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Third Edition
Engineering Fundarnerntals An Introduction to Engineering Saeed Moaveni M i n nesota State U n iversity,
Mankato THOTVtSON
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Tt{rotvtsoNEngineering Fundamentals: An Introdudion to Engineering, Third Edition by Saeed Moaveni
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Preface
CHANGES IN THE THIRD EDITION The third edition, consisting of 20 chapters, indudes a number of new additions that were incorporated in response to sugestions and requests made by professors and students using the second edition of the book The major changes include:
. A new section on Engineering Technology . Additional Ethics Case Studies . Additiond secdons on M,ffifAB " " " " "
Additional Professional Profiles Additiond Impromptu Designs Additional Engineering Marvels Case Studies Additional problems A new website to offer additional information for instructors and students including PowerPoint slides for each chapter
ORGANIZATIOl'I This book is organized into six parts andZ} chaprcrs; Each chapter begrns by stating its objectives and concludes by summarizing what the reader should have gained from studying that chapter. I have included enough m*erial for two semeterlong courses. The reason for this approach is to give tfre instructor sufficient materials and the fexibiliry to choose specific topics to meet his or her nee&. Relevant, weryday examples with which students can associate easily are provided in each chapter. Many of the problems at the conclusion of each chapter are handson, requiring the student to gather and analyze information. Moreover, information collection and proper utilization of that information are encour€ed in this book by asking studene to do a number of assignments that require information gathering by using the Internet as well as employing uaditional methods. Many of the problems at the end of each chapter require studena to make briefrepoms so that they learn that successfirl engineers need to have good written and oral communication skills. To emphasize t}re importance of teamwork in engineering and to encourage group panicipation, many of the assignment problems require group work; some require the panicipation of the entire class. The main parts. of the book are:
Pr.rrlcs
Part 0ne: EngineeringAn Exciting Profession In Pan One, consisting of Chapters I through
5, we
inuoduce the students to the engineering
profession, how to prepare for an exciting engineering career, the design process, engineering communication, and ethics. Chapter 1 provides a comprehensive inuoduction to the engineering profession and its branches. It introduces the students to what the engineering profession is and explains some of the common uaia of good engineers. Various engineering disciplines and engineering organizations are discussed. In Chapter 1, we also emphasize the fact that engineers are problem solvers. They have a good grasp of fundamental physical and chemical lan's and mathematics, and apply these fundamenel lars and principles to design, develop, test, and supervise the manufacnrre of millions of products and services. Through the use of examples, we also show that there are many satisfying and challenging jobs for engineers. W'e pointed out that atthough the activities of engineers can be quite varied, rhere are some personaliry uaits and work habia that
typifr most of today's successfi.rl engineers:
. Engineers are problem solvers. " Good engineers hane a firm grasp of the fundamental principles that can be used to solve many different problems. . Good engineers are analytical, detailed oriented, and creative. . Good engineers have a desire to be lifeJong learners. For example, they uke continuing edu. . " . . . "
cation classes, seminars, and workshops to stay abreast of new innovations and technologres. Good engineers have written and oral communication skills that equip them to work well with their colleagues and to convey their expenise to a wide range of clients. Good engineers have time management skills that enable tlem to work productively and efficiendy. Good engineers hane good "people skills" that allow them to interact and communicate effectively with various people in their organization. Engineers are required to write reports. These reports might be l""gthy, detailed, and technical, containing graphs, charts, and engineering dt*i"gs. Or the may take the form of a brief memorandum or an executive sutnmary. Engineers are adept at using computers in many &fferent ways to model and analyze various practical problems. Good engineers aaively panicipate in local and national disciplinespecific organizations by attending seminars, worlchops, and meetings. Many even make presentations at professional meetings. Engineers generally work in a team environment where they consult each other to solve complo< problems. Good inteqpersonal and communication skills have become increasingly im
portant now because of the global market. 1, we also enplain the difference berween an Engineer and an engineering technologist, and the difference in their career options. In Chaprcr 2, the transition from high school to college is explained in terms of the need to form good study habits and suggestions are provided on how to budget time effectively. In Chapter 3, an introduction to engineering desbn, 'We show that engineers, regardless of their teamwork, and standards and codes is provided. background, follow cerain steps when designing the products and services we use in our everyday lives. In Chapter 4, we explain that presentations are an integral pan of any engineering pro1ecr. Depending on the size of the project, presentations might be brief, lengthy, freguent,
In Chapter
Pnsrecr and may follow a certain format requiring calculations, graphs, charts, and engineering draltrings. In Chapter 4, various forms of engineering communication, including homework presentation, brief technical memos, progless reports, detailed technicd reports, and research papers are explained. A brief introduction to PowerPoint is also provided. In Chapter 5, engineering ethics is emphasized by noting that engineers design many products and provide many services that affect our quality of life and safety. Therefore, engineers must perform under a standard ofprofessional behavior that requires adherence to the highest principles ofethical conduct. A large number ofengineering ethics related case studies are also presented in this chapter.
Part Two: Engineering FundamentalsConcepts Every Engineer Should Know In Part Two, consisting of Chapters 6 duough 13, we focus on engineering fundamenals and introduce students to the basic principles and ph1'sical larvs that th.y *ill see over and over in some form or other during the next four years. Successfirl engneers hane a good grasp ofFundamentals, which they can use to understand and solve many different problems. These are concepts that wery engineer, regardless ofhis or her area ofspecialization, should know In these chapteis, we emphasize that, from 6ur obseryation of our surioundings, we hare learned that we need only a few physical quandties to flrlly describe events and our surroundings. These are length, time, mass, force, temperature, mole, and electric current. We also sr
plain that we need not only physical dimensions to describe our surroundings, but also some way to scale or divide these physical dimensions. For example, time is considered a physical dimension, but it can be divided into both small and large portions, such as seconds, minutes, hours, days, years, decades, centuries, and millennia'W'e discuss comrnon s;rctems of unin and emphasize that engineers must know how to conveft from one qystem of units to another and alwErs show the appropriare units that go with their calculations. \V'e also explain that the phlnical lars and formulas that engineers use are based on observations of our surroundings. W'e show that we use mathematics and basic physical quantities to express our observations, In these chapters, we also explain that ttrere are many engineering design variables that arg related to the fundamental dimensions (quantities). To become a successfi.rl engineer a student must first firlly understand these fundamental and related variables and the penaining governing larvs and formulas. Then it is imporant for the student to know how these variables are measured, approximated, calculated, or used in pracdce. Chapter 6 explains the role and imponance of fundamental dimension and units in analof engineering problems. Basic steps in the analysis of any engineering problem are disysis cussed in detail. Chapter 7 inroduces length and lengthrelated variables and explains their imponance in engineering work For example, the role of area in heat transfer, aerodynamics, load distribution, and stress analysis is discussed. Measurement of length, area, and volume, dong with numerical estimation (such as trapezoidal nrle) of these values, are presented. Chapter 8 conslders time arid timerelated engineering paiameters. Periods, ftequencies, linear and angular velocities and acceleradons, volumetric flow rates and fow of traffic are also discussed in Chapter 8.
Pnuecs Mass and massrelated parameters such density, specific weight, mass florv rate, and mass moment of inenia and their role in engineering analpis, are presented in Chapter 9. Chapter 10 covers the imporance of force and forcerelated parameters in engineering. 'W'hat is meant by force, pressure, modulus of elasticity, impulsive force (force acting over time), work (force acting over a distance) and moment (force acting at a distance) are discussed
in detail. Temperarure and temperaturerelated parameters are presented in Chapter 11. Concepts such as temperafure difference and heat transfer, specific heat, and thermal conductivity also are covered in Chapter 11. Chapter 12 considers topics such as direct and alternating current, elecuicity, basic circuits components, pov/er sources, and the tremendous role of electric motors in our wery day life. Chapter 13 presents energy and power and explains the distinction berween these two topics. The importance ofunderstandingwhat is meantbywork, energy, power'watm, horsepo$/er,
and efficiency is emphasized in Chapter 13.
Part Three: Computational Engineering ToolsUsing Available Software to Solve Engineering Problems 15, we inuoduce Microsoft Excel and MAI1AB computational tools that are used commonly by engineers to solve engineering probtwo lems. These compuationd tools are used to record, organize, analyze data using formule", and present the resulm ofan analysis in chart forms. MAILAB is also versatile enough that students cln use it to write their own programs to solve complor problems.
In Part Three, consisting of Chapters 14 and
Part Four: Engineering Graphical eommunication: Conveying Information to 0ther Engineers, Machinists, Technicians, and Managers In Part Four, consisting of Chapter 16, we inuoduce students to the principles and nrles of engineering graphical communication and engineering sfmbols. A good grasp of these principles '!fe explain that engiwill enable students ro convey and undentand information effectively. neers use technical drawings to convey useful informadon to others in a standard manner. An engineering drawing provides information, such as the shape of a product, its dimensions, materials from which ro fabricate the product, and the assembly steps. Some engineering drawings are specific to a particular discipline. For enample, civil engineers deal with land or boundary' topographic, consrrucdon, and route survey drarings. Electrical and electronic engineers, on the other hand, could deal with printed circuit board assembly drawings, printed circuit board drill plans, and wiring diagrams.'W'e also show that engineers use special symbols and signs to convey their ideas, analyses, and solutions to problems.
Part Five: Engineering Material SelectionAn lmportant Design Decisioll fu
engineers, whether you are designing a machine pa$, a toy, a frame of a car, or a structruer the selection of materids is an important design decision. In Pan Five, Chapter 17, we look
Pnrrecn
vtl
more closely at materials such as metals and their allop, plastics, glass, wood, composites, and concrete rhat commonly are used in various engineering applications.'We also drscuss some of the basic characteristics ofthe materials that are considered in design.
fart
Six: Mathematics, Statistics, and Engineering EconomicsWhy Are They lmportant? In Part Six, consisting of Chapters 18 through 20,we introduce students to important mathematical, statistical, and economical concepts. We orplain that engineering problems are mathematical models of physical situations. Some engineering problems lead to linear models, whereas
others result in nonlinear models. Some engineering problems are formulated in the form of differential equations and some in the form of integrals. Therefore, a good undersanding of mathematical concepts is essential in dre formulation and solution of many engineering problems. Moreover, statistical models are becoming common tools in the hands of practicing engineers to solve quahty control and reliability issues, and to perform failure andyses. Civil engineers use statistical models to study the reliabfity of construction materials and stnrctures, and to design for flood control, for example. Elecuical engineers use statistical models for signal processing and for developing voicerecognition software. Manufacturing engineers use statistics for qualiry control assurance of the products they produce. Mechanical engineers use statistics to study the failure of materials and machine parts. Economic factors also play important roles in engineering desigrr decision making. Ifyou design a product that is too expensive to manufacnue, then it qrn not be sold at a price that consumers can afford and still be profitable to your company.
CASE STUDIESENGINEERING MARVELS To emphasize that engineers are problem solvers and that engineers apply physical and chemical laws and principles, along with mathematics, to design products and services that we use in our everyday lives, seven case studies are placed throughout the book These projects are ruly engineering marvels. Following Chapter 7, the design of New York City W'ater Tunnel No. 3 is discussed. The design of the Cateqpillar 797 Mining Tiuck, the largest mining mrck in the world, follows Chaprcr 10. FollowingChapter 13, relwantinformationaboutthe design ofthe Hoover Dam is discussed. The design of the Boeing 777 :spresented.in a case sudyfollowing Chapter 16. Finally, the Pratt and Whimey Jet Engine is discussed at the end of Chapter 17. There are assigned problems at the end of those case studies. The solutions to these problems incorporate the engineering concepts and laws that are discussed in the preceding chapters. There are also a number of engineering ethics case studies, from the National Society of ProFessional Engineers, in Chapter 5, to promote the discussion on engineering ethics.
IMPROMPTU DESIGNS I have included seven inexpensive impromptu designs that could be done during class times. The basic idea behind some of the Imprompru Designs have come from theASME.
viii
Pnsrecn
REFERENCES In writing this book, sweral engineering books, Veb pages, and other marerials were consulted. Rather than giving you a list that contains hundreds of resources, I will cite some of the sources that I believe to be usefirl to you. I think all freshman engineering students should ov"n a handbook in their chosen field. Currendy, there are many engineering handbooks anailable in print or electronic format, including chemical engineering handbools, civil engineering handbools, electrical and electronic engineering handbooks, and mechanical engineering handboolis. I also beliwe all engineering students should own chemistry phpics, and mathematics handbooks. These texts c:rn serve as supplementary resources in all your classes. Many engineers may also
findusefirl theASHRAEhandbook, the,FzndammalVolume,byrheAmerican SocieryofHeating, Refrigeratin& and Ah Conditioning Engineers. In rhis book, some data and diagrams were adapted with permission from the following sources:
Baumeisrer, T., et al., Marh's Handbooh,8th ed., McGravr Hill, 1978. Electrical Viing, 2nd ed., AA VIM, 1981. Electric Motors,5th ed., AAVIM, 1982. Gere, J. M, Mechanics ofMateriak,6th ed., Thomson, 2004. Hibbler, C., Mechanics ofMateriak,6th ed., Pearson Prentice Hall'
k
SnndardAtrnoEhne, Vashington D.C., U.S. Government Printing Office, 1962, 'Weston, K C,, Energt Conuersion, Vest Publishing, 1992. U.S.
AEKNOWLEDGMENTS my sincere gratitude to the editing and production tenm at Thomson Engineering, especially Hilda Gown. I am also gratefirl to Rose Kernan of RPK Editorial Services, Inc., and NewgenAustin I would also like to thank Dr. Karen Chou of Minnesota State University, who reviewed the second edition carefirlly and made valuable suggestions. I am also thankful to the follouring reviewers who offered general and specific comments: N.lly M.Abboud, Universiry of Connecticut; Barbara Engerer, Valparaiso Universiqt Alex J. Fowler, Universiry of Massachusetrs, Darrmouth; Peter Golding, University of Texas at El Paso; Fadh Oncul, Fairleigh Dickinson University. I would also like to thank the following individuals for graciously providing their insighu for our Student and Professional Profiles sections: Katie McCullough, Celeste Baine, NahidAfsari, Dominique L. Green, Susan Thomas, and Ming Dong. Thank you for considering this book and I hope you enjoy the third edition.
