FE Reference Handbook 10.0 - Bagley College Of Engineering
This document may be printed from theNCEES Web site for your personal use,but it may not be copied, reproduced,distributed electronically or in print,or posted online without the expresswritten permission of NCEES.Contact permissions@ncees.orgfor more information.FE Reference Handbook 10.0.1
Copyright 2020 by NCEES . All rights reserved.All NCEES material is copyrighted under the laws of the United States. No part of this publication may be reproduced, stored in aretrieval system, or transmitted in any form or by any means without the prior written permission of NCEES. Requests for permissionsshould be addressed in writing to permissions@ncees.org.ISBN 978-1-947801-11-0Printed in the United States of AmericaSecond printing May 2020Edition 10.0.1
PrefaceAbout the HandbookThe Fundamentals of Engineering (FE) exam is computer-based, and the FE Reference Handbook is the only resourcematerial you may use during the exam. 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 theHandbook into the exam room. Instead, the computer-based exam will include a PDF version of the Handbook for your use.No printed copies of the Handbook will be allowed in the exam room.The PDF version of the FE Reference Handbook that you use on exam day will be very similar to the printed version. Pagesnot needed to solve exam questions—such as the cover, introductory material, index, and exam specifications—will not beincluded in the PDF version. In addition, NCEES will periodically revise and update the Handbook, and each FE exam willbe administered using the updated version.The FE Reference Handbook does not contain all the information required to answer every question on the exam. Basictheories, conversions, formulas, and definitions examinees are expected to know have not been included. Special materialrequired for the solution of a particular exam question will be included in the question itself.Updates on exam content and proceduresNCEES.org is our home on the web. Visit us there for updates on everything exam-related, including specifications, examday policies, scoring, and practice tests. A PDF version of the FE Reference Handbook similar to the one you will use onexam day is also available there.ErrataTo report errata in this book, send your correction using our chat feature or your account on NCEES.org. We will also posterrata on the website. Examinees are not penalized for any errors in the Handbook that affect an exam question.iii
CONTENTSUnits and Conversion Factors.1Ethics and Professional Practice.4Safety.13Mathematics.34Engineering Probability and Statistics.63Chemistry and Biology.85Materials Science/Structure of Matter.94Statics.107Dynamics.114Mechanics of Materials.130Thermodynamics.143Fluid Mechanics.177Heat Transfer.204Instrumentation, Measurement, and Control.220Engineering Economics.230Chemical Engineering.238Civil Engineering.259Environmental Engineering.310Electrical and Computer Engineering.355Industrial and Systems Engineering.417Mechanical Engineering.431Index.461FE Exam Specifications.471v
Units and Conversion FactorsDistinguishing pound-force from pound-massThe FE exam and this handbook use both the metric system of units and the U.S. Customary System (USCS). In the USCS system of units, both force and mass are called pounds. Therefore, one must distinguish the pound-force (lbf) from the pound-mass(lbm).The pound-force is that force which accelerates one pound-mass at 32.174 ft/sec2. Thus, 1 lbf 32.174 lbm-ft/sec2. The expression32.174 lbm-ft/(lbf-sec2) is designated as gc and is used to resolve expressions involving both mass and force expressed as pounds.For instance, in writing Newton's second law, the equation would be written as F ma/gc, where F is in lbf, m in lbm, and a is in ft/sec2.Similar expressions exist for other quantities. Kinetic Energy, KE mv2/2gc, with KE in (ft-lbf); Potential Energy,PE mgh/gc, with PE in (ft-lbf); Fluid Pressure, p ρgh/gc, with p in (lbf/ft2); Specific Weight, SW ρg/gc, in (lbf/ft3); ShearStress, τ (µ/gc)(dv/dy), with shear stress in (lbf/ft2). In all these examples, gc should be regarded as a force unit conversionfactor. It is frequently not written explicitly in engineering equations. However, its use is required to produce a consistent set ofunits.Note that the force unit conversion