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FEfundamentalsof engineeringThis document may be printed from the NCEES Web site, but it may not be copied,reproduced, distributed, or posted online without the express written permissionof the National Council of Examiners for Engineering and Surveying (NCEES ).Contact Ashley Cheney at acheney@ncees.org for more information.SUPPLIED-REFERENCE HANDBOOK8th edition, 2nd revision

Copyright 2011 by NCEES . All rights reserved.PO Box 1686Clemson, SC 29633800-250-3196www.ncees.orgISBN 978-1-932613-59-9Printed in the United States of AmericaApril 2011Second Revision

PREFACEAbout the HandbookThe FE is a closed-book exam, and the FE Supplied-Reference Handbook is the only reference material youmay use. Reviewing it before exam day will help you become familiar with the charts, formulas, tables, andother reference information provided. You won’t be allowed to bring your personal copy of the Handbook intothe 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 included. Special material required for the solution of a particular exam question will be included in thequestion itself.NCEES will periodically revise and update the FE Supplied-Reference Handbook. Each FE exam will beadministered using the latest version of the Handbook.Using the Handbook on exam dayDuring the exam, you may write in your exam book and on your answer sheet. However, you won’t beallowed 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 proceduresNCEES.org is our home on the Web. Visit us there for updates on everything exam-related, including ErrataTo report errata in this book, e-mail your correction using our feedback form on NCEES.org. Examinees arenot penalized for any errors in the Handbook that affect an exam question.iii

CONTENTS 1Units19Conversion Factors20Mathematics21Mechanics of Materials33Engineering Probability and Statistics40Statics49Dynamics54Fluid Mechanics62Thermodynamics73Heat Transfer84Transport Phenomena90Biology91Chemistry100Materials Science/Structure of Matter104Computer Spreadsheets109Measurement and Controls110Engineering Economics114Ethics121Chemical Engineering123Civil Engineering134Environmental Engineering170Electrical and Computer Engineering193Industrial Engineering215Mechanical Engineering231Index249v

EXAM SPECIFICATIONSFundamentals of Engineering (FE) ExaminationEffective April 2010s4HE &% EXAMINATION IS AN HOUR SUPPLIED REFERENCE EXAMINATION QUESTIONS IN THE HOUR MORNINGSESSION AND QUESTIONS IN THE HOUR AFTERNOON SESSION s4HE AFTERNOON SESSION IS ADMINISTERED IN THE FOLLOWING SEVEN MODULES #HEMICAL #IVIL %LECTRICAL%NVIRONMENTAL )NDUSTRIAL -ECHANICAL AND /THER ISCIPLINES s%XAMINEES WORK ALL QUESTIONS IN THE MORNING SESSION AND ALL QUESTIONS IN THE AFTERNOON MODULE s4HE &% EXAMINATION USES BOTH THE )NTERNATIONAL 3YSTEM OF 5NITS 3) AND THE 53 #USTOMARY 3YSTEM 53#3 s"EGINNING WITH THE !PRIL EXAMINATION THE 'ENERAL MODULE WAS RENAMED /THER ISCIPLINES 4HE MODULEWAS RENAMED TO BETTER DESCRIBE IT TO THE EXAMINEES FOR WHOM IT IS INTENDED .O OTHER CHANGES WERE MADE TOTHE &% EXAM SPECIlCATIONS FOR !PRIL MORNING SESSION (120 questions in 12 topic areas)ApproximatePercentage of TestContentTopic AreaI.Mathematics! !NALYTIC GEOMETRY" )NTEGRAL CALCULUS# -ATRIX OPERATIONS 2OOTS OF EQUATIONS% 6ECTOR ANALYSIS& IFFERENTIAL EQUATIONS' IFFERENTIAL CALCULUS15%II.Engineering Probability and Statistics! -EASURES OF CENTRAL TENDENCIES AND DISPERSIONS E G MEAN MODE STANDARD DEVIATION" 0ROBABILITY DISTRIBUTIONS E G DISCRETE CONTINUOUS NORMAL BINOMIAL# #ONDITIONAL PROBABILITIES %STIMATION E G POINT CONlDENCE INTERVALS FOR A SINGLE MEAN% 2EGRESSION AND CURVE lTTING& %XPECTED VALUE WEIGHTED AVERAGE IN DECISION MAKING' (YPOTHESIS TESTING7%III.Chemistry! .OMENCLATURE" /XIDATION AND REDUCTION# 0ERIODIC TABLE 3TATES OF MATTER% !CIDS AND BASES& %QUATIONS E G STOICHIOMETRY' %QUILIBRIUM( -ETALS AND NONMETALS9%IV.Computers! 4ERMINOLOGY E G MEMORY TYPES #05 BAUD RATES )NTERNET" 3PREADSHEETS E G ADDRESSES INTERPRETATION hWHAT IF v COPYING FORMULAS# 3TRUCTURED PROGRAMMING E G ASSIGNMENT STATEMENTS LOOPS AND BRANCHES FUNCTION CALLS7%EXAM SPECIFICATIONS—MORNING1

