the Psychrometric Chart 327

Humidiﬁcation 339

x Contents

Equipment 341

Describing Equations 343

Drying 347

Rotary Dryers 352

Spray Dryers 361

References 369

14. Crystallization 371

Introduction 371

Phase Diagrams 373

The Crystallization Process 379

Crystal Physical Characteristics 382

Equipment 391

Describing Equations 393

Design Considerations 397

References 404

15. Membrane Separation Processes 407

Introduction 407

Reverse Osmosis 408

Describing Equations 414

Ultraﬁltration 420

Describing Equations 421

Microﬁltration 427

Describing Equations 428

Gas Permeation 432

Describing Equations 433

References 437

16. Phase Separation Equipment 439

Introduction 439

Fluid– Particle Dynamics 442

Gas– Solid (G–S) Equipment 446

Gravity Settlers 447

Cyclones 449

Electrostatic Precipitators 454

Venturi Scrubbers 457

Baghouses 461

Contents

Gas– Liquid (G–L) Equipment 465

Liquid– Solid (L–S) Equipment 467

Sedimentation 467

Centrifugation 471

Flotation 472

Liquid– Liquid (L–L) Equipment 475

Solid– Solid (S–S) Equipment 477

High-Gradient Magnetic Separation 477

Solidiﬁcation 477

References 479

Part Three Other Topics

17. Other and Novel Sep aration Processes

483

Freeze Crystallization 484

Ion Exchange 484

Liquid Ion Exchange 484

Resin Adsorption 485

Evaporation 485

Foam Fractionation 486

Dissociation Extraction 486

Electrophoresis 486

Vibrating Screens 487

References 488

18. Economics and Finance 489

Introduction 489

The Need for Economic Analyses 489

Deﬁnitions 491

Simple Interest 491

Compound Interest 491

Present Worth 492

Evaluation of Sums of Money 492

Depreciation 493

Fabricated Equipment Cost Index 493

Capital Recovery Factor 493

Present Net Worth 494

Perpetual Life 494

Break-Even Point 495

Approximate Rate of Return 495

xii Contents

Exact Rate of Return 495

Bonds 496

Incremental Cost 496

Principles of Accounting 496

Applications 499

References 511

19. Numerical Methods 513

Introduction 513

Applications 514

References 531

20. Open-Ended Problems 533

Introduction 533

Developing Students’ Power of Critical Thinking 534

Creativity 534

Brainstorming 536

Inquiring Minds 536

Failure, Uncertainty, Success: Are They

Related?

537

Angels on a Pin 538

Applications 539

References 547

21. Ethics 549

Introduction 549

Teaching Ethics 550

Case Study Approach 551

Integrity 553

Moral Issues 554

Guardianship 556

Engineering and Environmental Ethics 557

Future Trends 559

Applications 561

References 563

22. Environmental Management and Safety Issues 565

Introduction 565

Environmental Issues of Concern 566

Health Risk Assessment 568

Risk Evaluation Process for Health 570

Contents

xiii

Hazard Risk Assessment 571

Risk Evaluation Process for Accidents 572

Applications 574

References 591

Appendix

Appendix A. Units

595

A.1 The Metric System 595

A.2 The SI System 597

A.3 Seven Base Units 597

A.4 Two Supplementary Units 598

A.5 SI Multiples and Preﬁxes 599

A.6 Conversion Constants (SI) 599

A.7 Selected Common Abbreviations 603

Appendix B. Miscellaneous Tables 605

Appendix C. Steam Tables 615

Index 623

xiv

Contents

Preface

Mass transfer is one of the basic tenets of chemical engineering, and contains many

practical concepts that are utilized in countless industrial applications. Therefore,

the authors considered writing a practical text. The text would hopefully serve as a

training tool for those individuals in academia and industry involved with mass

transfer operations. Although the literature is inundated with texts emphasizing

theory and theoretical derivations, the goal of this text is to present the subject from

a strictly pragmatic point-of-view.

The book is divided into three parts: Introduction, Applications, and Other

Topics. The ﬁrst part provides a series of chapters concerned with principles that

are required when solving most engineering problems, including those in mass transfer

operations. The second part deals exclusively with speciﬁc mass transfer operations

e.g., distillation, absorption and stripping, adsorption, and so on. The last part

provides an overview of ABET (Accreditation Board for Engineering and

Technology) related topics as they apply to mass transfer operations plus novel

mass transfer processes. An Appendix is also included. An outline of the topics

covered can be found in the Table of Contents.