factor gc [lbm-ft/(lbf-sec2)] should not be confused with the local acceleration of gravity g,which has different units (m/s2 or ft/sec2) and may be either its standard value (9.807 m/s2 or 32.174 ft/sec2) or some other localvalue.If the problem is presented in USCS units, it may be necessary to use the constant gc in the equation to have a consistent setof units.Constants and conversion factors provided are approximate, with sufficient accuracy to solve exam IC kMGTPECOMMONLY USED EQUIVALENTS1 gallon of water weighs1 cubic foot of water weighs1 cubic inch of mercury weighsThe mass of 1 cubic meter of water is1 mg/L is8.34 lbf62.4 lbf0.491 lbf1,000 kilograms8.34 10–6 lbf/galTEMPERATURE CONVERSIONSºF 1.8 (ºC) 32ºC (ºF – 32)/1.8ºR ºF 459.69K ºC 273.151
Units and Conversion FactorsSignificant FiguresSignificant figures of numbers in math operations will determine the accuracy of the result. General rules for significant digitsare:Rule 1: Non-zero digits are always significant.Rule 2: Any zeros between two significant digits are significant.Rule 3: All zeros in the decimal portion are significant.Rule 4 (Addition and Subtraction): The number used in the calculation with the least number of significant digits after the decimal point dictates the number of significant figures after the decimal point. The number with the most significant figures to theleft of the decimal point dictates the number of significant digits to the left of decimal point.Rule 5 (Multiplication and Division): The result of the operation has the same number of significant digits as the inputnumber with the least number of significant digits.Rule 6: In the solution of engineering problems, it is customary to retain 3–4 significant digits in the final result.Ideal Gas ConstantsThe universal gas constant, designated as R in the table below, relates pressure, volume, temperature, and number of moles of an idealgas. When that universal constant, R , is divided by the molecular weight of the gas, the result, often designated as R, has units of energyper degree per unit mass [kJ/(kg·K) or ft-lbf/(lbm-ºR)] and becomes characteristic of the particular gas. Some disciplines, notably chemical engineering, often use the symbol R to refer to the universal gas constant R .Fundamental ConstantsQuantitySymbolValueUnitselectron chargee1.6022 10 19C (coulombs)Faraday constantF96,485coulombs/(mol)gas constantmetricR8,314J/(kmol·K)gas constantmetricR8.314kPa·m3/(kmol·K)gas constantUSCSR1,545ft-lbf/(lb mole-ºR)R0.08206gravitation-Newtonian constantG6.673 gravitation-Newtonian constantG6.673 10–11N·m2/kg2gravity acceleration (standard)metricg9.807m/s2gravity acceleration (standard)USCSg32.174ft/sec2molar volume (ideal gas), T 273.15 K, p 101.3 kPaVm22,414L/kmolspeed of light (exact)c299,792,458m/sStefan-Boltzmann constantσ5.67 )
Units and Conversion FactorsMultiplyByTo Obtainacreampere-hr (A-hr)ångström (Å)atmosphere (atm)atm, stdatm, stdatm, stdatm, std43,5603,6001 10–1076.029.9214.7033.901.013 105square feet (ft2)coulomb (C)meter (m)cm, mercury (Hg)in., mercury (Hg)lbf/in2 abs (psia)ft, waterpascal 1 100.987421,0552.928 10–47783.930 10–40.2930.216Paatmgallons–oiljoule (J)kilowatt-hr (kWh)ft-lbfhorsepower (hp)watt (W)ft-lbf/seccalorie (g-cal)calcalcal/seccentimeter (cm)cmcentipoise (cP)centipoise (cP)centipoise (cP)centistoke (cSt)cubic feet/second (cfs)cubic foot (ft3)cubic meters (m3)3.968 10–31.560 10–64.1844.1843.281 10–20.3940.00112.4191 10–60.6463177.4811,000Btuhp-hrjoule (J)watt (W)foot (ft)inch (in)pascal sec (Pa s)g/(m s)lbm/hr-ftm2/sec (m2/s)million gallons/day (MGD)gallonliterselectronvolt (eV)1.602 10–19joule (J)5Multiplyfoot (ft)30.48cmft0.3048meter (m)ft of H2O0.4332psift-pound (ft-lbf)1.285 10–3Btuft-lbf3.766 10–7kilowatt-hr (kWh)ft-lbf0.324calorie (g-cal)ft-lbf1.356joule (J)ft-lbf/sec1.818 10–3horsepower (hp)gallon (U.S. Liq)3.785liter (L)gallon (U.S. Liq)0.134ft3gallons of water8.3453pounds of watergamma (γ, Γ)1 10–9tesla (T)gauss1 10–4Tgram (g)2.205 10–3pound (lbm)hectarehectarehorsepower (hp)hphphphp-hrhp-hrhp-hrhp-hr1 1042.4710442.4745.733,0005502,5451.98 1062.68 1060.746square meters (m2)acresBtu/minwatt (W)(ft-lbf)/min(ft-lbf)/secBtuft-lbfjoule (J)kWhinch (in.)in. of Hgin. of Hgin. of H2Oin. of H2O2.5400.033413.600.03610.002458centimeter (cm)atmin. of H2Olbf/in2 (psi)atm3ByTo Obtain10–4joule (J)JJJ/s9.478 0.737611Btuft-lbfnewton m (N m)watt (W)kilogram (kg)kgfkilometer (km)km/hrkilopascal (kPa)kilowatt (kW)kWkWkW-hour (kWh)kWhkWhkip 1.3413.6 1061,0004,448pound-mass (lbm)newton (N)feet (ft)mphlbf/in2 (psi)horsepower (hp)Btu/hr(ft-lbf )/secBtuhp-hrjoule (J)lbfnewton (N)liter (L)LLL/second (L/s)L/s61.020.26410–32.11915.85in3gal (U.S. Liq)m3ft3/min (cfm)gal (U.S.)