Fundamentals of engineering

FE
fundamentals
of engineering

This document may be printed from the NCEES Web site, but it may not be copied,
reproduced, distributed, or posted online without the express written permission
of the National Council of Examiners for Engineering and Surveying® (NCEES®).
Contact Ashley Cheney at for more information.

SUPPLIED-REFERENCE HANDBOOK
8th edition, 2nd revision


Copyright © 2011 by NCEES®. All rights reserved.
PO Box 1686
Clemson, SC 29633
800-250-3196
www.ncees.org
ISBN 978-1-932613-59-9
Printed in the United States of America
April 2011
Second Revision


PREFACE
About the Handbook
The FE is a closed-book exam, and the FE Supplied-Reference Handbook is the only reference material you
may use. Reviewing it before exam day will help you become familiar with the charts, formulas, tables, and
other reference information provided. You won’t be allowed to bring your personal copy of the Handbook into
the exam room, but you will be provided with a new one at your seat on exam day.
The Handbook does not contain all the information required to answer every question on the exam. Some

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included. Special material required for the solution of a particular exam question will be included in the
question itself.
NCEES will periodically revise and update the FE Supplied-Reference Handbook. Each FE exam will be
administered using the latest version of the Handbook.
Using the Handbook on exam day
During the exam, you may write in your exam book and on your answer sheet. However, you won’t be
allowed to write in or remove pages from the Handbook. A proctor will collect all your testing materials,
including the FE Supplied-Reference Handbook, before you leave the exam room.
Updates on exam content and procedures
NCEES.org is our home on the Web. Visit us there for updates on everything exam-related, including
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Errata
To report errata in this book, e-mail your correction using our feedback form on NCEES.org. Examinees are
not penalized for any errors in the Handbook that affect an exam question.

iii



CONTENTS

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1

Units

19

Conversion Factors

20

Mathematics

21

Mechanics of Materials

33

Engineering Probability and Statistics

40

Statics

49

Dynamics

54

Fluid Mechanics

62

Thermodynamics

73

Heat Transfer

84

Transport Phenomena

90

Biology

91

Chemistry

100

Materials Science/Structure of Matter

104

Computer Spreadsheets

109

Measurement and Controls

110

Engineering Economics

114

Ethics

121

Chemical Engineering

123

Civil Engineering

134

Environmental Engineering

170

Electrical and Computer Engineering

193

Industrial Engineering

215

Mechanical Engineering

231

Index

249

v



EXAM SPECIFICATIONS
Fundamentals of Engineering (FE) Examination
Effective April 2010
s

4HE&%EXAMINATIONISAN
HOURSUPPLIED
REFERENCEEXAMINATIONQUESTIONSINTHE
HOURMORNING
SESSIONANDQUESTIONSINTHE
HOURAFTERNOONSESSION

s

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#IVIL
%LECTRICAL

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-ECHANICAL
AND/THER$ISCIPLINES

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%XAMINEESWORKALLQUESTIONSINTHEMORNINGSESSIONANDALLQUESTIONSINTHEAFTERNOONMODULE

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"EGINNINGWITHTHE!PRILEXAMINATION
THE'ENERALMODULEWASRENAMED/THER$ISCIPLINES4HEMODULE
WASRENAMEDTOBETTERDESCRIBEITTOTHEEXAMINEESFORWHOMITISINTENDED.OOTHERCHANGESWEREMADETO
THE&%EXAMSPECIlCATIONSFOR!PRIL

MORNING SESSION (120 questions in 12 topic areas)
Approximate
Percentage of Test
Content

Topic Area
I.

Mathematics
! !NALYTICGEOMETRY
" )NTEGRALCALCULUS
# -ATRIXOPERATIONS
$ 2OOTSOFEQUATIONS
% 6ECTORANALYSIS
& $IFFERENTIALEQUATIONS
' $IFFERENTIALCALCULUS

15%

II.








Engineering Probability and Statistics
! -EASURESOFCENTRALTENDENCIESANDDISPERSIONSEG
MEAN
MODE
STANDARDDEVIATION

" 0ROBABILITYDISTRIBUTIONSEG
DISCRETE
CONTINUOUS
NORMAL
BINOMIAL
# #ONDITIONALPROBABILITIES
$ %STIMATIONEG
POINT
CONlDENCEINTERVALSFORASINGLEMEAN
% 2EGRESSIONANDCURVElTTING
& %XPECTEDVALUEWEIGHTEDAVERAGEINDECISION
MAKING
' (YPOTHESISTESTING

7%

III.









Chemistry
! .OMENCLATURE
" /XIDATIONANDREDUCTION
# 0ERIODICTABLE

$ 3TATESOFMATTER
% !CIDSANDBASES
& %QUATIONSEG
STOICHIOMETRY
' %QUILIBRIUM
( -ETALSANDNONMETALS

9%

IV.




Computers
! 4ERMINOLOGYEG
MEMORYTYPES