I would like to
enpress
Saeed
Moaueni
Gontents
Preface nl
PART 01{E:
 1.1 1.2 1.3 1.4 t5
ENGTNEERTNGAN ExcrTrNG
pRoFEssroN z
flntroduction to the Engineering Profession 4 Englneerlnq Work lg All Around
You
5
Englneerlng as a Professlon and Conmon Tnlts of Good Enqlneers 8 Conmon Traltg of Good Englneers 9 Englneerlng Dlsclpllnes 12
Accredltotlon Board for Englneerlng ond Technolory OBET) Professlonal
ltl
Proflle 23
Summary 23
Prcblem
23
lmBromptu Deslgn
2 2J 2.2 23 2,4 2,5 2.6
I
26
Freparing for an Engineering
eareer
Maklng the Transltlon from Hlgh School to
Colleqe 28
BudgetlngYourllne 28 Dally Studylng and Prepantlon
31
Get lnvolyed wlth an Englneerlng
0rganlzetlon 36
Your Graduatlon
Plan
?7
37
Gher Conslderatlons 3? Student
Proflle 38
ProfesslonalProflle 39
Sumnary 40
Problens 40
3 3.1 3.2 3.3 3.4 3.5 3.6
fintroduction to Engineering Design 4l EnglnecrlngDeslgnPfocess 42 Englneerlng Economlss 4i8
Materlal Selectlon 49
Teamwork 5l Common Tralts of Good
Teams 52
Confllct Resolutlon 53
lx
X
Coxrrrrs
3.7 3.8 3.9 3.10 3.ll 3.12 3.13 3.14 3.15
Prolect Schedullng and Task
Chart
53
Alternetlves 55 Patent, Trademark, and Copyrlght 56 Englneerlng Standards and Godes 5l Evaluatlng
Eramples of Standards snd Codes 0rganlzatlons ln the Unfted Exomples
ol lnternatlonal Standards
and
Drlnklng lTater Standards In the Unlted
States 60
Codes 62
States 67 States 68
0utdoor Alr Quallty Standards In the Unlted lndoor Alr Quallty Standards In the Unlted
states
70
Sunmary 72 Problems ?3 lmpromptu Deslgn
4
75
Engineering Communication 81
41 4,2 4.3 4.4 4.5 4.6 41 4.8
5
ll
Communlcatlon Skllls end Presentetlon of Englneerlng Baslc Steps lnvolved In the Solutlon of Englneerlng
Work 82
Problems 82
Homework Presentatlon 85 Progress Report, Erecutlve Sunmary end Short DetalledTeshnlcal
Report
Menos
0ral Gommunlcatlon and Presentatlon 90 PowerPolnt Presentatlon 91 Englneerlng Graphlcal Communlcatlon 100
Summary
101
Problens
102
Engineering
5.1 52 5.3 5.4
Ethics
Englneerlng
Ethlcs
105
106
The Gode of Ethlcs of the l{otlonal Socle$ of Prolerslonal .07 Gode ol Ethlcs for Englneers
Greed
Englneer's
111
Summary 1l?
Problem
117
Englneerlng Ethlcs: A Case Study from NSPE& 120
PART TWO:
ENGINEERING FUNDAMENTALS_
CONCEPTS EVERY ENGINEER SHOULD
5
87
87
Fundamental Dimensions and
6.1 6.2 6.3 6.4 65
KNOW 124
Units
126
Englneerlng Problemsand Fundamental Dlmenslons 127
Systens of
Unlts
128
Unlt Converslon 134 Dlmenslonal Homogenelty 136 Numerlcal versus Symbollc
Solutlons
138
Englneers l0?
CoNrprrs 6.6 6:l 6.8
Slgnlflcant Dlglts(Flgures) 139
Systems l4l
Englneerlng Components 8nd
Phyrlcal Laws of 0bservatlons In Englneerlng
ltlil
Summary t46 Problems
7
147
Length and LengthRelated Parametcrs tr52
7.1 7.2 73 7.4 7.5 7.6 7:I 7.8
Length as a Fundamental Dlmenslon 15il
length
Measurement of
157
llomlnal Slzes versus Actual
Slzes
160
lko lengths l6il StralnasRatloofTlrolengths 163 Radlans as Ratlo of
Area
16:!
Volume
172
Second Moment of
Summary
Areas 17
182
Problems 18:l lmpromptu Design
lll
188
An Englneerlng Marvel: The Nerv York Clty Water Tunnel No.
8 Time and TimeRelated Parameters 195 8.1 8.2 8.3 8.4 8.5 8.6
Tlme os e Fundanentol Dlmenslon 196 .98 Measurement ot nme
PerlodsandFrequencles Flow of
Trofflc
Parameten Inyolvlng length and
AngularMotlon Summary
215
Problems
215
Mass as a Fundamental
Measurement of
Parameters 218
Dlmenslon
Mass
219
222
Denslty, Specltlc Volume, snd Speclfls Mass
FlowRate 224
lnertla 2A
Mass Moment of
Momentum
Conservatlon of
205
214
Mass and Mass'Related
9.1 9,2 93 9.4 95 9.6 9.1
llme
212
ProfesslonalProflle
9
201
203
224
Mass 229
Sumnary 232 Problems 232 IMPROMPTU DESIGN
IV
235
onvlty
222
3*
189
xi
xii
Covrenrs
l0
Parameters 236
Force and ForceRelated
10.1 102 10.3 10.4
What We Mean by
Force
237
Newtonl Laws In Mechanlcs
241
Pressure snd StressForce Actlng Over an
Area
244
Modulus of Elastlclty, Modulus ot Rlgldlty, and Bulk Modulug of Gompresslblllty 256
105 10.6 l0:l
Dlstence 264
Moment, TorqueForces Actlng at a
WorkForce Actlnq 0ver a Dlstance 268 Llnear lmpulseForces Actlng 0ver
Summary
271
Problemr
271
IMPROMPTU OESIGII
V
Tlme
269
2r/
An Englneerlng Marvel: Caterplllar 797 Mlning
lf
278
Temperature and TemperatureRelated Parameters 282
It.l 1L2 ll.3 11.4 tls 11.6
Tempenture os a Fundrmentol Dlmemlon 283 Measurement of Temperature and lts
Unlts
286
Tenperature Dlfference and HeotTransfer 293 lhermal Comfort, Metobollc Ratg and Clothlng Insuletlon 306 Some Tenpemture'Related Materlals
Heatlng Values of
Fuels
ProlesslonolProflle
n2
Truck*
Summary
315
Problems
315
Propertles 309
312
314
Electric Currcnt and Related Parameters 319
121 12.2 123 l2A 12.5
Electrlc Gunent as a Fundenental Dlmenslon 320
Voltage
321
Dlrect Cunent and Alternatln0
Cunent 323
Electrlc Clrcults and Components 326 Electdc
Motors 334
ProfesslonalProflle 3il7 Summary 337 Problems 338
13 Energy and Power 341 l3.l 13.2 13.3 13.4 135
Work, Mechanlcal Energy,Thermal
Energy 342
Gonservatlon of EnergyFlrst Lrw of Thermodynonlcs 348 Understandlng What tfe Mean by
lfottsand Horsepower
Efflclency 355
351
Power 350
CoNrsNrs Student
Proflle 362
ProfesslonalProf,le 363 Summary 364 Problems 364 IMPROMPTU DESIGN
V[
366
An Englneerlng Marvel: Hoover
PART THREE:
Dam
367
coMpuTATroNAL ENGTNEERTNG
T00Ls
USING AVAILABLE SOFTWARE TO SOLVE ENGINEERING
14 Efectronic 14,1 14.2 l/t3 14.4 t4J 14.6 14:l 14.8
PROBLEMS 370
Spreadsheets 372
Mlcrosoft ErcelBaslc Cells and
ldeas 37il
lhelr Addresses 374
Crestlng Formulas In
Ercel
375
Functlons 383 Uslng Ercel Loglcal Functlons 387 Uslng Excel
Ploftlng wlth
Ercel
389
Matrlx Computatlon wlth
Ercel
400
CurveFlttlngwlthErcel 407 Sumnary 4ll Problems
15
412
MATLAE 419
15.1 152 15.3 15.4 155 15.6 15.7
MAT[ABBaslc
ldeas 420
Uslng MATLAB Bulltln
Functlons 429
Plottlng wlth MATUIB tl38 lmportlng Excel and Other Data Flles Into MATLAB 445
MatrhGomputatlongwlthMATLAB 447 Curve Flttlng wlth MATLAB 450 Symbollc Mathematlcs wlth MATLAB 451
ProfesslonalProflle 454 Summary 455 Problems 455
PART F0UR:
ENcTNEERTNG
cRApHrcAL coMMUNrcATroN
CONVEYING INFORMATION TO OTHER ENGINEERS, MACHINISTS,
TECHNICANS,ANDMANAGERS 460
16
Engineering Drawings and
16.1 16.2 16.3 16.4
lmportance ot Englneerlng
Symbols 462
Dnwlng 46il
0rthognphlc Vlews 4&l Dlmenslonlng and Toleranclng 467
lsometrlsVlew 469
xiii
xiv
CoxrrNrs
16.5 16.6 16:I 16.8 16,9
Sectlonal
Vlews
472
Clvll, Electrlcal, and Electronlc Solld
Dnwlngs
476
trlodellng 476
Why Do We l'leed Englneerlng
Symbols? tl83
Examples of Common Symbols used In Clvll, Electrlcal,
and Mechanlcal Englneerlng tl85
summary rts? Problems 487 An Engineerlng Marvel: Boelng 777* Commerclal
PART FIVE:
ENGTNEERTNG MATERIAL
Alrplane 493
sELEcTtoN
AN IMPORTANT DESIGN DECISION 498
l7
Engineering
17.1 172 t73 17.4
Materials 500
MaterlalSelectlon
501
Electrlcal, Mechanlcal, and lhermophyslcal Propertles of Materlals 503
Materlals 509
Some Common Solld Englneerlng
ilaterlals
Some Common Fluld
ProfesslonalProflle
519
521
Summary 522 Problems 522
VII
IMPROMPTU DESIGI'I
525
An Englneerlnq Marvel: The Jet
PART SIX: WHY ARE THEY
fB
Englne* 526
NnrnrMATrcs, sTATlsTtcs, AND IMPORTANT? 530
ENGTNEERING
Mathematics in Engineerinq 532
18.1 182 18.3 18.4 18.5 t8.5 18.7
trlathematlcal Symbols and Greek
LlnearModels
Alphabet 533
5:15
Nonllnearilodels
541
Erponentlal and logarlthmlc Models 546
MatrlxAlgebn
Glculus
551
562
Dlfferentlal Eguatlons 570
Summery 572 Problems 57!l
EcoNoMtcs
Corrslrrs
19
Probability and Statistics in Engineering 577
19.1 19.2 193 19.4 t95
ProbabllltyBaslc ldeas 510
StatlstlcsB$lc ldeos 59 FrequencyDlstrlbutlons 580 Heasuras ol Gntral Tendency Yarlotlonlllean, Medlon, and Standard
t{ormilDbtrllutlon
587
Sumn8rt 594 hoblems 594
20 Engineering 20.1 mA 20.3 2OA 20J 20.6 ZOJ 20.8 20.9
Carh Flow
Economics 597 Dlagnm 598
SlmpleandCompoundlntenit 599 FutureUlorthofaPnsentAmount 600 Efrectlve lnteregt
nde
60ll
PresentWorthofFutureAmount Present Worth of Serles
605
hynent or
hnutty
605
FuturEl{orthofSerlshynnnt 606 SummaryofEnglnesrlngEconomlcaAndysb 609 Chooslng the Best AlternatlvesDeclslon
Summory
617
PruUem
617
AppEndlr 620
Credlts 625 Index 626
l{aklng
613
Devlatlon 582
XV
Part
ENCTNEERING Al. Excmttc PnoFEssron
1
j@@ltryq'@qt
i
In Part One of this book, we will introduce you to the engineering profession. Engineers
.aregroblem solvers. They have a good grasp of fundamental physical and chemical laws and mathematics and apply these laws and principles to design, develop, test, and
supervise the manufacture of millions of products and services. Engineers, regardless of
their background, follow certain steps when designing the products and services we use in our everyday lives. Successful engineers possess good communication skills and are
team players. Ethics plays a very important role in engineering. As eloguently stated by
the National Society of Professional Engineers (NSPE) code of ethics, "Engineering is an important and learned profession. As members of this profession, engineers are
expected to exhibit the highest standards of honesty and integrity. Engineering has a
direct and vital impact on the quality of life for all people. Accordingly, the services provided by engineers require honesty, impartiality, fairness and equity, and must be dedicated to the protection of the public health, safety and welfare. Engineers must
perform under a standard of professional behavior which requires adherence to the highest principles of ethical conduct." In the next five chapters, we will introduce you to the engineering profession, how to prepare for an exciting engineering career, the design process, engineering communication, and ethics.
Chapter I
Introductlon to the Englneering Professlon
Chapter 2
Preparlng for an Engineerlng Career
Chapter 3
Introductlon to Englneering Design
Chapter 4
Englneering Communlcatlon
Chapter 5
Englneering Ethlcs
CHAPTE,R.
1
INrnoDUcrroN To THE ENcTNEERTNG PnoFEssroN [f
ngineers are problem solvers.
1
Successful engineers possess good
L
communication skills and are team
players. They have a good grasp of
fundamental physical laws and mathematics. Engineers apply physical and chemical laws and mathematics to design, develop, test, and supervise the
manufacture of millions of products and services. They consider important
factors such as efficiency, cost, reliability, and safety when designing products. Engineers are dedicated to lifelong
learning and service to others.
1.1
ENcTNEERTNc
Wom Is Ar.r. Anomlo You
ofloa are not yet ceTtain loa uant to study mginening during the nextfour years in college and may haue questions simikr to thefollowing
Possibfu sorne
I
really uant to study mgineering? is mgineeringand what do mgineers do? 'Vhat are some ofthe areas ofspecialization in mgineering? How many differmt mgineering disciplines are tbere? Do I want to become a rnechanical enginen, or shoull.I pursue ciuil mgineering? Or would I be happier becoming an electrical mginen? How will I hnow rhat I haue piched the bestfeldfor rue? Wll the dernand far rn! area of speciakm.tian be hi.gh whm I gradaate, and'
Do
Vhat
bryond that? The main objectiues of this chapter Are to prouidz sorne answers to these and other questi.ons loa may haue, and to i.nnodace you to tlte engineeri.ng profasion
and its aaious brancltes.
1.1 Engineering Work ls All Around
You
Engineers make products and provide services that make our lives beter (see Figue 1.1). To see how engineers contribute to the comfon and the betterment of our weryday lives, tomor
row morning when you get up, just look around you more carefirlly. During the night, your bedroom was kept at the right temperature thanks to some mechanical engineers who designed the heating airconditioning, and ventilating q/stems in your home. When you get up in the morning and turn on the lights, be assured that thousands of mechanical and elecuical engineers and technicians at po$'er plants and power stations around the country are making certain the fow of electricity remains uninterrupted so that you have enough pov/er to turn the lights on or flun on your TV to watch the morning news and weather repon for the dty. Th" TVyou are using to get your morning news was designed by electrical and elecronic engrneers. There are, ofcourse, engineers from other disciplines involved in creating the final product; for example, manu6curing and industrial engineers. When you are gening ready to take your morning shower, the clean water you are about to use is coming to yor[ home thanks rc civil
f,
Figurel.l
Eramples of products and serviees designed by engineers.
CnerrsR
I
IxrnopucrroNTo rnrExcwnsRrNc Pnorsssrox and mechanical engineers. Even if you live out in the country on a farm, the pump you use to bring water from the well to your home was designed by mechanical and civil engineers. The water could be heated by natural gas that is brought to your home thanls to the work and effon of chemical, mechanical, civil, and peuoleum engineers. After your moming shower, when you ger ready to dry yourself with a towel, think about what types of engineer worked behind the scenes to produce the towels. Yes, the cotton towel was made with the help of agriculturd, industrial, manufacnuing chemical, petroleum, civil, and mechanical engineers. Think about the machines that were used to pick the cotton, transport the cotton m a factory clean it, and dye it to a pretty color that is pleasing to your eyes. Then other machines were used to weave the fabric and send it to sewing machines that were designed by mechanical engineers. The same is uue of the clothing you are about to wear. Your clothing may contain some polyester, which was made possible with the aid of petroleum and chemical engineers. "V'ell," you may say, "I can at least sit down and eat my breakfast and not wonder whether some engineers made this possible as well." But the food you are about to eat rras made with the help and collaboration ofvarious engineering disciplines, from agricultural to mechanicd. Lett sayyou are about to have some cereal. The milk was kept fresh in your refrigerator thanls to the efforts and work of mechanical engineers who designed the refrigerator components and chemical engineers who investigated alternative refrigerant fluids with appropriate thermal properties and other environmentally friendly propenies that can be used in your refrigerator. Furthermore, electrical engineers designed the control and the electrical power units. Now you are ready to get into your car or take the bus to go to school. The car you are about to drive was made possible with the help and collaboration of automotive, mechanical, electricd, electronic, material, chemical, and peuoleum engineers. So, you see there is not much that you do in your daily life that has not involved the work of engineers. Be proud of the decision you have made to become an engineer. Soon you will become one ofthose whose behindthescenes efforts will be taken for granted by billions of people around the world. But you will accept that fact gladly, knowing that what you do will make peoplet lives bener.