The authors cannot claim sole authorship to all of the essay material and

illustrative examples in this text. The present book has evolved from a host of sources,

including: notes, homework problems and exam problems prepared by several faculty

for a required one-semester, three-credit, “Principles III: Mass Transfer” undergradu-

ate course offered at Manhattan College; L. Theodore and J. Bard en, “Mass Transfer”,

A Theodore Tutorial, East Williston, NY, 1994; J. Reynolds, J. Jeris, and L. Theodore,

“Handbook of Chemical and Environmental Engineering Calculations,” John Wiley

& Sons, Hoboken, NJ, 2004, and J. Santoleri, J. Reynolds, and L. Theodore,

“Introduction to Hazardous Waste Management,” 2nd edition, John Wiley & Sons,

Hoboken, NJ, 2000. Although the bulk of the problems are original and/or taken

from sources that the authors have been directly involved with, every effort has

been made to acknowledge material drawn from other sources.

It is hoped that we have placed in the hands of academic, industrial, and

government personnel, a book that covers the principles and applications of mass

transfer in a thorough and clear manner. Upon completion of the text, the reader

should have acquired not only a working knowledge of the principles of mass transfer

operations, but also experience in their application; and, the reader should ﬁnd him-

self/herself approaching advanced texts, engineering literature and industrial appli-

cations (even unique ones) with more conﬁdence. We strongly believe that, while

understanding the basic concepts is of paramount importance, this knowledge may

be rendered virtually useless to an engineer if he/she cannot apply these concepts to

real-world situations. This is the essence of engineering.

Last, but not least, we believe that this modest work will help the majority of indi-

viduals working and/or studying in the ﬁeld of engineering to obtain a more complete

understanding of mass transfer operations. If you have come this far and read through

most of the Preface, you have more than just a passing interest in this subject. We

strongly suggest that you try this text; we think you will like it.

Our sincere thanks are extended to Dr. Paul Marnell at Manhattan College for his

invaluable help in contributing to Chapter 9 on Distillation and Chapter 14 on

Crystallization. Thanks are also due to Anne Mohan for her assistance in preparing

the ﬁrst draft of Chapter 13 (Humidiﬁcation and Drying) and to Brian Bermingham

and Min Feng Zheng for their assistance during the preparation of Chapter 12

(Liquid– Liquid and Solid– Liquid Extraction). Finally, Shannon O’Brien, Kathryn

Scherpf and Kimberly Valentine did an exceptional job in reviewing the manuscript

and page proofs.

RANCESCO RICCI

April 2010 LOUIS THEODORE

NOTE: An additional resource is available for this text. An accompanying website

contains over 200 additional problems and 15 hours of exams; solutions for the

problems and exams are available at www.wiley.com for those who adopt the book

for training and/or academic purposes.

xvi

Preface

Part One

Introduction

The purpose of this Part can be found in its title. The book itself offers the reader

the fundamentals of mass transfer operations with appropriate practical applications,

and serves as an introduction to the specialized and more sophisticated texts in this

area. The reader should realize that the contents are geared towards practitioners in

this ﬁeld, as well as students of science and engineering, not chemical engineers per

se. Simply put, topics of interest to all practicing engineers have been included.

Finally,it should also be noted that the microscopic approach of mass transferoperations

is not treated in any required undergraduateManhattan College offering. The Manhattan

approach is to place more emphasis on real-world and design applications. However,

microscopic approachmaterial is available in the literature, as noted in the ensuing chap-

ters. The decision on whether to include the material presented ultimately depends on

the reader and/or the approach and mentality of both the instructor and the institution.

A general discussion of the philosophy and the contents of this introductory

section follows.

Since the chapters in this Part provide an introduction and overview of mass trans-

fer operations, there is some duplication due to the nature of the overlapping nature of

overview/introductory material, particularly those dealing with principles. Part One

chapter contents include:

1 History of Chemical Engineering and Mass Transfer Operations

2 Transport Phenomena vs Unit Operations Approach

3 Basic Calculations

4 Process Variables

5 Equilibrium vs Rate Considerations

6 Phase Equilibrium Principles

7 Rate Principles

Topics covered in the ﬁrst two introductory chapters include a history of chemical

engineering and mass transfer operations, and a discussion of transport phenomena

vs unit operations. The remaining chapters are concerned with introductory

engineering principles. The next Part is concerned with describing and designing

the various mass transfer unit operations and equipment.