V.Ethics and Business Practices! #ODE OF ETHICS PROFESSIONAL AND TECHNICAL SOCIETIES" !GREEMENTS AND CONTRACTS# %THICAL VERSUS LEGAL 0ROFESSIONAL LIABILITY% 0UBLIC PROTECTION ISSUES E G LICENSING BOARDS7%VI.Engineering Economics! ISCOUNTED CASH mOW E G EQUIVALENCE 07 EQUIVALENT ANNUAL &7 RATE OF RETURN" #OST E G INCREMENTAL AVERAGE SUNK ESTIMATING# !NALYSES E G BREAKEVEN BENElT COST 5NCERTAINTY E G EXPECTED VALUE AND RISK8%VII.Engineering Mechanics (Statics and Dynamics)! 3TATICS 2ESULTANTS OF FORCE SYSTEMS #ONCURRENT FORCE SYSTEMS %QUILIBRIUM OF RIGID BODIES &RAMES AND TRUSSES #ENTROID OF AREA !REA MOMENTS OF INERTIA &RICTION" YNAMICS ,INEAR MOTION E G FORCE MASS ACCELERATION MOMENTUM !NGULAR MOTION E G TORQUE INERTIA ACCELERATION MOMENTUM -ASS MOMENTS OF INERTIA )MPULSE AND MOMENTUM APPLIED TO A PARTICLESB RIGID BODIES 7ORK ENERGY AND POWER AS APPLIED TO A PARTICLESB RIGID BODIES &RICTIONVIII.Strength of Materials! 3HEAR AND MOMENT DIAGRAMS" 3TRESS TYPES E G NORMAL SHEAR BENDING TORSION# 3TRESS STRAIN CAUSED BY AXIAL LOADS BENDING LOADS TORSION SHEAR EFORMATIONS E G AXIAL BENDING TORSION% #OMBINED STRESSES& #OLUMNS' )NDETERMINANT ANALYSIS( 0LASTIC VERSUS ELASTIC DEFORMATION2EXAM SPECIFICATIONS—MORNING10%7%

IX.Material Properties! 0ROPERTIES CHEMICAL ELECTRICAL MECHANICAL PHYSICAL" #ORROSION MECHANISMS AND CONTROL# -ATERIALS ENGINEERED MATERIALS FERROUS METALS NONFERROUS METALS7%X.Fluid Mechanics! &LOW MEASUREMENT" &LUID PROPERTIES# &LUID STATICS %NERGY IMPULSE AND MOMENTUM EQUATIONS% 0IPE AND OTHER INTERNAL mOW7%XI.Electricity and Magnetism! #HARGE ENERGY CURRENT VOLTAGE POWER" 7ORK DONE IN MOVING A CHARGE IN AN ELECTRIC lELD RELATIONSHIP BETWEENVOLTAGE AND WORK# &ORCE BETWEEN CHARGES #URRENT AND VOLTAGE LAWS IRCHHOFF /HM% %QUIVALENT CIRCUITS SERIES PARALLEL& #APACITANCE AND INDUCTANCE' 2EACTANCE AND IMPEDANCE SUSCEPTANCE AND ADMITTANCE( !# CIRCUITS) "ASIC COMPLEX ALGEBRA9%XII.Thermodynamics! 4HERMODYNAMIC LAWS E G ST ,AW ND ,AW" %NERGY HEAT AND WORK# !VAILABILITY AND REVERSIBILITY #YCLES% )DEAL GASES& -IXTURE OF GASES' 0HASE CHANGES( (EAT TRANSFER) 0ROPERTIES OF ENTHALPY ENTROPY7%EXAM SPECIFICATIONS—MORNING3

