Mass transfer operations for the practic

Mass Transfer Operations
for the Practicing
Engineer


Mass Transfer Operations
for the Practicing
Engineer
Louis Theodore
Francesco Ricci


Copyright # 2010 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by
any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted
under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written
permission of the publisher, or authorization through payment of the appropriate per-copy fee to the
Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978)
750-4470, or on the web at www.copyright.com. Requests to the publisher for permission should be
addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030,
(201) 748-6011, fax (201) 748-6008, or online at />Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in
preparing this book, they make no representations or warranties with respect to the accuracy or completeness
of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for
a particular purpose. No warranty may be created or extended by sales representatives or written sales
materials. The advice and strategies contained herein may not be suitable for your situation. You should
consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of
profit or any other commercial damages, including but not limited to special, incidental, consequential, or
other damages.
For general information on our other products and services or for technical support, please contact our

Customer Care Department within the United States at (800) 762-2974, outside the United States at (317)
572-3993 or fax (317) 572-4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may
not be available in electronic formats. For more information about Wiley products, visit our web site at
www.wiley.com.
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
530.40 7501512—dc22
2010013924
Printed in the United States of America
10 9

8 7

6 5

4 3 2

1


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
References

3

7

10

3. Basic Calculations

11

Introduction
11
Units and Dimensions
11
Conversion of Units
15
The Gravitational Constant gc
17
Significant Figures and Scientific Notation
References
18
4. Process Variables
Introduction
19
Temperature
20
Pressure
22
Moles and Molecular Weight
Mass, Volume, and Density
Viscosity
25
Reynolds Number
28
pH
29
Vapor Pressure
31
Ideal Gas Law
31

References
35

17

19

23
25

vii


viii

Contents

5. Equilibrium vs Rate Considerations
Introduction
37
Equilibrium
37
Rate
38
Chemical Reactions
References
40

37

39

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
Vapor – Solid Equilibrium
64
Liquid – Solid Equilibrium
68
References
69

61

7. Rate Principles

71

Introduction
71
The Operating Line
Fick’s Law
73
Diffusion in Gases
Diffusion in Liquids

72
75
79

Mass Transfer Coefficients

80

Individual Mass Transfer Coefficients
81
Equimolar Counterdiffusion
83
Diffusion of Component A Through Non-diffusing Component B

Overall Mass Transfer Coefficients

87

Equimolar Counterdiffusion and/or Diffusion in Dilute Solutions
Gas Phase Resistance Controlling
89
Liquid Phase Resistance Controlling

89
Experimental Mass Transfer Coefficients
90

References

84

88

93

Part Two Applications: Component and Phase Separation Processes
8. Introduction to Mass Transfer Operations
Introduction

97

97


Contents

Classification of Mass Transfer Operations
Contact of Immiscible Phases
98
Miscible Phases Separated by a Membrane
Direct Contact of Miscible Phases
102

Mass Transfer Equipment

ix

97
101

102

Distillation
103
Absorption
104
Adsorption
104
Extraction
104
Humidification and Drying
105
Other Mass Transfer Unit Operations
The Selection Decision
106

105

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
Introduction
187
Description of Equipment
Packed Columns
Plate Columns

187
189

189
196

Design and Performance Equations—Packed Columns
Liquid Rate
200
Column Diameter
207
Column Height
210

Pressure Drop
224

200


x

Contents

Design and Performance Equations—Plate Columns
Stripping
235
Packed vs Plate Tower Comparison
241
Summary of Key Equations
242
References
243
11. Adsorption

227

245

Introduction
245
Adsorption Classification
Activated Carbon
Activated Alumina

Silica Gel
249
Molecular Sieves

247

248
248
249

Adsorption Equilibria
Freundlich Equation
Langmuir Isotherms

250
253
253

Description of Equipment
257
Design and Performance Equations
Regeneration
283
References
291

264

12. Liquid – Liquid and Solid – Liquid Extraction
Introduction

293
Liquid – Liquid Extraction

293

294

The Extraction Process
294
Equipment
295
Solvent Selection
298
Equilibrium
300
Graphical Procedures
301
Analytical Procedures
304

Solid – Liquid Extraction (Leaching)
Process Variables
313
Equipment and Operation
315
Design and Predictive Equations

References

312

317

325

13. Humidification and Drying
Introduction
327
Psychrometry and the Psychrometric Chart
Humidification
339

327
327


Contents
Equipment
341
Describing Equations

Drying

xi

343

347

Rotary Dryers

Spray Dryers

References

352
361

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

Ultrafiltration

420

Describing Equations

Microfiltration

421

427

Describing Equations

Gas Permeation

428

432

Describing Equations

References

414

433

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
Venturi Scrubbers
457
Baghouses
461

454

xii

Contents

Gas– Liquid (G– L) Equipment
Liquid – Solid (L – S) Equipment

465
467

Sedimentation
467
Centrifugation
471
Flotation
472

Liquid – Liquid (L – L) Equipment
475
Solid – Solid (S – S) Equipment
477
High-Gradient Magnetic Separation
Solidification
477

References

Part Three

477

479

Other Topics

17. Other and Novel Separation 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
Introduction
489
The Need for Economic Analyses
Definitions
491

489
489

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


Contents

xiii

Exact Rate of Return
495
Bonds
496
Incremental Cost
496

Principles of Accounting
Applications
499
References
511

496

19. Numerical Methods
Introduction
Applications
References

513

513
514
531

20. Open-Ended Problems

533

Introduction
533
Developing Students’ Power of Critical Thinking
Creativity
534
Brainstorming
536
Inquiring Minds
536
Failure, Uncertainty, Success: Are They
537
Related?
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
Future Trends
559
Applications
561
References
563