Engineers Deal with an Increasing World Population 'V'e
as people, regardless ofwhere we live, need the following things: food, dothing, shelter, and warer for drinking or cleaning purposes. In addition, we need various modes of transportation to get ro different places, because we may live and work in different cities or wish to visit friends and relatives who may live elsewhere. Ve also like to have some sense of security, to be able to 'We need to be liked and apprecixedby our friends and family, as well. relax and be entertained. At the turn of the 20th century, there were approximately six billion of us inhabiting the eafth. As a means of comparison, it is imporent to note that dre world population 100 years ago, at the turn of the 19th century, was one billion. Think about it. It took us since the beginning of human enistence to reach a populadon of one billion. It only took 100 years to increase the population by fivefold. Some of us have a good standard of living, but some of us living in developing countries do not. You will probably agree that our world would be a bemer place if wery one of us had enough to eat, a comfortable and safe place to live, meaningfirl work to do, and some time for relaxation. According to'the Iatest estimates and projections of the U.S. Census Bureau, the world
population will reach 9.3 billion people by the year 2050. Not only will the number of people inhabiting the eanh continue to rise but the age strucrure of the wodd population will also
1.1
EncnrBBnnlc W'onr Is Ar.r. A,nouuu You
1
0 1950
1960
lwo
1980 1990 2W
20LO
Year (a)
Over 1 00 population (thousands)
* estimate (b)
E figure t.2 (d ilre
latest pmjection of world population growth. (b) Ihe latest estimate of U.S. elderly population growth.
Smrce: Dacr hom U.S. Census Bureau.
people at least 65 yars of agewill more than 1.2). Figure double in the next 25 yers How is this information relevant? Well, now that you harre decided to study to become an engineer, you need to realize that what you do in a few years after your graduation is very importanr ro all ofus. You will design producs and provide services especially suited to the needs and demands of an increasing elderly population as well as increased numbers of people of all ages. So prepare well to become a good engrneer and be proud that you have chosen the engineering profession in order to conuibute to raising the living standard for weryone. Todry't world economy is very dynamic. Coqporations continually employ new technologies to maximize efficiency and piofits. Because ofthis ongoing change and emerging technologies, new jobs change. The world's eldedy
populationthe
(see
are created and orhers are eliminated. Computers and smart
elecronic devices are continuously
reshaping our way of life. Such devices infuence the way we do things and help us provide the
Cger"rsn
I
lNrnopucrroN To nrs
ENcrNnnRrNG PRoFEssroN
necessities of our livesclean water, food, and shelrcr. You need to become a lifelong leamer so that you can make informed decisions and anticipate as well as react to the global changes
caused by technological innovations as well as population and environmental changes. According to the Bureau of labor Statistics, U.S. Department of Labor, among the fastestgrowing occupations are engineers, computer specialists, and qystems analysts.
1.2
Engineering as a Profession and Common Traits of Good Engineers In this section, we will first discuss engineering in a broad sense, and then we will focus on se'W'e lected aspecs of engineering. will also look at the traits and characteristics common to many engineers. Next we will discuss some specific engineering disciplines. As we said earlier in this chapter, perhaps some ofyou have not yet decided what you want to study during yolu college years and consequendy may hane many questions, including: Wh.at is engineering and what do engineers do? !7hat are some of the areas of specialization in engineering? Do I really want to study engineering? How will I know that I have picked the best field for me? \Xrril the demand for my area of specialization be high when I graduate, and beyond that? The following sections are intended to help you make a decision that you will be happy with; and dorit worry about finding answers to all these questions right now You have some time to ponder them becluse most of the coursework during the fust year of engineering is similar for all engineering students, regardless oftheir specific discipline. So you have at least a year to consider various possibilities. This is true at most educational institutions. Even so, you should mlk to your advisor early to determine how soon you must choose an area of speciallzation. And dont be concerned about your chosen profession changrng in a way that makes your education obsolete. Most companies assist their engineers in acquiring further training and education to keep up with technologies. A good engineering education will en"h*grg able you to become a good problem solver throughout your life, regardless ofthe particular problem or situation. You maywonder during the ner>.Amount = 1000:250:3000; >>
IntereEt_Rate = 0.06;0. 01:0.08; Interest_Earaed. = (.Anount' ) * (IatereEt_Rate), fprlnrf (' \n\n\r\L\r\r\r\r\r rnrereEr Ratet ) ;fprLntf (' \a\t .Anount\t\t' ) I . .. fprLatf ( ' \t\t e"g[' , InterestRate) ; fprlntf ( ' \n' ; ; dtsp ( lihount ! ,IDterest Earned] ) >> >> >>
Interest Rate
Dollar Amount
0.06
o.a7
1000
50
t250
/)
70 87.5
80 100
1500
90
105
t20
t750
105
t22.5
140
2000 ?250 2500
120 135
t40
160
r57.5
180
150
175
?:750
r65
r92.5
3000
180
2t0
204 220 240
15.2
Usu.rc MATLAB Bur.rnr Frnrcrrorvs
429
,i,
[l
Figurc
15.5
The commands and result
for tmmple
14.2 (Revisited).
t:t
On the last command line, note that the three periods . . . (an ellipsis) represents a continuation marker in MAILAB. The ellipsis means there is more to follow on this command line. Note the use of fprinLf and disp commands. The final result for Example 14.2 (Revisited) is shown in Figure 15.5. ,l
15.2 [fsing MATLAB Built'in MATLAB offers
a large selection
Functions of builtin functions that you qln use to analyze data. fu we
discussed in the prwious &apter, by builtin funcdons we mean standard functions such as the sine or cosine of an angle, as well as formulas that calculate the totd value, the average value,
or the sandard deviation of a set of data points. The MlfILAB functions are available in various categories, including mathematical, trigonometric, statistical, and logical functions. In this chapter, we will discuss some of the common firnctions. MAI,AB offers a Help menu that you can use to obain information on various commands and functions. The Help button is marked by a question mark ? located to the left of the current directory. You can also rype help followed by a command name to leam how to use the command. Some examples of commonly used MATLAB functions, alongwith their proper use and descriptions, are shown in Thble 15.7. Refs to Example 15.2 when studying Tirble 15.7.
The following set of values will be used to introduce some of MAlfABt builtin functions. Mass: U02 lts 99 rc6 rc3 95 97 102 98 96l.WrenstudyingTableL5.T,theresults of the executed functions are shown under the "Result of the Example" column. More examples of MlflLAB's Functions are shown in Thble 15.8.
430
Cnu'rrn 15 MAILAB
'#;;
i meqn "'q i j i
;**;oor
;t
*i;i:;
It
sums the values
It
calculates the average value
dre data in
It daermines
max
*n"
a
in
a
,;
*orr1* ogthu n="pl" ,,,i til;lilrdfn
gilen array.
1013:
of
101.3
given array.
the largest value
in
the given array; ,It determines ttre smalle* value irt the given array, It calculates the standard deviadon fot the values in the giveqrena)r It sorts the values in the give$' ,,, , array in ascending order. It returns the value of zr,
i
r min ,l
sEq
:
joir; I,:
3.14151.926535897.. i
'
,.,'i;
.
It retums tangent value of the
9@l
argument. The argument must be
in radians,
cos
It
renrrns cosinevalue ofthe argument. The argument must be
in
It
returns sine value of the argument.
in radians, s
,',,,,,
frg*su**l**rh,h:ifT:,
;l
sqrt (x) f actorial (x)
Retums the square root ofvalue.t
ky"^ *:.:*e of factorial of*. For example, factorial(5) wlll return: (5)(4)(3)(2)(r) : 120.
Trigonornzt ix Functions (x) This is the inverse cosine function ofx. It is used to determine the value of an angle when its cosine value is kno\trn. asin (x ) This is the inverse sine function of*. It is used to determine the value of an angle when its sine value is known. atan (x) This is the inverse tangent function of r. It is used to determine the value :. of an angle rylieg its glgent value is knor,rn. '',1 ,,
acos
,
',
'
kponcntial and Ingarithmic Functiot s exp
(x)
los (x) 1og10 (x) 1og2 (x)
Retums the value of a". Retums rhe value of the natural logarithm of *. Note that
* must
greater than 0.
Returns the value ofthe common (base 10) logarithm of.r. Returns the value of the base 2 loSanthm of x.
be
15,2 Usnc MAIIAB Bur.rnv FuNcrroxs
431
Usiag MAil.AB, compure the aver4ge (ari hmecic mean) and the sandard deviation of the density of water data given in Thble 15.9. Refer to Chapter 19, Section t9.4, to learn about what the vdue of the standard deviation for a set of data points represents.
1,,
GroupAFindingq
GroupB Flndings
1.,
ffi* The final resuks for Example 14.4 (Revisite$ are shown in Figure 15.6. The commands leading to these results are:
MAILAB
>>DensJ.tyA = [1020 1015 990 1060 1030 950 975 1020 980 950] t >>DeasLtyB = [950 9AO 890 1080 1120 900 ].040 1150 910 10201; >> DensLty_A_Avela![e = nean (Denstty_A) DensityA_Av€rdg€ = 1000.00 >> DenEl.ty_B_Aver?![€ = mean (DensLty_B) DensiLyBAv€rdg€ = 1000.00 > > Standard._Xlevlat lon_For_croup_l\ = std ( Dengity_A) StandardDeviat i on_For_Group_A = 34.56 > > Standard_DevLat Lon_For_Group_B = std ( Deagity_B ) SLandard_Deviat. ion_For_Group_B = 93 .22
432
CHer"rsR
15
MAILAB
e
Edt uew w& wln*w
He
rdi&'ce@*l&jt
I
figumls.O
Command l{indow
iATIAB'S
for trample
14.4
(Revhited).
Li.!l:l:r.':.t:
I::
:l:t:,:r
tlt: ;l:a:a:lt: _t:
::ri.,::::::
The Loop eontrol
.
 forand while commands
When writing a computer program, often it becomes necessarl to execute a line or a block ofyour computer code many times. MAIf,AS providesprand ubilocnmmands for such situations.
forloop
Using theprloop, you can execute number of times. The sfnax of aforloop is
The
a
line or a block of code a specified (defined)
for index = sLartvalue : incremenL : endva1ue a line or a block of your computer code end For example, suppose you want to evaluate the function ! : x2 * 10 for r values of 22.00 22.50,23.00,23.50, and24.00. This operation will result in correspondingTvalues of 494.00, 516.25,539.00,562.25,and 586.00. The MlftIAB code forthis enample then couldhave the following form:
x = 22.0; Fnr
i

1.1.R
Y=xn2+IO i
disp(lx',y'l) x = x + 0.5;
end
I5.2
UsrNc MAIIA,B BunrrN FuNc"rrors
433
Note that in the preceding example, the index is the integer i and its startvalue is 1, it is incremented by a value of 1, and ia endvalue is 5.
rfile Loop Using the whilzloop,you c:ur execute condition is met. The qyntax of a while loop is
The
whi
a
line or a block of code until
a
specified
Le control I ing  expres s ion
a 1ine or a block of vour comouLer
code
end 'With the while command,
as
long
as
the controllingexpression is true, the line or a block of code using rhe whib com
will be enecuted. For the preceding example, the MIIILAB
code
mand becomes:
x = 22.0; while x >pressur6=[20 tS 22 26 L9 1,9 2L L27i >>fprlotf('\t Line Pressure (pgt) \t VaLve FosLtlon\n\n');
for L=1:8 if pressure(t) >=20 fPrLntf (' \t e"9 \t\t\ts\t\t else
fpriatf ( '\t
end end
I
rigurel5.8
The solution
ol Ennple
14.5 (Revhited).
?"9
\t\t\t\t\t
OFEN\n'rBreEsure(L) CITOSED\n'
)
,pregsure (L) )
436
Cneprsn
15
MAILAB
The Mfile As explained previously, for simple operations you c:m use M,{'l,AB's Command lTindow to enter variables and issue commands. However, when you write a program that is more than a few lines long, you use an Mfrle. It is called an Mfile because of its .zz extension. You can cre
Mfile using any text editor or using MAIT,ABI Editor/Debugger. To crqrte an MfiIe, open the Mfile Editor and MlfIl,AB opens a new window in which you can type your program. fu you type your program, you will notice that MAILAB assigns line numbers in the left column of the window. The line numbers are quite useftrl for debugging your program. To save the file, simply click File * Save and type in the filename. The name of your file must begin with a letter and may include other characters such as underscore and digits. Be carefirl not to name your file the same as a MAILAB command. To see if a filename is used by a MATIAB command, type exist ('filenamd) in the M,$LAB's Command'S7indow. To run your program, click on Debug + Run (or use the function key F5). Don't be discouraged to find mistakes in your program the first time you attempt to run it. This is quite normal! You can use the Debugger to find your mistakes. To learn more about debugging opuons, type help ate an
dtbug
It
n
the
MATU.B Command !7indow.
has been said that when Pascal was 7 years old, he qrme up with the formula
rdn f l\ ttt
determine the sum of 1,2,3, . . . , through n. The story suggests that one day he was asked by his teacher to add up numbers I through 100, and Pascal came up with the answer in few minutes. It is believed that Pascal solved the problem in the following manner: First, on one line he wrote the numbers I *uough 100, similar to
1 2 3 4.. ,........99
100
Then on the second line he wrote the numbers backward
100 99 98
97
...........2
1
Then he added up the numbers in the nvo lines, resulting in one hundred identical values
of
101
101 101 101
101
...........
101
101
Pascal also realized that the result should be divided by
1 through 100 twiceleading to the answer:
.
approach and came up with the formula
100(10 I )
;:
n(n+ r)
 ,
2since
he wrote down the numbers
5050. l,ater, he generalized his
15.2
Flle Edt
Tqt
Bdffitr ,
Cell T@h Dehrg De$ktop Wrdow
&EB
UsrNc MAILAB Burr,trN Funcrrous
437
Ftalp
"leitmTl aelc*eareeli:
F{iF
rtil 4.. ":,i :
g Ask the usar lo input the uFper vaLue ,, upper_value=input('Please input th€ upper vlaue of the nunLters.'), . 4;'t ,:
,1i
:
:l
6:, i,
q iFt
1: for
'8,.:
a! 1,:
1.0
i i
;:1 Figure
fhF
crrn onil:l
r^
zero
surn=o,
k=1:1:upper_value sum=sum+kt
end
g Print the results
fprintf('\n
?he eum of numbors from 1 to $g is eqaul to: tg\nr,upper_value'sum)
15.9 lhe lrfile for Enmple
15.3.
Dcktop Wftew Heb
rFilei
rgjeFi3e d.H? shortcuts E Howto Add m
Figure
15.10
uJffis tgfd
The results 0f Example 15.3.
