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 530.407501512—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 3

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 gc 17 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 viii Contents

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 Transfer Operations 97 Introduction 97 Contents ix

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 x 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 Contents xi

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 xii 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 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 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 Contents xiii

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 xiv Contents

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 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 him- self/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.

FRANCESCO 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. 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 approachof masstransferoperations 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.

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 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 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

1880 1888 1892 1894 1908 1916 1920 1960 1990 Today

The Tulane George Davis Manhattan Unit Operations Massachusetts begins its William H. Walker ABET; stresses proposes a College begins vs Institute of Chemical and Warren K. once again the “Society of its Chemical Transport Technology Pennsylvania Engineering The Lewis, two The emphasis on the Chemical Engineering Phenomena; begins “Course University curriculum American prominent Massachusetts practical/design Engineers” in curriculum. the profession X”, the first four- begins its Institute of professors, Institute of approach England Adoption of the at a crossroad year Chemical Chemical Chemical establish a Technology starts R. Bird et al. Engineering Engineering Engineers School of an Independent “Transport program in the curriculum is formed Chemical Department of Phenomena” United States Engineering Chemical approach(4) Practice Engineering George Davis provides the blueprint for a new profession with 12 lectures on Chemical Engineering in Manchester, England

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 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: 8 9 8 9 8 9 8 9 < quantity = < quantity = < quantity = < quantity = : : into ; : out of ; þ : generated in ; ¼ : accumulated ; (2 1) system system system in system

This equation may also be written on a time rate basis: 8 9 8 9 8 9 8 9 < rate = < rate = < rate = < rate = : : into ; : out of ; þ : generated in ; ¼ : accumulated ; (2 2) system system system in system

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 9

Fluid in Fluid out

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 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 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 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 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

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, degree Rankine, degree horsepower . hour Fahrenheit British Engineering foot second slug pound (force) British thermal unit, degree Rankine, degree foot pound (force) Fahrenheit