557

22. Environmental Management and Safety Issues
Introduction
565
Environmental Issues of Concern
Health Risk Assessment
568
Risk Evaluation Process for Health

534

566
570

565


xiv

Contents

Hazard Risk Assessment

571

Risk Evaluation Process for Accidents

Applications
References

572

574
591

Appendix
Appendix A. Units
A.1

A.2
A.3
A.4
A.5
A.6
A.7

The Metric System
595
The SI System
597
Seven Base Units
597
Two Supplementary Units
598
SI Multiples and Prefixes
599
Conversion Constants (SI)
599
Selected Common Abbreviations

595

603

Appendix B. Miscellaneous Tables

605

Appendix C. Steam Tables

615

Index

623


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” undergraduate course offered at Manhattan College; L. Theodore and J. Barden, “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 himself/herself approaching advanced texts, engineering literature and industrial applications (even unique ones) with more confidence. We strongly believe that, while
understanding the basic concepts is of paramount importance, this knowledge may
xv


xvi

Preface

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 individuals 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.

April 2010

FRANCESCO RICCI
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.


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 transfer operations
is not treated in any required undergraduate Manhattan College offering. The Manhattan
approach is to place more emphasis on real-world and design applications. However,
microscopic approach material is available in the literature, as noted in the ensuing chapters. 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 transfer 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
Copyright # 2010 John Wiley & Sons, Inc.

1


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 principles 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
Copyright # 2010 John Wiley & Sons, Inc.

3

4

Chapter 1 History of Chemical Engineering and Mass Transfer Operations

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 Chemical 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 committee 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


History of Chemical Engineering and Mass Transfer Operations

5

“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 education/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. THEODORE, “Heat Transfer for the Practicing Engineer,” John Wiley & Sons, Hoboken, NJ, 2011
(in preparation).
3. N. SERINO, “2005 Chemical Engineering 125th Year Anniversary Calendar,” term project, submitted to
L. Theodore, 2004.
4. R. BIRD, 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.

6

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 fouryear Chemical
Engineering
program in the
United States

1888

Pennsylvania
University
begins its
Chemical
Engineering
curriculum

1892

Figure 1.1 Chemical engineering time line.(3)

George Davis
proposes a
“Society of
Chemical
Engineers” in
England

1880

Tulane
begins its
Chemical
Engineering
curriculum

1894

The
American
Institute of
Chemical
Engineers
is formed

1908

William H. Walker
and Warren K.
Lewis, two
prominent
professors,
establish a
School of
Chemical
Engineering
Practice

1916

The
Massachusetts
Institute of
Technology starts
an Independent
Department of
Chemical
Engineering

1920

Manhattan
College begins
its Chemical
Engineering
curriculum.

Adoption of the
R. Bird et al.
“Transport
Phenomena”
approach(4)

1960

ABET; stresses
once again the
emphasis on the
practical/design
approach

1990

Unit Operations
vs
Transport
Phenomena;
the profession
at a crossroad

Today


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 engineering, society’s needs have changed tremendously and so has
chemical engineering.
The teaching of Unit Operations at the undergraduate level has remained relatively 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 understanding of both fundamental physical and chemical processes. However, in terms
Mass Transfer Operations for the Practicing Engineer. By Louis Theodore and Francesco Ricci

Copyright # 2010 John Wiley & Sons, Inc.

7


8

Chapter 2 Transport Phenomena vs Unit Operations Approach

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:
9
9 8
9 8
9 8
8
< quantity = < quantity = < quantity = < quantity =
þ generated in ¼ accumulated
À
out of
into
;
; :
; :
; :
:
in system
system
system
system

(2:1)

This equation may also be written on a time rate basis:
9
9 8
9 8
9 8
8
rate

rate
=
= <
< rate = < rate = <
À out of þ generated in ¼ accumulated
into
;
; :
; :
; :
:
in system
system
system
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


Transport Phenomena vs Unit Operations Approach

1

9

2
Fluid out

Fluid in

1

2

Figure 2.1 Flow system.

(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 concerning 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 compared 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 practicing 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 conservation 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, cylindrical, 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)


10

Chapter 2 Transport Phenomena vs Unit Operations Approach

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 overall 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. THEODORE, “Heat Transfer for the Practicing Engineer,” John Wiley & Sons, Hoboken, NJ, 2011
(in preparation).
3. P. ABULENCIA and L. THEODORE, “Fluid Flow for the Practicing Engineer,” John Wiley & Sons, Hoboken,
NJ, 2009.
4. L. THEODORE, “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

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, gc
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 engineering 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 convenient 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 engineering 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
Copyright # 2010 John Wiley & Sons, Inc.

11


12

meter
centimeter
foot

foot

foot

American Engineering

British Engineering

Length

SI
egs
fps

System

Table 3.1 Common Systems of Units

second

second

second
second
second

Time

slug

pound

kilogram
gram
pound

Mass

pound (force)

pound (force)

Newton
dyne
poundal

Force

British thermal unit,
horsepower . hour
British thermal unit,
foot pound (force)

Joule
erg, Joule, or calorie
foot poundal

Energy

Kelvin, degree Celsius
Kelvin, degree Celsius
degree Rankine, degree
Fahrenheit
degree Rankine, degree
Fahrenheit
degree Rankine, degree
Fahrenheit

Temperature