Mass Transfer Operations for the Practicing Engineer. By Louis Theodore and Francesco Ricci

Chapter 1

History of Chemical

Engineering and Mass

Transfer Operations

A discussion on the ﬁeld of chemical engineering is warranted before proceeding to

some speciﬁc details regarding mass transfer operations (MTO) and the contents of

this ﬁrst chapter. A reasonable question to ask is: What is Chemical Engineering?

An outdated, but once ofﬁcial deﬁnition provided by the American Institute of

Chemical Engineers is:

Chemical Engineering is that branch of engineering concerned with the development

and application of manufacturing processes in which chemical or certain physical

changes are involved. These processes may usually be resolved into a coordinated series

of unit physical “operations” (hence part of the name of the chapter and book) and chemical

processes. The work of the chemical engineer is concerned primarily with the design,

construction, and operation of equipment and plants in which these unit operations and

processes are applied. Chemistry, physics, and mathematics are the underlying sciences of

chemical engineering, and economics is its guide in practice.

The above deﬁnition was appropriate up until a few decades ago when the profession

branched out from the chemical industry. Today, that deﬁnition has changed.

Although it is still based on chemical fundamentals and physical principles, these prin-

ciples have been de-emphasized in order to allow for the expansion of the profession to

other areas (biotechnology, semiconductors, fuel cells, environment, etc.). These areas

include environmental management, health and safety, computer applications, and

economics and ﬁnance. This has led to many new deﬁnitions of chemical engineering,

several of which are either too speciﬁc or too vague. A deﬁnition proposed here is

simply that “Chemical Engineers solve problems”. Mass transfer is the one subject

area that somewhat uniquely falls in the domain of the chemical engineer. It is

often presented after ﬂuid ﬂow

(1)

and heat transfer,

(2)

since ﬂuids are involved as

well as heat transfer and heat effects can become important in any of the mass transfer

unit operations.

Mass Transfer Operations for the Practicing Engineer. By Louis Theodore and Francesco Ricci

A classical approach to chemical engineering education, which is still used

today, has been to develop problem solving skills through the study of several

topics. One of the topics that has withstood the test of time is mass transfer operations;

the area that this book is concerned with. In many mass transfer operations, one

component of a ﬂuid phase is transferred to another phase because the component

is more soluble in the latter phase. The resulting distribution of components between

phases depends upon the equilibrium of the system. Mass transfer operations may also

be used to separate products (and reactants) and may be used to remove byproducts

or impurities to obtain highly pure products. Finally, it can be used to purify raw

materials.

Although the chemical engineering profession is usually thought to have

originated shortly before 1900, many of the processes associated with this discipline

were developed in antiquity. For example, ﬁltration operations were carried out

5000 years ago by the Egyptians. MTOs such as crystallization, precipitation, and

distillation soon followed. During this period, other MTOs evolved from a mixture

of craft, mysticism, incorrect theories, and empirical guesses.

In a very real sense, the chemical industry dates back to prehistoric times when

people ﬁrst attempted to control and modify their environment. The chemical industry

developed as did any other trade or craft. With little knowledge of chemical science

and no means of chemical analysis, the earliest chemical “engineers” had to rely on

previous art and superstition. As one would imagine, progress was slow. This changed

with time. The chemical industry in the world today is a sprawling complex of

raw-material sources, manufacturing plants, and distribution facilities which supply

society with thousands of chemical products, most of which were unknown over a

century ago. In the latter half of the nineteenth century, an increased demand arose

for engineers trained in the fundamentals of chemical processes. This demand was

ultimately met by chemical engineers.

The ﬁrst attempt to organize the principles of chemical processing and to clarify

the professional area of chemical engineering was made in England by George E.

Davis. In 1880, he organized a Society of Chemical Engineers and gave a series of

lectures in 1887 which were later expanded and published in 1901 as A Handbook

of Che mical Engineering. In 1888, the ﬁrst course in chemical engineering in the

United States was organized at the Massachusetts Institute of Technology by

Lewis M. Norton, a professor of industrial chemistry. The course applied aspects of

chemistry and mechanical engineering to chemical processes.