Nexr, we will wdte a computer program using an Mfile that asls a user to input a value for a and computes the sum of 1 through n. To make the program interesting, we will not make use of Pascal's formula; instead, we will use a for loop to solve the problem. \(e hane used MATI"A.B'S Editor to create the program and have named it ForIoopF,xample"m, as shown in Figure 15.9. In r:he shown program, the 7o symbol denotes comments, and any text following tle %o symbol will be ffeated as comments by MAII,AB. Also, note that you can find the Line (Ln) and Column (Col) numbers corresponding to a specific location in your program by moving the cursor. The line and the column numbers are shown in the right side, bocom corner of the Editor window. As you will see, the knowledge of line and column numbers are use'We frrl for debugging your program. run the program by clicking on Debug * Run, and the result is shown in Figure 15.10. , ..,:ri:i:1rtrj.I i:
. .i
438
Cneprun
15
MAIL.AB
tr5.3 Plotting with MATLAB M.{flAB
offers many choices when it comes to creating chats. For example, you c:m crezrte columl charts (or histograms), contour, or surface plorc. As we mentioned in Chapter 14, as an engineering student, and later as a practicing engineer, most of the charts that you will create will be tclt We charts. Therefore, we will explain in deeil how to ueztte an
xy
charts,
x!
chart.
Starting with a 10 cm X 10 cm sheet of paper, what is the largest volume you c:rn create by cuning out r cm X r cm from each corner ofthe sheet and then folding up the sides? See Figure 15.11. Use Ml[f,AB to obtain the solution. The volume created by cutting out r cm X r cm from each corner of the 10 cm X 10 cm sheet of paper is given by V: (10  2r)(10  2.a)*. Moreover, we know that, for r : 0 and x : 5, the volume will be zero. Therefore, we need to create a range of x values from 0 to 5 using some small increment, such as 0.1. We then plot the volume versus r and look for the maximum value of volume. The MAIIAB commands that lead to the solution are:
I The
>>x = 0:0.1:51 >>volune = (102*x) .*(102*x) .*xi >> Blot (x,vohme) >>tLtle ('VoJ.ume aE a functlon of x') >> xLabel ( 'x (cn) ' )
rigurct5.ll l0 cm
x
l0 cn
sheet in
Erample 15.4.
>> >>
I
y1abeL ( 'VoLu.me
grid. mLnor
figure
15.12
(cm^3 ) ' )
The IIAIIAB Command lindow
for txample 15.4.
The MAILAB CommandWindow for ExampleL5.4 is shown in Figure 15.12. The plot of volume versus r is shown in Figure 15.13.
ld
Figurc
fi1ii.lftrxT,ff{idi.iRBiEt:
15.13
nIF,Il
The plot ot volune versus
r
for Erample 15.4.
?j
Let us now discuss the MAIT.AB commands that commonly are used when plotting data. command plots yvalues versus xvalues. You can use various line types, plot symbols, or colors with the command pLoE(x,x,E), where s is a characer suing that defines a particular line type, plot symbol, or line color. The E can take on one of the properties shown in Thble 15.12.
The pLot (x, y)
DataSvmbol
lb
lo ,o
ic im iv ik
Blue Green
o
Point Circle
Red
x
rmark
+
Plus Star
cy* Magenta
ltllow Black
Solid
Doned Dashdot Dashed
Square
d
Diamond Triangle (down)
Triangle (up) Tiiangle (left) Triangle (right)
439
440
I
Cnaprsn
15 MAILAB
Figurcl5.l4
l'lATLABl Line Property Editor.
For example, ifyou issue the cornmand pL
ot, ( x, y t t k*   ),
MAILAB will plot the curve using a black solid line with an * marker shown at each dara point. If you do not spec' ify a line color, MAlf.AB automatically asslgns a color to the plot. Using the tttle ( 'text' ) commandr /ou crrn add text on top of the plot. The
xlabel
(
t
text' )
command creates the tide for the xaris. The text that you enclose will be shown below the xaxis. Similady, the ylabeL ( 'text' ) command creates the tide for the yaxis. To turn on the grid lines, type the command grLd on (or just grtd). The command grLd off removes the grid lines. To flrn on the minor grid lines, as shown in Figure 15.13, type the command grLd between single quotation marks
mlnor.
L5.3 Plorrrrcvrrn MAILAB
I
441
tigurelS.tS
The plot of
tranple
15.3 with
nodified properties.
Generally, it is easier to use the Graph Property Editor. For enample, to make the curve line thicker, change the line color, and to add markers to the data points (with the rnouse
pointer on the curve) doubleclick the left mouse button. Make sure you are in the picking mode first. You may need to click on the arrow next to the print icon to activate the picking mode. After doubleclicking on the line, you should see the line and the Marker Editor window. As shovrn in Figure t5.T4,weincreased dre line thickness from 0.5 to 2, c,hanged the Iine color to black, and set the daapoint marker sryle to Diamond. These new seaings are reflected in Figure I 5.15. Next, we will add an arrow pointing to the maximum value of the volume by selecting the TixtArrow under *re Insert option (see Figure l5.LG), and add the text'Maximnm volume occurs at x: 1.7 cm." These additions are reflected in Figure 15.17. V'e can also change the font size and style and make the title or the axes labels boldface. To do so, we pick the object that we want to modify and then, from the Menu bar, select Edit and then Current Object Properties . . . . Then, using the Propercy Editor shown in Figure 15.18, we c:rn modi& the propenies of the selected object.'We have changed the font size and the font weight of dre tide and the labels for F,xample 15.3 and shown the changes in Figure 15.19.
\firh MAILAB, you c:ln generate other types of plots, including contour and surface plos. You can also control the r and yaxis scales. For enample, the MAIT,AB's
Loglog(x,y)
usesthebasel0logarithmicscalesforrandyaxes.Note.randyarethevariplot. The command LogLog (x, y) is identical to the plot (x, y) ,
ables that you want to
K
figurets.t6
Using the lnsert Tert Arow
options, you can add anows or text to the plot.
I
Figurel5.lT
The solution of
M2
tnmple
15.4.
15.3 Pr.orrrNcwrnr MAILAB
t
443
Figurel5.l0
MAIIAB5
Ie*
Property Editor.
it
uses logarithmic axes. The command semlLogx(x,y) or semilogy(xry) plot with basel0 logarithmic scales for either only dre raxis oryaxis. Finally, it is wonh noting that you can use the hold command to plot more than one set of daa on the
except
creates a
same chan.
A reminder, when creating an engineering chart, whether you are using MAIT,AB, Excel, other drawing software, or a freehand dranring; an engineering chan must contain proper labels with proper units for each axis. The chart must also contain a figure number with a tide exptaining what the chart rcpresents. If more than one set of data is plomed on the same chart, the chan must also contain a legend or list showing symbols used for different data sets,
43
Cueprnn
I
15 MAIAB
FigurelS.lg
The result of Erample 15.4.
Using the resula of F:rample 14.1, create a graph showing the value of the air density as a funcdon of temperature. The Command'l7indow and the plot of the density of air as a function of temperature are shown in Figures 15.20 and 15.21, respectivelp
I
Figure
15.20
Command $lindow
for Erample t4.6 (Revhited).
15.4 Iuponrrxc E:rcrr,aNo Orrrrn Dere
L
Figure
15.?l
Frr.ss rNro
MAil,AB
445
Plot of density of air for Erample 14.6 (Revhited).
i] t1
IttA,.i,
r:ff1&1i.lilr,,t,t 
.i,r"lllta?nji:11lftlfiil!:
15.4
ii,!liijitii!.'i iiirxlitiijliirrrtii

ii,rXitilrl!ii111ta lr,iilril'liTrlTi1.ir'rrira
l:
Jli:1ii,1ir,irlrirl.. .'lTlLr.li4lltl
Nmporting Exeel and Other Data Filcs into MATLAB At times, it might
be
convenient to impon data files tlat were generated by other programs, such
MAilAB for additional analpis. To demonsrate how we go about imponing a daa file into MATLAB, consider the Fxcel file shown in Figure I5,22.The Excel file was created for Example 15.4 with two columru: the r values and the corresponding volume. To impon this file into MAIIAB, from the Menu bar, we select File *1sn Irnport Data . . . , t}ren go to the appropriate directory, and open the file we want. The Impon'Wizard window, as
Excel, into
in Figure L5.23,r ,ilappear next. Select the "Create vectors from each column using column nameso and the \Pizard will iport the data and will sare them as x and voXu:ne
as shown
variables.
Now lett the
MIIIIAB
Figure 15.25.
'We
that we want to plot the volume as a function of r. then simply type commands that are shoiyn in.Figtire 15,24.Tlte resulting plot is shown in
say
*r; ; .';I"***"
t11
:A
,
,:.9.i,
:'l
x
:.t:,
2 0.1
0.0 9.6
A:
na
18.4
sl
0.3
20.5
6
9.4
l,1.9 40.5
8l
0 0.
116.€
0.€
58.4
r:,$
10
I
[:]
D:I
rrolumo it:,;
iril!,
51.8
lr;
m,{ 6{.(
iii
fa\=rX.i;, r"#?fizr;; ri
I
Figurel5.Z
The Ercel data
L
;rr:
file used in tranple 15.4.
Figurul5.Z3
iAIIABI lmport ltizad.
@:..:
n aiI*, a
fo';
4'g.i'1i;;**l.rryffii!
Ar Sat rtst d, el,el ..qdfl!8 Ealtn trs l&r E ls &m $Frg 61ffid o!e*d @l,ablo, ln rhe ol@9 @tt!D€R. > al@ ta.wlwel > td.tla lr9ol@ e a 6Mt@ ot r'l I ilib€t (,a a@l'l > Itd!€r, (190r@ le.3lrl
il
t *ld Figurel5.Z4
The commands leading to the plot
shown in Figure 15.25.
46
>l
"
"
.
t.
::
""ll.f
:';: "'
15.5 Mernor CouputetroNs wrrg MAILAB
L
Figure
15.25
Plot of uolume venus
r
using data imported frorn an Ercel file.
15.5 lVatrix Computations with MATLAB fu
explained earlier, MATI/,B offers many tools for matrix operations and manipuladons. Thble 15.4 shows er) A=[0 5 0;8 3 7;9 2
91
A
0 50 8 37 929 >> B=tA 6 2;7 2 3;1 3 El
4 0 z
72 3 1 3 4 >> C=[1; 2; 5l 12 5
>> A+B
ans
=
4It2 15 5 10 1
10 5
>> AB alfD
_A

_1
')
r14 tt
f
LJ
>>3*A
0 15 0 24 9 21zt
o
zt
>>A*B
35 10 15 60 75 35 31 77 50 >>A*C AIfD

10 33
>>det (.4)
ans
I
_4tr' Figurel5.26
Ihe solution to Example 15.5.
448
=
41
15.5 Mernnr CoupurerroNs wrrH MAILAB The formulation of many engineering problems leads to
a
449
qrstem of dgebraic equations. As you
will learn later in your math and engineering classes, there are a number ofwaln to solve a set of linear equations. Solve the following set of equations using the Gauss elimination, by invening dte [r4] matrix (the coefficients of unknowns), and multiplying it by i6] matrix (the values on the right hand side of equations. The Gauss elimination method is discussed in detail in Section 18.5. Here, our intent is to show how to use MAITAB to solve a set of linear equations.
2qI x2* 4:13 3x1*2x2*4xu=i2 5qx2t34:17 For this problem, the coefficient matrix [r4]
"nd
the righthand side matrix
Ibl
are
",:l', ii].,,u,,, ={1i\
I(e will first use the Mltil,AB matrix left division operator \ to
solve this problem. The
\
operator solves the problem using the Gauss elimination. W'e then solve the problem using the inv command.
To get started, select "MATLAB Help" from the Help menu.
>>A
=
12 7.
Li3 2 4;5 1 3l
11 IJ
24 l_ 3
J
>>b = lL3t32iL71
1\ 
l_
t
JZ L7 >>
X=
x = .4,\b
2.0000 5.0000 4.0000 >>x = invla'1 *5 X= 2 .0000 5.0000 4.0000
450
CHaprsn
15
MAILAB
:
:
Note that if you substitute the solution xr: 2, x2 5, and, x3 4 into each equation, you find that they satisfy them. That 2(2) + 5 + 4= 13,3Q) + 2(5) + 4(4) 32, and
k
:
5Q)5+3(4)=17. llr.:    :il r.r:i
15.6
"..:.l
Curve Fitting with MATLAB In Section 14.8, we discussed the concept of curve fitti"g. MAIIA.B offers a variety of curve' fitting options. V'e will use Example L4.ll to show how you can also use MAlfAB to obtain an equation that closely fits a set of data points. For Example 14.11 (Revisited), we will use the command POLYFIT (x, y, n) , which determines the coefEcients (ca, c1, c21 . . . t e) of a polynomial of order a that best fits the data accordrng to:
!= cox'*
c1x"l
*
c2xo2
*
car"3
* "' *
co
Find the equation that best fits the following set of data poins in Thble 15.13. In Section 14.8, ploa of data points revealed that the relationship betrveeny and x is quadradc (second order polynomial). To obtain the coefficients of the second order polynomial that best fie the given daa, we will rype the following sequence of commands. The MAIIA,B Command Window for Example 14.11 (Revisited) is shown inFigte 15.27:
>>format compact
))x=0:0.5:3 ))! = t2 O.75 0 0.25 0 0.75 2J >> COefficients = poLtrfit (x,y,2)
0.00
2.00
0.50
4.75
1.00 1.50
0.00
2.00 2.50 3.00
0.25 0.00 Q,75
2.04
I
Figuru
15.27
T[e Comnand Window for Example
l4.ll (Rwhited).
15.7 Upon execution of the d0 :
iji 1i
,l
1, c1 : 3t
polyfit
and c2
=
Snvmor.rc M.mrBuerrcs wrrH
command,
MAILAB
Mdfl{B will return the following
2, which leads to the equationy
:
x2

451
coefficients,
3x t 2.
.''...'.''
fl5.7 Symbolic Mathematies with
MATLAB
use MAI.AB to solve engineering problems with numerical values. In this section, we briefy explain the syrnbolic capabilities of MATLAB. In rymbolic mathematics, as the name implies, the problem and the solution are presented using symbols, such as x instead of numerical values. \Wb will demonstrate MALAB's symbolic capabilities using F.xamples 15.7 and 15.8.
In the previous sections, we discussed how to
\7e will use the fo[owing functions to perform MAnA.Bt qymbolic operations,
as
Thble 15.14.
f(*):*5x+6 rtQ): * t
: (x+ 5)2 fsk):5*tr2xY
fi(r)
I
Function
Description of the Function
ExamFle
It
Flx = qfm('x^25\+6') F2x = sfm('x3')
creates a
sfmbolic
function.
'When
F3x F4x possible,
it facorizes
the function into simpler terms. simplifies the funcdon.
simplify
It
expand co11ect,
It expands the function. It simplifies a s)'mbolic expression
solve
It
aryn]
It
vavlve
nt \ f!,
min,
max)
by collecting like coefficients. solves tfie orpression for its roots. plots the function f in the range of min and max.
= sfm('(x+5)^2') = sym('51y+2\y')
Flx = x^2*5*x*6
F2x: x3 = (x*5)^2
p31
F4x=
5\y+2\y
faao(Fxl)
(x2).(x3)
simplifr(Flx/F2x) expand(F3x)
x2 x^2*10\*25
collea(F4x)
7*x2*y
solve(Flx)
x=2andx=3
ezplot(F1x,0,2)
See
Figure 15.27
shown in
452
Cru.prnn
15
MAilAB
t
Figuru
15.28 lhe ezplot
for Erample l5J;
see lhe last row in
labh
1514.
::::l.'I
Solutions of Simuftaneous Linear Equations In this secdon, we will show how you to a set oflinear equations.
c:rn use
MAIIABI symbolic
Consider the following three linear equations with three unknowns:
2x*y*z=t3 3xt 2y * 4z:32 5x !t3z=t7 In MAILAB, the solve equations. The basic form
solvers to obtain solutions
I
y, arrdz
to obein solutions to symbolic algebraic of the solve command is solve('eqal r, teqn2t,
command is used
. , 'eqnr ) . fu shown below, we define each equation first and then use the goLve command to obtain the solution.