AFTERNOON SESSION IN CHEMICAL ENGINEERING(60 questions in 11 topic areas)Topic AreaApproximatePercentage of TestContentI.Chemistry! )NORGANIC CHEMISTRY E G MOLARITY NORMALITY MOLALITY ACIDS BASES REDOXVALENCE SOLUBILITY PRODUCT P( P ELECTROCHEMISTRY" /RGANIC CHEMISTRY E G NOMENCLATURE STRUCTURE QUALITATIVE AND QUANTITATIVEANALYSES BALANCED EQUATIONS REACTIONS SYNTHESIS10%II.Material/Energy Balances! -ASS BALANCE" %NERGY BALANCE# #ONTROL BOUNDARY CONCEPT E G BLACK BOX CONCEPT 3TEADY STATE PROCESS% 5NSTEADY STATE PROCESS& 2ECYCLE PROCESS' "YPASS PROCESS( #OMBUSTION15%III.Chemical Engineering Thermodynamics! 4HERMODYNAMIC LAWS E G ST ,AW ND ,AW" 4HERMODYNAMIC PROPERTIES E G INTERNAL THERMAL ENERGY ENTHALPY ENTROPYFREE ENERGY# 4HERMODYNAMIC PROCESSES E G ISOTHERMAL ADIABATIC ISENTROPIC 0ROPERTY AND PHASE DIAGRAMS E G 4 S H 0 X Y 4 X Y% %QUATIONS OF STATE E G VAN DER 7AALS 3OAVE 2EDLICH WONG& 3TEAM TABLES' 0HASE EQUILIBRIUM AND PHASE CHANGE( #HEMICAL EQUILIBRIUM) (EATS OF REACTION* #YCLIC PROCESSES AND EFlCIENCY E G POWER REFRIGERATION HEAT PUMP (EATS OF MIXING10%IV.Fluid Dynamics! "ERNOULLI EQUATION AND MECHANICAL ENERGY BALANCE" (YDROSTATIC PRESSURE# IMENSIONLESS NUMBERS E G 2EYNOLDS NUMBER ,AMINAR AND TURBULENT mOW% 6ELOCITY HEAD& &RICTION LOSSES E G PIPE VALVES lTTINGS' 0IPE NETWORKS( #OMPRESSIBLE AND INCOMPRESSIBLE mOW) &LOW MEASUREMENT E G ORIlCES 6ENTURI METERS* 0UMPS TURBINES AND COMPRESSORS .ON .EWTONIAN mOW, &LOW THROUGH PACKED BEDS10%4EXAM SPECIFICATIONS—CHEMICAL

V.Heat Transfer! #ONDUCTIVE HEAT TRANSFER" #ONVECTIVE HEAT TRANSFER# 2ADIATION HEAT TRANSFER (EAT TRANSFER COEFlCIENTS% (EAT EXCHANGER TYPES E G PLATE AND FRAME SPIRAL& &LOW CONlGURATION E G COCURRENT COUNTERCURRENT' ,OG MEAN TEMPERATURE DIFFERENCE ,-4 AND .45( &OULING) 3HELL AND TUBE HEAT EXCHANGER DESIGN E G AREA NUMBER OF PASSES10%VI.Mass Transfer! IFFUSION E G &ICK S ST AND ND LAWS" -ASS TRANSFER COEFlCIENT# %QUILIBRIUM STAGE METHOD EFlCIENCY 'RAPHICAL METHODS E G -C#ABE 4HIELE% IFFERENTIAL METHOD E G .45 (%40 (45 .40& 3EPARATION SYSTEMS E G DISTILLATION ABSORPTION EXTRACTION MEMBRANE PROCESSES' (UMIDIlCATION AND DRYING10%VII.Chemical Reaction Engineering! 2EACTION RATES AND ORDER" 2ATE CONSTANT E G !RRHENIUS FUNCTION# #ONVERSION YIELD AND SELECTIVITY 3ERIES AND PARALLEL REACTIONS% &ORWARD AND REVERSE REACTIONS& %NERGY MATERIAL BALANCE AROUND A REACTOR' 2EACTIONS WITH VOLUME CHANGE( 2EACTOR TYPES E G PLUG mOW BATCH SEMI BATCH #342) (OMOGENEOUS AND HETEROGENEOUS REACTIONS* #ATALYSIS10%VIII.Process Design and Economic Optimization! 0ROCESS mOW DIAGRAMS 0& " 0IPING AND INSTRUMENTATION DIAGRAMS 0 ) # 3CALE UP #OMPARISON OF ECONOMIC ALTERNATIVES E G NET PRESENT VALUE DISCOUNTEDCASH mOW RATE OF RETURN% #OST ESTIMATION10%IX.Computer Usage in Chemical Engineering! .UMERICAL METHODS AND CONCEPTS E G CONVERGENCE TOLERANCE" 3PREADSHEETS FOR CHEMICAL ENGINEERING CALCULATIONS# 3TATISTICAL DATA ANALYSIS5%X.Process Control! 3ENSORS AND CONTROL VALVES E G TEMPERATURE PRESSURE" YNAMICS E G TIME CONSTANTS ND ORDER UNDERDAMPED# &EEDBACK AND FEEDFORWARD CONTROL 0ROPORTIONAL INTEGRAL AND DERIVATIVE 0) CONTROLLER CONCEPTS% #ASCADE CONTROL& #ONTROL LOOP DESIGN E G MATCHING MEASURED AND MANIPULATED VARIABLES' 4UNING 0) CONTROLLERS AND STABILITY E G -ETHOD OF :IEGLER .ICHOLS 2OUTH 4EST( /PEN LOOP AND CLOSED LOOP TRANSFER FUNCTIONS5%EXAM SPECIFICATIONS—CHEMICAL5