(3)

Chemical engineering began to gain professional acceptance in the early years of

the twentieth century. The American Chemical Society had been founded in 1876 and,

in 1908, it organized a Division of Industrial Chemists and Chemical Engineers while

authorizing the publication of the Journal of Industrial and Engineering Chemistry.

Also in 1908, a group of prominent chemical engineers met in Philadelphia and

founded the American Institute of Chemical Engineers.

(3)

The mold for what is now called chemical engineering was fashioned at the 1922

meeting of the American Institute of Chemical Engineers when A. D. Little’s commit-

tee presented its report on chemical engineering education. The 1922 meeting marked

the ofﬁcial endorsement of the unit operations concept and saw the approval of a

Chapter 1 History of Chemical Engineering and Mass Transfer Operations

“declaration of independence” for the profession.

(3)

A key component of this report

included the following:

Any chemical process, on whatever scale conducted, may be resolved into a

coordinated series of what may be termed “unit operations,” as pulverizing, mixing,

heating, roasting, absorbing, precipitation, crystallizing, ﬁltering, dissolving, and so on.

The number of these basic unit operations is not very large and relatively few of them

are involved in any particular process...An ability to cope broadly and adequately with the

demands of this (the chemical engineer’s) profession can be attained only

through the analysis of processes into the unit actions as they are carried out on the

commercial scale under the conditions imposed by practice.

It also went on to state that:

Chemical Engineering, as distinguished from the aggregate number of subjects

comprised in courses of that name, is not a composite of chemistry and mechanical and

civil engineering, but is itself a branch of engineering...

A time line diagram of the history of chemical engineering between the

profession’s founding to the present day is shown in Figure 1.1.

(3)

As can be seen

from the time line, the profession has reached a crossroads regarding the future edu-

cation/curriculum for chemical engineers. This is highlighted by the differences of

Transport Phenomena and Unit Operations, a topic that is treated in the next chapter.

REFERENCES

1. P. ABULENCIA and L. THEODORE,“Fluid Flow for the Practicing Engineer,” John Wiley & Sons, Hoboken,

NJ, 2009.

2. L. T

HEODORE,“Heat Transfer for the Practicing Engineer,” John Wiley & Sons, Hoboken, NJ, 2011

(in preparation).

3. N. S

ERINO, “2005 Chemical Engineering 125th Year Anniversary Calendar,” term project, submitted to

L. Theodore, 2004.

4. R. B

IRD,W.STEWART, and E. LIGHTFOOT,“Transport Phenomena,” 2nd edition, John Wiley & Sons,

Hoboken, NJ, 2002.

NOTE: Additional problems are available for all readers at www.wiley.com. Follow

links for this title. These problems may be used for additional review, homework,

and/or exam purposes.

History of Chemical Engineering and Mass Transfer Operations 5

1880

George Davis

proposes a

“Society of

Chemical

Engineers” in

England

George Davis

provides the blueprint

for a new profession

with 12 lectures on

Chemical Engineering

in Manchester,

England

The

Massachusetts

Institute of

Technology

begins “Course

X”, the first four-

year Chemical

Engineering

program in the

United States

The

Massachusetts

Institute of

Technology starts

an Independent

Department of

Chemical

Engineering

Pennsylvania

University

begins its

Chemical

Engineering

curriculum

Tulane

begins its

Chemical

Engineering

curriculum

Manhattan

College begins

its Chemical

Engineering

curriculum.

Adoption of the

R. Bird et al.

“Transport

Phenomena”

approach

(4)

ABET; stresses

once again the

emphasis on the

practical/design

approach

Unit Operations

Transport

Phenomena;

the profession

at a crossroad

William H. Walker

and Warren K.

Lewis, two

prominent

professors,

establish a

School of

Chemical

Engineering

Practice

The

American

Institute of

Chemical

Engineers

is formed

1888 1892 1894 1908 1916 1920 1960 1990 Today

Figure 1.1 Chemical engineering time line.

(3)

Chapter 2

Transport Phenomena vs Unit

Operations Approach

The history of Unit Operations is interesting. As indicated in the previous chapter,

chemical engineering courses were originally based on the study of unit processes

and/or industrial technologies. However, it soon became apparent that the changes

produced in equipment from different industries were similar in nature, i.e., there

was a commonality in the mass transfer operations in the petroleum industry as with

the utility industry. These similar operations became known as Unit Operations.

This approach to chemical engineering was promulgated in the Little report discussed

earlier, and has, with varying degrees and emphasis, dominated the profession to

this day.