>>equatioa 1 = '2*x+y+z=13'i >>equatJ.on 2 = I 3*2i1!*y+4*z=32' i >>equat,Lon3 = '5*xy+3*z=L7' i >>[x,Yrz] = golve(equatlon l,equatlon 2,equation 3)
15.7 The soludon is given
by, :
2,
!:
Svmnor,rc
5, and a
:
Menrpuencs wrrn MAILAB
453
4. The MAIL"EB Command Vindow for
Example 15.8 is shown in Figure 15.29.
H '::
Figure
15.29 I[e
::1r: :
solution of the set of linear equations discussed in Eranple 15.8.
ll
As we said at the beginning of this chapter, there are manygood textbools that discuss the capabilities of MAIfAB to solve a firll range of problems. Here, our intent was to introduce only some basic id6as so that you can perform some essential operadons,'fu you continue your engineering education in other classes, you will lsarn more about how to use MAILAB effectively to solve a wide range of engineering problems.
454
CrrnPrsR
15 MAILAB
PnonreMs
455
SUMMARY Now that you hane reached this point in the text you should:
.
MAILAB is a tool that can be used to solve engineering problems. Moreover, you MAILAB to present the results of an analysis in chan form. You can input your own formulas or use the buihin funcdons provided by MAII,AB. know that can use
o know how to edit the content of a MIILAB file.
.
be familiarwith MAILABI builtin functions. o know how to import data files into MAILAB.
"
. . .
r5J.
Using the
know how to creirte a proper engineering chart using MAILAB. know how to perform mauix computations with MAIIAS. be
familiarwith MAIIA.8I curvefiting capabilities.
be familiar with
MAILABI symbolic mathematics capabilities.
MAfLAB Help menu, discuss howthe fo[
lowing functions are used. Create a simple example, and demonsuate the proper use of the function. a. ABS (X)
b. TIC, TOC
c. SIZE (x) d. FD( (x) e. FLOOR
(x)
f.
CEIL (x) g. CALENDAR r5.2.
Create a table that shovss the water pressure in lb/in'z in a pipe located at the base of the water tower as you
varythe heightofthewater in incremen$ of 10 ft.Also, plot the water pressrue 0b/in1 versus the height of water in feet. V'hat should the water level in the water tower be to create 80 psi of water pressrue in a pipe at the base of the water tower? 15.3. As we explained in Chapter 10, viscosit,' is a measure of how easily a fuid fows. The viscosity of water can be determined from the following correlation.
In
Chapcer 10, we discussed fluid pressure and the role of water towers in small towns. IJse MAILAB to create a able that shows the relationship berween the height of water above ground in the water tower and the water pressure in a pipeline located at the base of the water tower. The relationship is given by
p: :
p
:
g: h:
/:\ : ,r1g\T"/
where ;r,
=
viscosiry (Nls. rn'z)
T = temperature (IQ ct=2.414x 105NA.m2
pgh
where
P
11
c2= 247.8K water pressure at the base of the water tower in pounds per square foot (lbiff)
density ofwater in slugs per cubic foot (p 1.94 slugs/ff) acceleration due to gravity (S
= 32.2 ftl*)
height ofwater above ground in feet (ft)
:
cz= l40K Using MAITA3, create a able that shows the viscosas a function of temperature in the range of 0'CQ73.15 K) to 100"C(373.15 K) inincrements of 5'C. Also, create a graph showing the value of viscosity as a function of temperature.
ity of water
456 15.4.
CHePrsR
15 MAILAB
Using MAIIAB, create a table that shows the relationship between the unia of temperature in degrees Celsius and Fahrenheit in the range of 50oC to
The frontal area./4 represents the frontal projecdon area and could be approximated simply by multiplying 0.85 times the width and the height of a rectangle that oudines the ftont of the car. This is the area that you see when you view the car from a direction normal to the front grill. The 0.85 factor is used to adjust for rounded corners, open space below the bumper, and so on. To give you some idea, rypi"d drag coefficient values for sports c:us are between 0.27 to 0.38 and for sedans are between 0.34 to 0.5. The power requirement to overcome air resistance is computed by
of the cart
150"C. Use increments of 10"C. 15.5.
t5.6.
15.7.
t5.8.
t5.9.
1510.
Using M,{ILAB, create a table that shows the relationship among units of the height of people in centimeters, inches, and feet in the range of 150 cm to 2 m. Use increments of 5 cm. Using MAILAB, create a table that shows the relationship among the unim of mass to describe people's mass in kilograms, slugs, and pound mass in the range of 20I
iE
Integral Facorialr forexample,
!
Not equal to
i
, ,,
,
*f: !?q
it' i*,"
Frequency Midpoint Rarye
fn
5059 6A69
3
7A79
8089 9A99
i
tc
)4.>
74.9
64.5
74.9
9
//+.>
6
84.5
74.9 74,9
3
94.5
74.9
tc
(*
 7)'f
*20.4 1248.5 540.8 10.A *0.4 1.44 552.96 9.6 19.6 1152.5 i ' E(rV)2f=34g6
Using Equation (I9.7), the mean of the scores is
>("/)= re47 = 74.9 i: T 26 Similarly, using Equation (19.8), we cdculate the sandard deviation, as shown in Table 19.8.
n: 2f: nt:25
26
It4%
\25
. l,,11'rarit..I,
Normal disuibution is discussed next.
11.8
.l .: .:f.rli::,:lli.',i.I
 
rtii
:,


_:l
19.5 NonrvrarDrsrnrsurroN
587
19.5 NormalDistribution In Section 19.1, we explained what we mean by a statistical e"Feriment and outcome. Recall that the result ofan experiment is called an outcome. In an engineering situation, we often perform enperiments that could have many outcomes. To organize the outcomes of an experiment, it is customary to make use of probability distributions. A probability distribution shows the probability values for the occurrence of the outcomes of an ."T'eriment. To better undersand the concept of probability disuibution, let's turn our affenuon to Example 19.2. Ifwe were to consider the chemistryrcst as an experimentwith outcomes represented bystudent scores, then we can calculate a probability value for each range of scores by divifing each frequency by 26 (the total number of scores). The probability disuibution for F:rample L9.2 is given in Tirble 19.9. From examining Tirble I9.9, you should note ttrat the sum of probabilities is 1, which is rue for any probability disuibution. The plot of t}re probability distribution for Example 19.2 is shown in Figure 19.4. Moreover, if this was a grpical chemistry test with rypical
Range
5059
6069 7079 8089
9099
Probabilitv
Frequency 3
0.1 15
26
0.192
26
1
9
0.346
26 5
0.231
26 3
0.115
26
}p=l
h
0.250 0.200
P
0.150 0.100 0.050
D
Figurelg.4
Plot of probability distribution
for Elample
19.2.
0.0m
i
:
1
I
588
CH^IITSR
19
PnosABrlrryeNo Sransrrcs rN Er.IcrNEsRrNc students, ttren we might be able to use the probability distribudon for this class to predict how srudenrs might do on a similar test next year. Often, it is difficult to define what we mean by a typical class or a tfpical test. However, ifwe had a lot more students take this test and incorporate their scores into our analysis, we might be able to use the results of this eirperiment to
predict rhe ourcomes of a similar tesr to be given later. As the number of students taking the tesr increases (leading to more scores), the line connecting the midpoint of scores shown in Figure 19.4 becomes smoother and approaches a bellshaped curve.'We use the next example to funher explain this concept.
In order to improve the production time, the supervisor of assembly lines in
a manufacturing sening of computers has studied rhe time that it takes to assemble ceftain parts of a computer at various stations. She measures the time that it takes to assemble a specific part by 100 people at different shifts and on different dqrs. The record of her study is organized and shown in Thble 19.10.
TABLE
I
1
19.19
Dgta Pgrtaininq to Example 19.4
TimeThatlt t"ker aPenson
itoAssemblethe
.
Part (minutes) Frequency
Probability 0.05
5
8
0.08
I
7 8
II
0.I
t5
0.15
9
17
0.17
10
t4
o.r4
1l
t1
0.13
l2
8
0.08
t3
6
0.06
r4
3
0.03
Based on data provided, we have calculated the probabilities corresponding to the time intervals that people took to assemble the parts. The probability distribution for Fxample 19.4 is shown in Thble 19.10 and Figure 19.5. Again, note that the sum of probabilities is equal to 1. Also note that if rve were to connect dre midpoints of time results (as shown in Figure 19.5), we would have a curve that approximates a bell shape. As the number of data points increases and the intervals decrease, the probabilitydistribution curve becomes smoother. A probability distribution that has a bellshaped cun'e is called a nornaal distribution. The probability distribution for many engineering experiments is approximated by a normal
distribution.
19.5 NonruarDrsrnrsurroN
589
0.18 0.16 0.1"4
o.L2 0.10 0.08 0.06 0.04
I
0.02
tigurelg.S
0.00
8910rL Time (minutes) 
...tdrnn
The detailed shape of a normaldistribution curve is determined by its mean and standard deviation values. For example, as shown in Figwe 19.6, an enperiment with a small standard deviation will produce a tall, narrow curve; whereas a large sandard deviarion will result in a shon, wide curve. However, it is important to note that since the normal probabiliry distribution represents all possible outcomes of an experiment (with the total of probabilities equal to 1), the area under any given normal distribution should always be equal to 1. Also, note normal disaibution is qfmmeuical about the mean. In statistics, it is custornary and easier to normalize the mean and the sundard deviation values of an enperiment and work with what is called the standard norrnal dis*ibutioa which has a mean value of zero (x : 0) and a standard deviation value of 1 (s = l). To do this, we define what commonly is referred to as a z score acrr,rding to
z: xV
fi9.e)
J
In Equation (19.9), arepresenc the number of sandard deviations from the mean. The mathematical function that describes a normaldistribution curve or a standard normal curve is ratfier complicated and may be beyond the level of your qurent understanding. Most of you will learn about it later in your statistics or engineering classes. For now, using Excel, we have generated a table that shows the areas under ponions of the standard normaldisaibudon curve, shown in Thble 19.1 1 . At this stage ofyour education, it is imponant for you to know how to use the table and solve some problems. A more detailed explanation will be provided in your future classes.
f
Ihe shape of a nonnal dishibntion curve
[y its
will next demonsffaJe how to
use
Thble 19. 1 I , using
A
Figurelg.6
determined
'We
as
mean and
standard deviation.
/\
/*:""\ Small standard
large standard
deviation
deviation
a
number of example problems.
iiii
ffi
Note that the standard normd curve is qmrmetrical about the mean.
z=1.@
Mean:0
z =3.N
z=2.@
t:i o
e t
0.0000 i O,AL 0.0040 i, a.oz 0.00s0 1 ,0.03 0.0120 i ,'A.M 0.0160 1 i0.05 0.0199 10.06 a.0239 iit':a.97 0.0279 I ]O.OS 0.0319 1
i
Z
A
0.51 0,1950 r.o2 a.3461
O.52 0.1985 r.03 0.3485 0.53 0.2019 La4 a350s 0.54 0.2054 1.05 0.3531
Z 1.53
r.54 t.55
t,56
0.2088 r.06 0.3554 1.57 0.2123 r.07 a3577 1.58 0.2157 r.08 0.3599 t.59 0.2190 1.09 0.3621 1.6 0.2224 1.1 0.3643 1.6r i ioos 0.0is9 0.6 0.2252 r.rl 0.i665 r.62 i lO.r 0.0398 0.61 0.2291 r.r2 0.3686 1.63 i)t ,0.11 0.04i8 a.62 0.2324 t,r3 0.3708 l.g* ,o.tz 0.a478 0.63 0.2357 L.r4 0.3729 r.65 r 0.13 0.0517 O.g+ 0,2i89 r.15 0.3749 r.65 t o.r4 0.0557 a,65 0.2422 1.16 0.3770 r.67 i o.t5 0.0596 0.66 0.2454 r.r7 0.3790 1.6s i .,o.ta '0.06i6 0.67 0.2486 t.tg 0.3810 1.69 ',,,,a.L7 '0.0675 0.68 0.2517 1.r9 0.3t30 t,7 i.r0.r8 ,0.A714 0.69 0.2549 rA 0.3849 r.7r i ',0.19 0.0753 oJ 0.258a L.zr 0.3869 lJz ', 0a' :,0,029s o,7l 0.26il 1.22 0.3s88 L:73
0.55 0.56 o,57 o.58 0.59
A
0.4370 0.4382 0.4394 0.4406 0.4415 0.4429 0.4441 0.4452 0,4463 0.4474 0.44s4 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 0.4554 0.4564 0.4573 0.4582
z
Ai
A
z
2.O4 0.4793 '::2,55 0.4946 ,.a6 2.O5 0.4798 2.56 0.4948 ?,O7 2.06 0.48A3 '2;57 0.4949 3,A8 2,O7 0.4805 ,2,58 0.4951 3.09 2.A8 0:4812 2.59 0.4952 3.L 209 0.4817 2.6 0.4953 3.r1 2.t 0.4821 2.61 0.4955 3.r2 2.rr 0..4826, 2.62 0.4956 3.r3 2,t2 0;483A " 2161' 0.4957 !.L4 2.13 0;4814' \& 0.4959 3.15 2,14 0.4s35 2,65 0.4960 3.16 2.L5 0:4842 ,',2.66 0.4961 5.L7 2.16 0,4s46 2,67 ' 0.4962, 3.18 2,17 0,;4850' '2.68, 0.4963,' 3.r9 2.18 0,4854 2.69 0.4964 3.2 2.t9 0,4857 :2:7 0.4965 3.21 22 0,4861 2.7t ' 0.4966 3.22 2,2t 0,4864 2.72 0.4967 3.23 2;22 0.4s65' 2.73 0.4968 324 223 0,4871 ',2,74 0.4969 3,25 2.24 0.4875 2J:5 0.4970, ,.26
0.4989 0.4959 0.4990 0.4990 0.4990 A.4991 0,4991
0.4991 0.4992 0.4992 0.4992 0:4992 0.4993 014993
0.4993 0.4993 0.4994 0.4994 0.4994 0,4994 0.4994 Continucd
590
19.5 Nonruar DrsrnrsurroaT
o.2t 0.0832 0.72 022 0.0871 0,73 o.23 0.091A O,74 0.24 0.0948 0.75 0.25 0.0987 0.76 0.26 0.1026 0,77 a.z7 0.1064 0.7& 0.28 0.1103 0.79 a.29 0.1141 0.8 0.3 0.1179 0.81 0.31 0.1217 0.82 o.32 0.1255 0.83 0.33 0.1293 0.84 a.3.4 0,1i31
0.85
o.35 0.1368 0.86 0.36 0J4A6 0.87 a$7 0.1443 0.88 0.38 0.1480 0.E9 439 4.15t7 0.9 o.4 0.1554 0.91 o.At 0.1591 0.92 0.42 0.1628 0.93 o.43 0.1664 0.94 o.u 0,1700 a.95 a,45 0.1736 0.96 0.46 0.1772 0.97 o,47 0.1808 0.98 0.48 0.1844 0.99 o.49 0.1879 I 0.5 0.1915 1.0r
a.2642 0.2673 0.27A4 0.2734 0.2764 0.2794 0.2823 0.2852 0.2881 0.2910
L,23
t.24
L25 L.26
r.27 1.28
L29 L.3
t,'r 1,32
0,29i9
L.33
0.2967 0.2995 a.3023 0.3051 0.3078
t.Yt
0.ir06
r,35 t.36 r.37 r.38 1.39
0.3133 L,4 0.3159 r.4l 0.3186 1.42
0.j212
r.43
0.3238 t.M 0.3264 r.45 0.3259 t,46 0.3315 L.47 0,3340 1.48 0.3365 t.49 0.3389 t.5 0,3413 1.51 0.3438 t.52
0.3907 t,74 0.3925 r.75 0.3944 rJ6 0.3962 r,77 0.3980 1.78 0.3997 L:79 0.4015 1.8 0.4032 1.8r 0.4049 t.82 0.4066 1.83 0.4082 t.84 0.4099 1.85 0.4115 1.86 0.4131 r.87 0.4147 1.88 0.4162 1.89 0.4177 r.9 0.4192 1.91 0.42A7 L92 0.4222 19t 0,4236 t.94 0.4251 t.95 0.4265 r.96 a.4279 r.97 0.4292 1.98 0.4306 r.99 0.4319 2 0.4332 2.Or 0.4345 2.02
a.457
2.O5
0.4591 0.4599 0,4608 0.4616 0.4625
2.29
0.463i
2.3
0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 0.4713 0.4719 0.4726 0.4732
0.47i8
2.25 2,26
2,27 2.28
2.3t 2.32 2.33
2.34 2.35
2.36 2.37
238 2.39 2.4
2.4t 2.42 2.43
2.4* 2.45
0.4744 2.46 0.4750 2.47 0.4756 2.4 0.4761 2.49 0.4767 2.5 0.4772 2.5r 0.4778 2.52 0.4783 2.53 0.4788 2.54
591
2J6 0.4971 ?.27 0.4995 2,77 0.4972 3,28 0.4995 2.78 0,4973 3.29 0.4995 2.79 0.4974 33 0.4995 2,8 0.4974 3.?t 0.4995 2.8r 0.4975 3.32 A.4995 2.82 0.4976 3.33 0.4996 2.83 0.4977 3.34 0.4996 2.84 0.4977 3.35 0.4996 2.85 0.4978 3.36 0.4996 2.86 0.4979 3.37 0.4996 2.87 0.4979 3.38 0.4996 0.49r t 2.88 0.4980 3.39 0.4997 0.4913 2.89 0.4981 3.4 0.4997 0.4916 2.9 0.4981 3.4r 0.4997 0.4918 2.9r 0.4952 3,42 0.4997 0.4920 2.92 0.4982 3.43 0.4997 0.4922 2.93 0.4983 3.4* 0.4997 0.4925 2.94 0.4984 0.4997 '.45 0.4997 0.4927 2.95 0.4984 1.46 0.4929 2.96 0.4955 3,47 0.4997 0.4878 0.4881 0.4884 0.4887 0.4890 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909
0.4931 2.97 0.4985 5,48 0.49i2 2.98 0.4956 3.49 0.4934 2.99 0.4986 3.5 0.4936 0.4987 3,5r ' 0.4938 3.0r 0.4987 3.52 0.4940 0.4987 3.53 '.O2 0.4988 0.4941 3.O3 0.4943 3.04 0.4958 0.4%5 3.05 0.4989 3.9
0.4997 0.4995 0.4998 0.4998 0.4998 0.4998
0.5000
Using Table 19. 1 1, show tiat for a standard normal distribution of a data set, approximately 68%o of the data will fall in the interval of s to s, about 95olo of the data falls between 2s to 2s, and approximately all of the data points lie benreen 3s to 3r. In Thble t9.ll, z: 1 represents one standard deviation above the mean and 34.13o/o of the total area under a sandard normal curve. On the other hand, s, : I represen$ one sran; dard deviation below the mean and 34.73o/o of the total area, as shown in Figure 19.7. There, fore, for a standard normal distribution, 6870 of the data fall in the interval of a :  I to g = 1 (r to s). Similarly, z: 2 and z = 2 (nvo standard dwiations below and above the
s92
Cnepren
19
PnosABrrrrv.oxo Srarrsrrcs nr ENcnvssRrNc mean) each represent 0.4772o/o of the toal area under the normal curve. Then, as shown in Figure 19.2 95o/o of the data fall in the interval of 2s to 2s. In the same way, we can show
rhat99,7o/o(forz= 3then.r4 =0.4987and.2:3thenA:0.4987) ordmostallofthe
data points lie between
3s to 3s. A  0.4772 + 0.4772*0.95
A=03413+0.3413=0.68
z:1.00 e:1.00 e=1.00 e=1.00
;
tigure
19.7
The area under a norlnal curve
for
z=2.00
z
=2.ffi
Example 19.5.