XI.6Safety, Health, and Environmental! (AZARDOUS PROPERTIES OF MATERIALS E G CORROSIVE mAMMABLE TOXIC INCLUDING -3 3" )NDUSTRIAL HYGIENE E G NOISE 00% ERGONOMICS# 0ROCESS HAZARD ANALYSIS E G USING FAULT TREE ANALYSIS OR EVENT TREE /VERPRESSURE AND UNDERPRESSURE PROTECTION E G RELIEF REDUNDANT CONTROLINTRINSICALLY SAFE% 3TORAGE AND HANDLING E G INERTING SPILL CONTAINMENT& 7ASTE MINIMIZATION' 7ASTE TREATMENT E G AIR WATER SOLIDSEXAM SPECIFICATIONS—CHEMICAL5%

AFTERNOON SESSION IN CIVIL ENGINEERING(60 questions in 9 topic areas)Topic AreaApproximatePercentage of TestContentI.Surveying! !NGLES DISTANCES AND TRIGONOMETRY" !REA COMPUTATIONS# #LOSURE #OORDINATE SYSTEMS E G '03 STATE PLANE% #URVES VERTICAL AND HORIZONTAL& %ARTHWORK AND VOLUME COMPUTATIONS' ,EVELING E G DIFFERENTIAL ELEVATIONS PERCENT GRADES11%II.Hydraulics and Hydrologic Systems! "ASIC HYDROLOGY E G INlLTRATION RAINFALL RUNOFF DETENTION mOOD mOWS WATERSHEDS" "ASIC HYDRAULICS E G -ANNING EQUATION "ERNOULLI THEOREM OPEN CHANNELmOW PIPE mOW# 0UMPING SYSTEMS WATER AND WASTEWATER -UNICIPAL WATER DISTRIBUTION SYSTEMS% 2ESERVOIRS E G DAMS ROUTING SPILLWAYS& 'ROUNDWATER E G mOW WELLS DRAWDOWN' 3EWER COLLECTION SYSTEMS STORM AND SANITARY12%III.Soil Mechanics and Foundations! )NDEX PROPERTIES AND SOIL CLASSIlCATIONS" 0HASE RELATIONS AIR WATER SOLID# ,ABORATORY AND lELD TESTS %FFECTIVE STRESS BUOYANCY% 2ETAINING WALLS E G ACTIVE PRESSURE PASSIVE PRESSURE& 3HEAR STRENGTH' "EARING CAPACITY COHESIVE AND NONCOHESIVE( &OUNDATION TYPES E G SPREAD FOOTINGS PILES WALL FOOTINGS MATS) #ONSOLIDATION AND DIFFERENTIAL SETTLEMENT* 3EEPAGE 3LOPE STABILITY E G lLLS EMBANKMENTS CUTS DAMS, 3OIL STABILIZATION E G CHEMICAL ADDITIVES GEOSYNTHETICS15%IV.Environmental Engineering! 7ATER QUALITY GROUND AND SURFACE" !IR QUALITY# 3OLID HAZARDOUS WASTE 3ANITARY SEWER SYSTEM LOADS% "ASIC TESTS E G WATER WASTEWATER AIR& %NVIRONMENTAL REGULATIONS' 7ATER TREATMENT AND WASTEWATER TREATMENT E G PRIMARY SECONDARY TERTIARY12%EXAM SPECIFICATIONS—CIVIL7