The Unit Operations approach was adopted by the profession soon after its

inception. During the 130 years (since 1880) that the profession has been in existence

as a branch of enginee ring, society’s needs have changed tremendously and so has

chemical engineering.

The teaching of Unit Operations at the undergraduate level has remained rela-

tively unchanged since the publication of several early- to mid-1900 texts. However,

by the middle of the 20th century, there was a slow movement from the unit operation

concept to a more theoretical treatment called transport phenomena or, more simply,

engineering science. The focal point of this science is the rigorous mathematical

description of all physical rate processes in terms of mass, heat, or momentum crossing

phase boundaries. This approach took hold of the education/curriculum of the

profession with the publication of the ﬁrst edition of the Bird et al. book.

(1)

Some,

including both authors of this text, feel that this concept set the profession back several

decades since graduating chemical engineers, in terms of training, were more applied

physicists than traditional chemical engineers. There has fortunately been a return to

the traditional approach to chemical engineering, primarily as a result of the efforts of

ABET (Accreditation Board for Engineering and Technology). Detractors to this

pragmatic approach argue that this type of theoretical education experience provides

answers to what and how, but not necessarily why, i.e., it provides a greater under-

standing of both fundamental physical and chemical processes. However, in terms

Mass Transfer Operations for the Practicing Engineer. By Louis Theodore and Francesco Ricci

of reality, nearly all chemical engineers are now presently involved with the why

questions. Therefore, material normally covered here has been replaced, in part, with

a new emphasis on solving design and open-ended problems; this approach is

emphasized in this text.

The following paragraphs attempt to qualitatively describe the differences

between the above two approaches. Both deal with the transfer of certain quantities

(momentum, energy, and mass) from one point in a system to another. There are

three basic transport mechanisms which can potentially be involved in a process.

They are:

1 Radiation

2 Convection

3 Molecular Diffusion

The ﬁrst mechanism, radiative transfer, arises as a result of wave motion and is not

considered, since it may be justiﬁably neglected in most engineering applications.

The second mechanism, convective transfer, occurs simply because of bulk motion.

The ﬁnal mechanism, molecular diffusion, can be deﬁned as the transport mechanism

arising as a result of gradients. For example, momentum is transferred in the presence

of a velocity gradient; energy in the form of heat is transferred because of a temperature

gradient; and, mass is transferred in the presence of a concentration gradient. These

molecular diffusion effects are described by phenomenological laws.

(1)

Momentum, energy, and mass are all conserved. As such, each quantity obeys the

conservation law within a system:

quantity

into

system

;



quantity

out of

system

;

quantity

generated in

system

;

quantity

accumulated

in system

;

(2:1)

This equation may also be written on a time rate basis:

rate

into

system

;



rate

out of

system

;

rate

generated in

system

;

rate

accumulated

in system

;

(2:2)

The conservation law may be applied at the macroscopic, microscopic, or

molecular level.

One can best illustrate the differences in these methods with an example. Consider

a system in which a ﬂuid is ﬂowing through a cylindrical tube (see Fig. 2.1) and deﬁne

the system as the ﬂuid contained within the tube between points 1 and 2 at any time. If

one is interested in determining changes occurring at the inlet and outlet of a system,

the conservation law is applied on a “macroscopic” level to the entire system. The

resultant equation (usually algebraic) describes the overall changes occurring to the

system (or equipment). This approach is usually applied in the Unit Operation

Chapter 2 Transport Phenomena vs Unit Operations Approach

(or its equivalent) courses, an approach which is highlighted in this text and its

two companion texts.

(2,3)

In the microscopic/transport phenomena approach, detailed information con-

cerning the behavior within a system is required; this is occasionally requested of

and by the engineer. The conservation law is then applied to a differential element

within the system that is large compared to an individual molecule, but small com-

pared to the entire system. The resulting differential equation is then expanded via

an integration in order to describe the behavior of the entire system.

The molecular approach involves the application of the conservation laws to

individual molecules. This leads to a study of statistical and quantum mechanics—

both of which are beyond the scope of this text. In any case, the description at the

molecular level is of little value to the practicing engineer. However, the statistical

averaging of molecular quantities in either a differential or ﬁnite element within a

system can lead to a more meaningful description of the behavior of a system.