For Example 19.4, calculate the mean and standard deviation, and determine the probability that it will take a person between 7 and, ll minutes to assemble the computer parts. Refer to Table 19.12 when following solution steps.
r Time r (minuts) ;x
Frequency
*f
tc fr
5
25 48
4.22
89.04 82.95
77 r20
2,.22
t.22
54.2t' 22.33
x
6 7
 v)'f
f
1l
8
(*
4 )1
9
1'7
r53
Q.22
a.82
10
r4
140
1l t2
L3
r43
0.78 1.78
4r.r9
B
96
14
6
t4
3
78 42
2.78 47R 4.78
2*f=gzz
x: 2*f n :
K:9.22
minutes
': ,ffi:'{#:2'28minutes
8.52
6r.83
.
s5.73 168.55
2(xx)2f=515.16
19.5 NonuelDrstnnrrrron
593
The value 7 is below the mean valae (9.22) and the z value corresponding to 7 is deter
minedfrom
xV 79.22 ,: ;: rE:
o.97
From Table l9.ll, A = A334O. Similarly, tlre vdue 1 1 is above the mean value and the sscore corresponding to 11 is computed from
It  9.22 :0,78 z: xV t 2.28 : From Thble l9.ll, A= 0.2823, Therefore,
the probability that it will take a penon be+ 0.2823 0.6163 as shoqrn
tween 7 and I L minutes to assemble the compffer paft is 0.3340
:
in Figure 19.8.
A
z0.97
I
:
03340 + 0.2823 = 0.6t63
z=0.78
figuretg.g
Area under tfie probability dishibuthn curtte for Emtnple 19.6.
For Example 19.4, deterrnine the probability that it will take a person longsr than 10 minutes to assemble the computer parts. For this problem, the .6score is
xV ro9.22 Zff:0.34 =;=: ": From Thble 19.11, A = 0.1331. Since we wish to determine the probabiliry that it tak"s longer than 10 minutes to assemble the part, we need to calculate the area 0.5  0.1331 : 0.3669, as shov"n in Figure 19.9. The probability t6o il lyill take a person longer than 10 minutes to assemble tfre compurer pan is approximately 0.37.
594
Cneprsn
19
Pnonasrr,rrverp Sterrsrrcs
rN ENcrrvnsR$Ic
A:0.L331"
z = 0.34
I
Figurelg.g
Areas under the probability distribution curve for Erample 19.7. ril.
In closing, keep in mind that the pqpose of this chapter was to make you arvare of the importance ofprobability and statistics in engineering, not to provide a detailed coverage ofstatistics. As you ake setistics classes and advanced classes in engineering, you will learn much more about stadsticd concepts and models.
SUMMARY Now that you have reached this point in the text n You should undersand the imporant role of statistics in various engineering disciplines. . You should be familiar with basic probability and statistics terminologies. . You should have a good underssnding of frequency distribution and cumulative frequenry disnibution and what kind of information they provide. . You should have a good grasp of statistical measures of cenual tendenry and variation. . You should know how to compute basic statistical information such as mean, variance, and sandard deviation for a set of daa points. . You should know what is meant by normal disuibution and standard normal distribution. . You should know how to use Thble 19.1 1.
of a test for an
engineering class of 30 students is shown here. Organize the data in a manner similar to Thble 19.1 and use Excel to creare a
l9J. The
scores
19.2.
t9.3.
histogram.
For Problem 19.1, calculate the cumulative frequency and plot a cumulativefrequency polygon. ForProblem 19.1, usingEquations (19.1) and (L9.6), calculate the mean and sandard deviation of the class scores.
Scores: 57, 94, 8I, 77, 66, 97, 62, 86, 7 5, 87, 9I, 7 8, 61, 82, 74,72,70, 88, 66,75, 55, 66, 58, 73, 79,
51,63,77,52,94
t9.4.
For Problem 19.1, using Equations (19.7) and (19.8), calculate the mean and standard deviation of the class scores.
PnosLEnIs 595 r9.5.
For Problem 19.1, calculate the probability distribu
19.9.
tion and plot the probabilitydistribution curve. r9.6.
In order to improve the production time, the supervisor of assembly lines in a manufacturing setting of cellular phones has studied the time that it akes to assemble cerain parts of a phone at various stations. She
 i
2 x 4 Lumber Steel Spherical Balle (cm) Width (ir.)
The record of her study is organized and shown
3.50
3.40
1.00 0.95 1.05 1.10 1.00 0.90 0.85
20
3.65 3.35
0.95
28
3.60
0.90
in the accompanying able.
3.55
Time that it takes a person to assemble the part (minutes)
Frequency
4
r5
5
6
are
]':"""1
measures the time that it akes to assemble a specific pan by 165 people at different shifts and on different days.
Determine the average, variance, and standard devia
tion for the following parts. The measured values given in the accompanying table.
3.45 3.60 3.55 3.40
',
I
1.05
34
191.
t9.8.
8
28
9
24
10
L6
Plot the data and calculate the mean and sandard deviation. For Problem 19.6, calculate the probabiliry disuibution and plot the probabilitydisuibution curve. Determine the average, variance, and standard dwi
ation for the following parr. The measured values are given in the accompanying able.
Screw length
(cm)
19.X0.
ance, and standard deviation for the cereal boxes. Does
the manufacturer's information noted on the box fall
within your meruurement? l9.ll. 19J2.
Pipe Diameter (in )
t.25
2.55 2.45 2,55 2.35
1.18 1.22 1.15
2.60
r.l7
2.40 2.30
L.r9
2.40 2.50
1.18 1 la
2.50
t.25
The next time you make a trip to a supermarket ask the manager if you can measure the mass of at least 10 cereal boxes ofyour choice. Choose the same brand and the same size boxes. Tell the manager this is an assignment for a class. Repon the anerage mass, vari
Repeat Problem 19.10 using tluee other products, such as cans ofsoup, tuna, or peanu6. Obtain the height, age, and mass ofplayers for your favorite professional basketball team. Determine the average, variance, and sandard deviation for the height, age, and mass. Discuss your findings. Ifyou do not like basketball, perform the experiment using daa from a soccer team, football team, or a sports team of your choice.
r9J3.
For Example 19.4, determine the probability that it will take a person benrreen 5 and 10 minutes to assemble the computer parts.
1914.
For Example 19.4, determine the probabiliry that
will take a person longer than 7 minutes to
1.22
it
assemble
the computer parts. 1915.
For Problem 19.6 (assuming normal distribution), determine the probability that it will take a person between 5 to 8 minutes to assemble the phone.
596 Class
Csaprcn
PnosABrlrrr.al.tn Sranrsrrcs rx ErvcrxnrnrNc
are
pafonned in
class.
Your instructor will pass along an unopened bag of Hershey's kisses. You are to estimate the number of kisses in the bag and write it down on a piece of paper. Your instructor will then collect the daa and share the results with the class. Your assignment is to organize the data per your insructor's suggestion and calculate the mean and standard dwiation. Compute the prob
ability distribution. Does your data disuibution ap
19.17.
proximate a normal distribution? Answer any additional questions that your instructor might ask. Your instructor will ask for a volunteer in class. You are to estimate his or her height in inches (or in cm) and write it down on a piece of paper. Your instructor will then collect the daa and share the results with the class. Your assignment is to organize the data per your
instrucort suggestion and calculate the mean and sandard deviation of the data. Compute the probability
1918.
a normal disuibution? Answer any additional ques
Experi.mentsProblems I 9. I 6 througb I 9.20 are acpn
immx that 19.16.
19
distribution. Does your data disuibution approximate a normal disuibution? Answer any additional quesrions that your instructor might ask Your instrucor will ask for a volunteer from class. You are to estimate his or her mass in lb. (or in kg) and write it down on a piece of paper. Your instructor will then collect the data and share the results with the class. Your assignment is to organize the data per your insmrctor's suggestion and calculate the mean and sandard dwiation of the data. Compute the probability disuibution. Does your data disuibution approximate
19.t9.
$"20,.
t9.2r.
tions that your instructor might aslc You are to write down on a piece of paper the number ofcredits you are taking this semester. Your irutructor will then collect the data and share the resuhs with the class. Calculate the mean and standard deviation of the data. Assuming a normal distribution, determine the probability that a student is taking benreen 12 to 15 credits this semester. !?hat is the probability that a student is taking less than 12 credits? You are to write down on apiece of paper how much (to the nearest penny) money you have on you. Your instnrctor will then collect the data and share the results with the class. Your assignment is to organize the daa per your instructort suggestion and cdculate the mean and scandard deviation of the data. Assuming a normal distribution, determine the probability that a student has between $5 to $tO.'What is the probabiliry that a student has less than $10? You are to ffiite down your waist size on a piece of pa
per.
If you don't know your waist size, ask your in
structor for
a
measuring tape. Your instructor will then
collect the dam and share the results with the class. Your assignment is to organize the data per your instruccort suggestion and calculate the mean and standard deviation of the data. Assuming a normal disuibution, determine the probability that a student will '\V'hat have a waist size that is less than 34 inches. is the probability that a student will have a waist size that is between 30 in. to 36'n.?
CHAPTER
ENcTNEERTNG
r lr r
conomic considerations play
20
EcoNoMrcs
a
vitat role in product and service development and in engineering
design decision making pfocess.
597
598
Cnepren20 ExcrxnrnrNcEconourcs
in Chapter 3, economicfactors alwals play important roles i.n mgineering daign decision making. Ifyou drsigrc a product that is too erpmsiae to rtantr.faaure, then it cAn not be sold at a price that consurners can afford and still be
As we explained
prof.table to your colnpanJ/. Thefact is that companies design producx andprouide smtices not only to rnahe our liaes bener but ako to make rnone/ In this section, we will discuss the basics of engineering econornics. The information proaidcd here not only applies to mgineering projecx bwt can ako be applied to financing A car or A house or borcowingfrorn or inaesting mons! i.n bank* Some of you rnd! want to apply the knowledge gained here to dzterrnine lour srudent ban payrnmts or lour credit card paltments. Therefof€, t!)e aduise you to deuelop a good und.erstanding of mgineering economics; the information presmted here could help you manage yoar rnone! more wisely.
20.1 Gash Flow Diagrams Cash flow diagrams are visual aids drat show the flow of costs and revenues over a period of time. Cash flow diagrams show whm the cashfuw occurs, tlte cashfuw magnitudc, and' whaher the cash fnw is out ofyur pocha (cost) or into your pocha (reumae). It is an imponant visual tool that shows the timing, the magnitude, and the direction of cash flow. To shed more light on the concept of the cash fow diagram, imagine rhatyouare interested in purchasing a new car. Being a firstyear engineering student, you mqf not hane too much money in your sarings account at this time; for the sake of this example, let us say that you have $1200 to yotu name in a sarings account. The car that you are interested in buying costs $ 15,500; let us further assume that including the sales tax and other fees, the total cost of the car would be $16,880. Assumingyou can afford to put down $1000 as a down payment for your new shiny car, you askyour bank for a loan. The bank decides to lend you the remainder, which is $15,880 at 87o interest. You will sign a contract that requires you to pay $315.91 every month for the next five years. You will soon learn how to calculate these monthly payments, but for now let us focus on how to dravr the cash fow di"Sr. The cash fow diagram for this activity is shown in Figure 20.1 . Note in Figure 20.1 the direction of the arrows representing the money given to you by the bank and rhe payments that you must make to the bank over the next five years (60 months).
$1s,880
I
Figure2o.t
A cash flow diagram
for honowed
money and the monthly payments.
$315.91
20.2
Srtvrpr,s AND
CoupouNp [NrsREsr
599
cash fow diagram for an investment that includes purchasing a machine that costs $50,000 with a maintenance and operating cost of $1000 per year. It is expected that the machine will generate revenues of$15,000 per year for five years. The expected salvage value of the machine at the end of five years is $8000. The cash flow diagram for the investment is shown in Figure 20.2. Agaun, note the directions of anows in the cash flow diagram. Ve hare represented the initial cost of $50,000 and tfi.e maintenance cost by arrows pointing down, while the revenue and the sdvage value of the machine are shown by arrows poindng up.
Drav the
$15,000
$8000
I
0
2
3
4 $1000
t
Figure?0.Z
T[e cash flow diagram
lor Erample 20J.
$50,000
i,
it  ii.1rlfi:lii:ilrllltirriinllilf,illi'riitl
ili.i.liri1ii,r,.l:ir',r.::i
.,:iirlrr,i,rililllii'i.li
20.2 Simple and Compound Interest Interest is the exua money in addirion to the borrowed amount thar one must pa)r for the purofhadng access to the borrowed money. Simph interastis rhe interest that would be paid only on the initial borrowed or deposited amount. For simple interest, the interest accumulated on the principle each year will not collect interest itself. Only the initial principal will collect interest. For example, if you deposit $100.00 in a bank at 6% simple interest, after six years you will have $136 in your account. In general, ifyou deposit the amount P ar a rate of io/o for a period of n years, then the total future valu e F of the P at the end of the ath year is grven by pose
F:P+(PXrXtx):P(r+ni\
(20r)
Compute the future value of a $ 1500 deposit, after eight years, in an account that pqrs a simple interest rate of 7o/o. How much interest will be paid to this account? You can determine the future value ofthe deposited amount using Equation (20.1), which results
in
F:
P(r
*
ni) = r5oo[1 + 8(0.07)]
:
$2340
And the total interest to be paid to this account is
intere*: (p)(n)(i) l:. :::: .
:
(1500x8x0.07) = 634s
600
Cno,prsn20 Excnwrnruc Ecoxourcs
Interestfor BalanceattheEnd Bqfnring of the Year (dollars and cents)
t
tfieYear 60lo
at
(dollars
and
oftheYear, Includirg the Interest (dollare
cents)
and cents)
106.00
,
t12.36
'
3
r12.36
6.00 6.36 6.74
4
I 19.10
7.r4
rv,6.24
,
5
126.24
r33.8r
'
6
133.81
7.57 8.02
100.00 106.00
I 19.10
t4 t.65
Simple interests are very rare these days! Almost all interest charged to borrow accounm or interest earned on money deposited in a bank is computed using conqpound interest The concept of compound interest is discussed next.
Compound Interest Under the compounding interest scheme, the interest paid on the initial principal will also collect interest. To better understand how the compound interest earned or paid on a principal works, consider the following example. Imagine that you put $100.00 in a bank that pq/s you 67o interest compounding annually. At the end of the first year (or the beginning of the second year) you will have $106.00 in your bank account. You have earned inrerest in the amount of $6.00 during the first year. Howwer, the interest earned during the second year is determined by ($106.00X0.06) : $6.36. That is because the $6.00 interest of the first year also collecs 6%o interest, which is 36 cena itself. Thus, the total interest earned during the second year is $6.36, and the total amount available in your account at the end ofthe second year is $1 12.36. Computing the interest and the total amount for the thfud, fouffh, fifth and the sixth year in a similar fashion will lead ro $141.83 in your account at the end of the sixth year. Refer to Thble 20.1 for detailed calculations. Note the difference between $100.00 invested at 6%o simple interest and 60/o interest compounding annually for a duration of six years. For the simple interest case, the total interest eamed, after six years, is $36.00, whereas the total interest accumulated under the annual compounding case is $41.83 for the same duration.
20.3
Future Worth of a Present Amount Now we will dwelop a general formula that you can use to compute the future value Fof any present amount (principd) 4 after nyears collecting zolo interest compounding annually. The cash
fow
di"S"
for this situation is shorrn in Figure 20.3.In order to demonsffate, stepby
step, the compounding effect of the interest each year, Table 20.2 has been developed. As shown
in Thble 20.2, sardng with the principal P, at the end of the first year we will hare P * Pi or P(l + i). During the second year, dre P(l * i) colleca interest in an amount ofP(l + i)i' au;.d. by adding the interest to the P(l * i) amount that we stamed with in the second year, we will have a toal amount of P(L + i) + P(l * i)i. Fae'oling out the P(1 * /) term, we will hare
2O.3 Ftmrnr Wonmr or e PnEseNT Arvrorlxr
I
601
Figure20.3
The cash flow diagram for future
wort[ of a deposit made in the bank today.
Balance at the
Year
Begimiryof
Interest for
theYear
the Year
i1
P
t3 :4 i
P(l + r) P(t + ilz PU + i)3
ll ,A
5
Balance at the Eqd
P+(P)(i)=P(r+i) P0+i) +P(l + DQ)=P(L+i)z
(P)(t P(t + t)(i) P(r
+
P0 + il2 + P(l + i)2(t) : P(r + il3 P0 + il3 + I{1 + i)3(i): P(L + il4 P$+ il4 +P(l + i)4{i\: ?(1 +rt
ilz?)
P(l+
t)4
p0 + i)'Q) PIL + il4(il
P(r +
i),l
P(r +
ilt(i)
ofthe Year,
Inclu,f ing the Interest
P(l + i)L + P(l + i)"11;1: P(l + i)
P0 + il2 doilars at the end of the second year. Now by following Tirbl e 2A.2 youcan see how the interest earned and the total amounr are computed for the third, fourth, fifth, . . . , and the nth yan. Consequently, you c:rn see that the relationship beween the present worth P and the future value.Fof an amount collecting iolo interest compounding annually after a years is given by
F: P(r + i)"
(20.21
Compute the future value of a $1500 deposit made today, after eight years, in an account that of 7o/o that compounds annually. How much interest will be paid to this
pays an interest rate
account?
P,
i,
The future value of the $1500 deposit is computed by subsdruting in Equation Q0.2) for and zl, which results in the amount that follows:
F= p(L + i)n:1500(t + .07)8 = $2577.27 The total interest earned during the eightyear life of dris account is determined by calculating the difference beween the future value and the presenr deposit value.
L ..,._
inwest:
$2577.27

$1500
:
$1O77.27 ::.:,:
,:
:
:':::
r::I
602
CHrprsR20 ENcrNsrRrNcEcoxourcs Many financial instirutions pay interest that compounds more than once a year. For example, a bank may pay you an interest rate that compounds semiannudly (mice a year), or quanerly (four times ayqi, or monthly (12 periods ayar).If the principal Pis deposited for a duration of n yars and the interest given is compounded n periods (or zz dmes) Per year, then the future value.Fof the prin"tpal P is determined from
r=n(t.*)
(20.3)
Compute the future value of a $1500 deposit, after eight years, in an account that paln an interesr rate of 7o/o that compounds monthly. How much interest will be paid to this account?
To determine t'he future value of the $1500 deposit, we substitute in Equation (20.3) for P, i, rn and z. The substitution results in the future value shown next.
/ q{Z) = / s.s7\(8)(tz) I':1500[1+ =1500t1+ J 12/ r2l \ 
\
s262r.73
And the total interest is n
interest: $262I.73
iL,,r*,,r.lr.,l,..,,.

$1500
=
$11.21.73 _i ..
:r
__.i_1
The results of ExamplCI 20,2, 20,3, and 20.4 are compared and summarized in Table 20.3. Note the effecs of simple interest, interest compounding annually, and interest compounding monthly on the total future value of the $1500 deposit.
Exanple Numbet
D qration
Principal (dollars)
Example 20.2 Example 20.3
1500 1500
Example 20.4
1500
lnterest Rate
(y€ars)
Futrrre Yalue (dollarc and centr)
Interest Earned (dollars and cents)
7olo simple
8
2340,00
840.00
compounding annually 7%o compounding
8
2577.27
1077.27
2621.73
112r.73
7olo
monthly
20.4 Errucrrw
20.4
603
INrsREsr RArs
Effeetive Interest Rate If you deposit $1OO.OO in a savings account, at 60/o compounding monthly, then, using Equation (20.3), at the end ofone year you will have $106.16 in your account. The $6.16 earned during the first year is higher than the stated 60lo interest, which could be understood as $6.00 for a $100.00 deposit over a period of one year. In order to aroid confusion, the stared or the quoted interest rate is called the noninal interest rate, and" the actual earned interest rate is called the effeaioe i,ntercet rate. The relationship benveen the nominal nte, i, and the effective rate, ia,, is given by
t&:
('*t)'
(20.4)
where rn represents the number of compounding periods per year. To bener understand the compounding effect of interest, let us see what happens if we deposit $100.00 in an account for a year based on one of the following quoted interests: 6%o compounding annually, 67o semiannually, 60/o qwterly,6olo monthly, and 6o/o daily. Thble 20.4 shows the difference among these compounding periods, the total amount of money at the end of one year, the interest sarned, and the effective interest rates for each case. \[hen comparing t]re five different interest compounding frequencies, the difference in the interests earned on a $100.00 investment, over a period of ayear, may not seem much to you, but as the principal and the time of deposit are increased this value becomes significant. To better demonstrate the effect of principal and time of deposit, consider the following orample.
Totel Number of Conpounding Compounding
Period
Periods
TotalAmount after I Year (dollars and cents)
6.00
60/o
10011+  l:106.09 2/ \
\'
6.09
6.090/o
/ I+=l:106.13 o.otr\4
6.13
6.130/o
6.16
6.160/o
6.18
6.180/o
Annually
I
100(1+0.0O:106.00
Semiannually
2
Monthly
D*ily
/
o.o6
1001
Quanerly
4/
\
12
365
lnterest Effective (dollars Interest andcents) Rate
1oo( r
*
Y)": 106.16 roo(r *#)"' = 106.18
604
CneprsR
20
ENcrNErRrNcEcoNourcs Determine the interest earned on $5000 deposited in a savings account, for 10 years, based on one ofdre following quoted interest rates: 670 compounding annually, semiannually, quarterly, mondrly, and daily. The solution to this problem is presented in Thble 20.5.
Period
Periods
Annually
5000(1
10
8954.23
/ *i), o.oe \m =9030.55 / o.oe \& : eo7o.oe 5o0o(1 .; ) 1 0.06\'20 5ooo(1 *i),,:eoe6e8
Qu".t"rly
40
Motrthlv
120
/ *d) o.o6 \ trto , = e11o'14
i
I
+ 0.00,lo:
and cents)
5000(1
Semiannually
ii'
(dollan
UsrngEq. (16,8) (dollars and cents)
Compounding Compounding
Dnily
5ooo[1
3650
':_'
,.
: :
::.:.::L:.,.:.:,
3954.23
'4030.55
4o7o.oe
4ae6.e8
4710'14
t'
:,.
Determine the effective interest rates corresponding to the nominal rates: (a) 7olo compounding monthly, (b) 16.50/o compounding monthly, (c) 6Vo compounding semiannually, (d) 9o/o
compounding quanerly. We can compute the (a)
i.r=
(b)i.n
i"6.
for each
case by
substituting for
/ * ; \ 1  / *t/o.oz \'2  I (t \, ;) 
i and m n
E4uation
(20 ,4) .
0.0722or7.22o/o
( o.t6j\'2  0.1780 orr7.80o/o = . *. i \, )  = (t  ,:o.o6oe or6.oeo/o
" ry)'
(d) z"s'
: (t .
?)n  ,:o.oe3o ore.3oo/o iirrlfifilii.lii.:liirrif.EJ
i
20.6 PnrsmmVoRrrr
20.5 Prescnt
oF Senrss PeuvrsNT
onArvNurrr
605
Worth of a Future Amount
Let us now consider the following situation. You would like to hare $2000 available to you for down payment on a car when you graduate from college in, say, five years. How much money do you need to put in a cenificate of deposit (CD) with an interesr rate o f 6.50/o (compounding annually) today? The relationship between the future and present value was dweloped earlier and is given by Equation (20.2). Rearanging Equation Q\.Z),wehxe a
' !(r+;)" p=
(20.5)
and substituting in Equation (20,5) for the future value we hane
2N9p ' = (1 + 0.065)t
:
4
the interest rate
i,
and the period
re,
$1459.76
This may be
a relatively large sum to put aside all at once, especially for a fustyear engineering student. A more realistic option would be to put aside some money each year. Then rhe question becomes, how much money do you need to put aside every year for the next 6ve years ar the given interest rate to hare that $2000 available ro you at the end of the fifth year? To answer this question, we need to develop the formula that deals with a series of payments or series of deposits. This situation is discussed next.
20.6
Present Worth of Series Payment or Annuity In this section, we will firsr formulate the relationship between a present lump sum, 4 and future uniform series payments,r4, and then from ttrat relationship we will develop the formula that relates the uniform series payments,4 to a future lump sum F. This approach is much easier to follow as you will see. To derive these reladonships, let us first consider a situation where we hane borrowed some money, denoted by P, at an annual interest rate i from a bank, and we are planning to pay the loan yearly, in equal amouns l, in n years, as shown in Figure 20.4.
I
Figure20.n
The casiflory diagram for a
borrowed sum of money and its equivalent seiles payntents.
605
Cnqprsn20
ElvcrrvsERnrc EcoNourcs To obtain the relationship between P andA, we will treat each future payment separately and relate each payment to its present equivalent value using Equation Q0.5); we then add all the resulting terms together. This approach leads to the following relationship:
AAAAA P+_ (r+4 (1 +;y*G;t+"'+OiAa*0*ny
Q0''61
As you can see, Equation (20.O is not very userfriendly, so we need to simplify it somehow. 'What ifwe were to multiply borh sides ofEquation Q0.6) by the term (1 + z)? This operation results in the following relationship:
P(t +
A,=+, A,r+"'+ . n..+;4* + i)=A+, "' (r !, (t + i)'z (t + i)"^' + i)' (r + ;)z' (t + 4r
QL.tt
Now ifwe subtract Equation (20.6) from Equation (20.7), we have
P(l
+i)P=A+L+r,A.+A * + i) rY1t*
\1
_
1r* o,
+"'+
A L(l + 4' (1 + i)',', (r + ;72'
I a
A
l_l!rI
A
A
O;;l;;* 1t* o'''A A I + (r + i)',t (l 4"1 Il
(20.8)
Simplifying the righthand side of Equadon (20.8) leads to the following relationship:
P(r+i)PA
i
€0.8b)
(r + i)"
And after simplifying the lefthand side of Equation (20.8), we have
P(i) =
A((L+i)"r)
(20.8c)
Q+i)"
Now if we divide both sides of Equation (20.8c) by i, wehave
tl p=nl\!il'. ' '^L i(r + i)'
ao.,
I
Equation (20.9) esablishes the relationship bewveen the present value of a lump sum P and its equivalent uniform series payments ,4. We can also rearrange Equadon (20.9) , to represent r4 in terms of Pdirecdy, as given by the following formula:
.l r)' ! 0 + i)'  t: 'L0 + i)"  r)
. P(i)(r + i)" :,l A:
.(t)(r
o.r,
?0.7 Future Worth of Series Payment To dwelop a formula for computing dre future worth of a series of uniform payments, we begin with the relationship betrveen the present worth and the furure worth, Equation (20.2), and then we substitute for P in Equation Q0.2) in terms of
.r4,
using Equation (20.9). This
20.7
Ftrnrns'WonrH or Srnrss PeuvrrNr
607
procedure is demonsuated stepby+tep, next. The relation berween a presenr value and a future value is given by Equation (20.2):
F
= P(r
* i)"
(20.2)
And the relationship between the present wonh and a uniform series
is
given by Equation (20.9):
[(t+z')'tl P=Al n * I L i(l+i)"
CO.tt
Substituting into Equation (20.2) for P in terms ofr4 using Equation (20.9),we have
P F
= P(r
*
i)" =
lfl + t)'
^L 4r;
1.l
n
l(1
+
,)'
(20.10
Simplifying ftuation (20.11) rCIults in the direct relationship between the future wonh Fand the uniform payments or depositsr4, which follows:
,=^lsTl
G0.ta
And by rearranging Equation Q0.12), we c:rn obain a formula for A in terms of future worth F:
.s=Fl I L(l + 4' ll
aomt
Now that we have all the necessary tools, we fllrn our attention to the question we asked eadier about how much money you need to put aside wery year for the next five years to have $2000 for the down payment of your car when you graduate. Recall that the interest rate is 6,50/o ampounding annually. The annual deposits are calculated from Equation (20.13), which leads to the following amounr:

s'oe\
n = ,oool L(l + 0.065),

I
:
$351.25
Puttingaside $351.26 in abankweryyear for the nortfiveyears maybe more manageable than depositing a lump sum of $1459.76 today, especially if you don't currendy have access ro that large a sum!