Both the microscopic and molecular approaches shed light on the physical

reasons for the observed macroscopic phenomena. Ultimately, however, for the practi-

cing engineer, these approaches may be valid but are akin to attempting to kill a ﬂy

with a machine gun. Developing and solving these equations (in spite of the advent

of computer software packages) is typically not worth the trouble.

Traditionally, the applied mathematician has developed differential equations

describing the detailed behavior of systems by applying the appropriate conser-

vation law to a differential element or shell within the system. Equations were derived

with each new application. The engineer later removed the need for these tedious

and error-prone derivations by developing a general set of equations that could

be used to describe systems. These have come to be referred to by many as the

transport equations. In recent years, the trend toward expressing these equations in

vector form has gained momentum (no pun intended). However, the shell-balance

approach has been retained in most texts where the equations are presented in

componential form, i.e., in three particular coordinate systems—rectangular, cylindri-

cal, and spherical. The componential terms can be “lumped” together to produce a

more concise equation in vector form. The vector equation can be, in turn, re-expanded

into other coordinate systems. This information is available in the literature.

(1,4)

Fluid in

Fluid out

Figure 2.1 Flow system.

Transport Phenomena vs Unit Operations Approach 9

ILLUSTRATIVE EXAMPLE 2.1

Explain why the practicing engineer/scientist invariably employs the macroscopic approach in

the solution of real world problems.

SOLUTION: The macroscopic approach involves examining the relationship between

changes occurring at the inlet and the outlet of a system. This approach attempts to identify

and solve problems found in the real world, and is more straightforward than and preferable

to the more involved microscopic approach. The microscopic approach, which requires an

understanding of all internal variations taking place within the system that can lead up to an over-

all system result, simply may not be necessary. B

REFERENCES

1. R. BIRD,W.STEWART, and E. LIGHTFOOT,“Transport Phenomena,” John Wiley & Sons, Hoboken,

NJ, 1960.

2. L. T

HEODORE,“Heat Transfer for the Practicing Engineer,” John Wiley & Sons, Hoboken, NJ, 2011

(in preparation).

3. P. A

BULENCIA and L. THEODORE,“Fluid Flow for the Practicing Engineer,” John Wiley & Sons, Hoboken,

NJ, 2009.

4. L. T

HEODORE,“Introduction to Transport Phenomena,” International Textbook Co., Scranton, PA, 1970.

NOTE: Additional problems are available for all readers at www.wiley.com. Follow

links for this title. These problems may be used for additional review, homework,

and/or exam purposes.

Chapter 2 Transport Phenomena vs Unit Operations Approach

Chapter 3

Basic Calculations

INTRODUCTION

This chapter provides a review of basic calculations and the fundamentals of

measurement. Four topics receive treatment:

1 Units and Dimensions

2 Conversion of Units

3 The Gravitational Constant, g

4 Signiﬁcant Figures and Scientiﬁc Notation

The reader is directed to the literature in the Reference section of this chapter

(1 – 3)

for

additional information on these four topics.

UNITS AND DIMENSIONS

The units used in this text are consistent with those adopted by the engineering

profession in the United States. For engineering work, SI (Syste

me International)

and English units are most often employed. In the United States, the English engineer-

ing units are generally used, although efforts are still underway to obtain universal

adoption of SI units for all engineering and science applications. The SI units have

the advantage of being based on the decimal system, which allows for more con-

venient conversion of units within the system. There are other systems of units;

some of the more common of these are shown in Table 3.1. Although English engin-

eering units will primarily be used, Tables 3.2 and 3.3 present units for both the

English and SI systems, respectively. Some of the more common preﬁxes for SI

units are given in Table 3.4 (see also Appendix A.5) and the decimal equivalents

are provided in Table 3.5. Conversion factors between SI and English units and

additional details on the SI system are provided in Appendices A and B.

Mass Transfer Operations for the Practicing Engineer. By Louis Theodore and Francesco Ricci

Table 3.1 Common Systems of Units

System Length Time Mass Force Energy Temperature

SI meter second kilogram Newton Joule Kelvin, degree Celsius

egs centimeter second gram dyne erg, Joule, or calorie Kelvin, degree Celsius

fps foot second pound poundal foot poundal degree Rankine, degree

Fahrenheit

American Engineering foot second pound pound (force) British thermal unit,

horsepower

hour

degree Rankine, degree

Fahrenheit

British Engineering foot second slug pound (force) British thermal unit,

foot pound (force)

degree Rankine, degree

Fahrenheit