It is importanr to note thar Equations (20.9), (20.10), (20.12), and (20.13) apply to a situation wherein the uniform series of paymen$ or revenues occur annua$t, Vell, the next question is, how do we handle situations where the payments are made mondrly? For example, qu or a house loan paymens occur monthly. Let us now modi& our findings by considering the relationship benareen present value ? and uniform series paymenrs or revenuer4 that occur more than once a year at the same frequency as the frequency of compounding interest per year. a
608
CllePrsn
20
ENcrNsERrNc EcoNourcs For this situation, Equation Q0.9) is modified to incorporate the frequency of compounding interest per year, m, inthe following maruler:
l(r*.)_]'l tv *)" *l'*  )
n: nl \tT!/
(20.14)
Note that in order to obtain Equation Q\.I ),we simply substituted in Equation (20.9) for i, ilm. andfor n" nm.Equation (20.14) can be rearranged to solve for.r4 in terms ofPaccording to
(*)('.
,="[
*)
(' * t)* ,
Similarly, Equations Q0,12) and (20.13) can be modified for situations wherer4 occurs more than once a y@r_at the same frequency as the compounding interestleading to the following relationship:
a= rL
('**)''""''
I (20.16)
t 7n
ltl
ml .l n:,17
t.7m '_l
(2017)
L\'*;)
Finally, when the frequency of uniform series is different from the frequency of compounding interest, i"6 must first be calculated to match the frequency of the uniform series. Ler us retum to the question we asked earlier about how much money you need to put aside for the next five ycrfs to have $2000 for the down payment on your car when you graduate. Now consider the situation where you make your deposis every month, and the interest rate is 6.50/o compounfing monthly. The deposits are calculated from Equation (20.17), which leads to the following:
*  lt :^"1 ^:'15;7ll
0.065 __..v
('*
T2
o.o6t
\('
n)
=
2)(5)
$28.29
1
Putting aside $28.29 in the bank every month for the next five years is even more manageable than depositing $l5t.Ze in a bank every year for the next five years, and it is cenainly more manageable than depositing a lump sum of $1459.76inthe bank todal L,,,u,,r,,,,.,,.,.,.,,,,
::,'',, .l 
l 
:t,r:al:l
2A.8 Suvuany or
ENcrNpsRrNc EcoNourcs ANer,ysrs
609
Determine the mon$Iy paymeng for a fiveyear, $10,000 loan ar an interest rare of 87o com
pounding monthly. To calculate the monthlypayments, we use Equation
^:,lV)l:?).1 L\'.;) rJ 20.8 Summary
:,o,ooo[(;,
LT
(2O.Ir.
x* )1 ):$20276
of Engineerinq Economies Analysis
The engineering economics formulas that we have dweloped so far are summarized in Thbles 20.6 and20.7. The definitions of the terms in the formulas are given here:
P: F:
costlump sum ($) future wofth, or fuguss ssstlump sum ($) I : uniform series payment, or uniform series revenue ($) i : nominal interest rare z"n'= effecrive interest rate a : number of years rn = number of interest compounding periods pet yeet present worth, or present
The interesttime factors shown in the fourth column of Thble 2A.6 arc used as shoncuts to artoid writing long formulas when waluating equivalent values ofvarious cash fow occurrences.
F
P
P
F
F= P(l * i)
(FIP, i, n)
o F '(1+i), f(t+i)"ll P:AI' i(r+i)' , , L l
I
(rxr + i)" I
F
:6+S
ffl+;\t1'1 (PtA,i.n):Ld;1
 A=Pl:l
(Atp,,,o)=l#++]
': ^Li)
(FtA,i,n):lga#]
LQ+irrJ f(l + r)' 1l
A
(PIF,i,n)
= (l + i)
.f
(4
I
^ "l1r * ;1,  t1
(AtTi,n)=
ltr#_,]
Cnerrsn20
ExcrNsERrNcEcoNomrcs
ur"
ffi, ro"J"
r*,= (,r + *))
i
t
r= i"(r * *)*
,:G# I
(,. *)* ,:^l 17*t\ry
,1
;\1+;)
r /;\/ A= ?l
P
L
,=
^f L
I ,="L
(;/(1+;)

J ;\ou1
776
\'*;)

'J

1 ;\@)t") I ' \'*;)
=l
I
ln
l:
nl
t:
rl,
('**)'""'I1
For example, when evaluating the series payment equivalence of apresent p.itt"ip"l, instead
of
writing,
O0 + i)" A pl 'L(l +i)"r)f wewtiteA: P(A/4 (Atp, L
t, n),where, of course,
J,il" .f o' :1,!'),0 L(r +i)"rJ
In this example,the (AIP, a z) term is cdledt\einteresttimefaaor,andit reads.d gSven P at io/o inreresr rate, for a duradon of n years,It is used to findA, when the present principal value P is given, by multiplying P by the value of the interesttime fa*or (AIP, A n). As an otample' the numerical values of interesttime factors for i = 8o/o are calculated and shown in Table 20.8.
I
1.08000000 1.16640000 7,219V1200 4 ,. 1.3664s396 r.4.6932808 t 6 r.58687432 r.71382427 7 1.85093021 2 5
t,
I
lo
,.
Ti; t2
0.92592593 0.85733882
4,92592593
p.79r53224
2.5770if)699
g:/3t02985
3.31212684 3,99271004 4,62287966
0.65058320 0.63016963 0.58349040 0.54026888 r.99900463 0.50024897 2.t5592500 0.46319349 2.33163900 0.42888286
251817012 0.397rr376 2.71962373 036769792
T3
2.93719362 0.34046104 3.L72169rr A3r524r7o 3.42594264 0.29189047
L4 15
l6
t7',, 3]0001805 0.27026895
l8
3.99601950 0.25024903
' 43\57On6,:
A.23171206
4.66095714 zt.: 5.03383372 ',?2 ;, 5.43654041 2t 5.87146365 6.34118074 2/t 25 6.84847520 26 7.39635321 7.98806147 2l 8.62710639 29 9.31727490 30 10.06265689 31 , 10.86766944
0.2145482r
19
I
2A:,,
',
n
:
1,7832&7'
5,VA697A06
5:/4663894 6.2468:8791
6.71008140 7,13896426 7.536fr7802 7.94377594
8.2U23698 8sr:94786e 8.85136916
91216381t
937188714 e.6fi35?92a
0.r0r8522r
0.19865575
9.818r4V41 r0,01680316
0.1539405r
rc20A7$66
o.og8o32w
0.09642217 ra.12875525 0.09497796 0J4601790 'r0.674n619 0.09367878
a.17045&5 a.j.36nr559 o.t:tz,arz^o a.094a1476
a,a80wg7r 0$6902949 0.060a7&4 ,0n52695.02
0.04652t8r ,0.04129685 0,a3682954 ,a,03297697
0,a2962943
0.a267\2n '0.a24r276' a,a2$522t:' O.OtgglZZS"
0'9199??07
10.37105895
60.89329557 66.76475922
0,ar642217 a:frt497796
73.10593995
0,01367878
0.13520176 0.12518682 0.11591372 0.10732752 0.09937733 0.09201605
10.80997795
0.0925W13 79.95U15r5 a.ar2507l'3 0.09144810 87.35076836 0.01144810 0.09048891 95.33882983 b.olor))rO logarithmic models, 54955 I
outd@r air quality slandaids, 6870 Safe Drinking VaterAct, 65 Sufae Varer Tiernent Rule
(svTR),68 Enos, typs of in *pedmtal obsemtion,582 E*iq, L05I22. See afu Code ofethio
dsignprm,45 
32, 54L 546,
normal distdbution, 587 594
372
role of, 52 418, 445  447.
prcbab{rty,5V579
mlc K% oL J/JJla
@J1s.374376,380382 we fiaing 407411 FilIomlffi4 380382
sK6, )//)/y stopping sight
disuna,
532, 541543
temperatue distribution aaos
a
plain
wall,536538 time, rcle of in, 197198 Engineing profesi on, 2 l 22 Accrediation Bord for Enginedng and Technologr
(ABE$,
An
262
@.S.),
4748 Fibs (qptic) gl,s' 517518 Fill ommd,380382 Filet, dwings,468469
Fihn rcistane (o#cimt), 302303 Finishs, tm rcle o(,52 Fim lm of themodynmic,348350
emn, 582 nte,210211,224 volme,210211
Fixed
Fls
M,224
Fluid friction, re Vrmsity Fluid matqials, 5 1 9521 Foot (ft), U, S. Cutomaryuit oflength,
l)o
MAILAB,432
pmetm, 236
z8l
ra,
mingover
a,2442i6
bu& modulu of omprcibility, 263264 Caterpillar 797 miaiag t ,r"ls *Ctneerng Wg, z/dl6r omprshe (ultimate) strength, 261
d6^d,237 disvne, aarng at a, 2& 267 distane, acting ovo a 268269 facmr of ufety @,S,), 262
fnaton,240241 gaitanoml 237,242244 See
ako
imFul*, 269271 modulu of elasticity, 256 259, 260 modulu of rigidity, 259263 momertof a,?14267 Nswton! lM, 241244
fomulo,376380 tunaons3763W,387389 imponane in ngindhg, 372373 ioponing fila into MAfl{B, 445447
insningells, olmm, ad rom,376
eeprepmtion for,2740
logiel functiom, 387389
ommon uaits of 812
mari: compuradom,
400 
Hnke\lm,238,258259
lia6
Cells: Ercel fuoaiom uithmetic operatioro, 376
slution o[,8284
of*fety
&fuenheit fF), U.S. Cretomarymitof tmpemtue, 291293 Fmd (F), boic uit for qpacitors, 334 Faible rclution region, dcign prre,
xtage racrion,2.69271.
112
dsign altematim, 5556
ErqL
5
122
Evalvdot,45,5556
nonlina
models,
LzO
112
tm
Factor
Fora ad forerelated
enginert med, 111l12 enginsin& 106109 Ndonal Sciery of Profesional Enginen (NSPE), 107, 120 122 plagiaisn, 112 prcfmional mpomibility, I 12
Evalutoc
385
MATLAB,43O Extmion linc,468
for omd,
for euginm aademic dishoncty, 112 @e studis fo!, ll21I7, ode of, 107111
mthematia h,532 576
)4tJttu
Exc€I, 1
lryel onaminmt goal
@ntram
Pste,383
Exponential functiorc, 385, 430
lwel ontamimt (MCL)
onfliaofinterct,
logiel,387389
nigonomeaic 385
EPA, ree Environmqtal Protection Agqcy (EPA)
546549,549
togmmc, 16)
Xxmtiresrmic,87
(MsG),67
57 6,
.h ffowdiagm,598599
onomio m4 597619
r95217 See
Enginering organiatiom, involvement with,36
ooling
timerdated
mim
r97 198, 530 53r, 577596,597619
pamet6,
t52
tmpemtm od
lroimm
Enginering papu, 8586 Enginering prcblem, 8284, 127 128,
236281
innoduction to, 12J length md lengthrelatd
st€I,511512 water,520527
pmetes,
specialiatioro of, ll, I3L4 technologr progm, 2l 22 U.S. Buru of Iabor Satistia for I world PoPrl'iion' altr€ts of 68
387,387389 rc of, 3M
engin@irg arab{is qponential,3S5
relational opemton, 388 todsy ( ), 384
56
Air Act, 65, 6869 drinking water mdads, 5768 function of,65 indor air qualiry GACD, 70 hdmr air quality sandarls, /0l2
rcod,514515
l5l
o6,
Clm
503508
tianim,509510
128,3t9340 enerry md power, 34136! fore md forcrelared llmetes,
497.
o4,
wie
Enviromental enginering prcfesion o4, 1819 Enviromental Protation Agacy (EPA), 65,6772
soli4 509519
of labor Statisia for,
dimmiom md unis,
ad
l0
ofmatter, 502503
prcpenic
\Feb sitc for, 1213 Enginering findmenels, 124 369
time
wel,526
silion,5l
spaialiaion md, 1314
128,
mgineing
plasic,5l5516
nucla, 1920 petloleu, 19
Buru
(water vapor), 520
lightweight neals, 5095
phm
of Enginming
15
l5
mgn$im,510
19
materials,2021 minir& f,$
U.S.
F.sm,
ircn,511 Jet enghe,
14
ud Pmaie
Principla
)r/>rd
hmidity
wg6,5/)5/O Ercel functiom, 376
Fmdanentals of Enginering Eem (FE), 15 inuoduction m, 23, 426 Ntional Sociery of Profesioual Engins (NSPE),3
@nqetg'5L2514 opper md its allqre, 5 105 1 I dcign pr>2, >>5))+ mr:ftipliccion of, 553554 time, a a phpiel prcperty of, 206 Srundmommtof m,177182
bem, mmpls
of in, 180182
akoBn
(EPA)
Amaim
National Standtrds Insdtute
terials
(ASIM,6l62 FmFis & nomalistim
(ATNOR),63
599
British Stadrds Instituts (BSt), 63 Ce standarcls, 63 Chim Sate Bua of cllatry *4 Tirhniel Supwisioa (CSBTS), 63 @nmirms, methods of nmaging
nrle, 159, 621 Singu&r marix, 559 Sir, nomiasl w actnal, 160162
Deutschc Initut fiu Nomung @IN), 63
139
l4I
Silion,51 Simple
intact,
Sine
Slidc, PwuPoint pwntarioro, 9397, 9798, IOO mimation of, 9798 imting ftom otha PmrPoint 6lc,
mcta,94 of, 131
Solid linc, onhogra.phic dwings, 465 Solid marerials, 5095 19 Solid modeling, 476 482,493497 Bcing 777 omerciat airylane, engi
nuingmd493497 Bmlru
openriom for, 479, 481 bonomup, 478479
onputer nmaielly onrolled (CNC) mchines 47 imporane of in enginedng
42
84. 138138, 197198. See aho Engineing Problem; Linear
muatiom malFis of,83 defining the prcblm, 8283
mple ofpmtation
fur,84
ronoiel,
138139 pametric fom' 83
simpli$ing the prcblm, 83 197198
of, 8283 symbolic, 138139 time rcle of in, 197198 steps
(EPL),65,6712 of U.S., 6567
mmpls
(NFPA),62 D@Afor,5860 orymiations for, 60 62, 064 outdmr air quality, 6870 Star