/min (gpm)meter (m)mm/second (m/s)mile (statute)mile (statute)mile/hour (mph)mphmm of Hgmm of H2O3.2811.094196.85,2801.60988.01.6091.316 10–39.678 10–5feet (ft)yardfeet/min (ft/min)feet (ft)kilometer (km)ft/min (fpm)km/hatmatmnewton (N)newton (N)N mN m0.22510.73761lbfkg m/s2ft-lbfjoule (J)pascal (Pa)PaPa sec (Pa s)pound (lbm, avdp)lbflbf-ftlbf/in2 (psi)psipsipsi9.869 here (atm)newton/m2 (N/m2)poise (P)kilogram (kg)NN matmft of H2Oin. of HgParadian (rad)180/πdegreeslugstokes32.1741 10–4pound-mass (lbm)m2/steslathermton (metric)ton (short)1,0001 1051,0002,000weber/m2Btukilogram (kg)pound-force (lbf)watt (W)WWweber/m2 (Wb/m2)3.4131.341 10–3110,000Btu/hrhorsepower (hp)joule/s (J/s)gauss
Ethics and Professional PracticeCode of EthicsEngineering is considered to be a "profession" rather than an "occupation" because of several important characteristicsshared with other recognized learned professions, law, medicine, and theology: special knowledge, special privileges, andspecial responsibilities. Professions are based on a large knowledge base requiring extensive training. Professional skillsare important to the well-being of society. Professions are self-regulating, in that they control the training and evaluationprocesses that admit new persons to the field. Professionals have autonomy in the workplace; they are expected to utilizetheir independent judgment in carrying out their professional responsibilities. Finally, professions are regulated by ethicalstandards. (Harris, C.E., M.S. Pritchard, & M.J. Rabins, Engineering Ethics: Concepts and Cases, Wadsworth Publishingcompany, pages 27–28, 1995.)The expertise possessed by engineers is vitally important to societal welfare. In order to serve society effectively, engineersmust maintain a high level of technical competence. However, a high level of technical expertise without adherence toethical guidelines is as much a threat to public welfare as is professional incompetence. Therefore, engineers must also beguided by ethical principles.The ethical principles governing the engineering profession are embodied in codes of ethics. Such codes have been adoptedby state boards of registration, professional engineering societies, and even by some private industries. An example of onesuch code is the NCEES Rules of Professional Conduct, found in Section 240 of the Model Rules and presented here. Aspart of his/her responsibility to the public, an engineer is responsible for knowing and abiding by the code. Additional rulesof conduct are also included in the Model Rules.The three major sections of the Model Rules address (1) Licensee's Obligation to the Public, (2) Licensee's Obligation toEmployers and Clients, and (3) Licensee's Obligation to Other Licensees. The principles amplified in these sections areimportant guides to appropriate behavior of professional engineers.Application of the code in many situations is not controversial. However, there may be situations in which applyingthe code may raise more difficult issues. In particular, there may be circumstances in which terminology in the code isnot clearly defined, or in which two sections of the code may be in conflict. For example, what constitutes "valuableconsideration" or "adequate" knowledge may be interpreted differently by qualified professionals. These types of questionsare called conceptual issues, in which definitions of terms may be in dispute. In other situations, factual issues may alsoaffect ethical dilemmas. Many decisions regarding engineering design may be based upon interpretation of disputed orincomplete information. In addition, tradeoffs revolving around competing issues of risk vs. benefit, or safety vs. economicsmay require judgments that are not fully addressed simply by application of the code.No code can give immediate and mechanical answers to all ethical and professional problems that an engineer may face.Creative problem solving is often called for in ethics, just as it is in other areas of engineering.Model Rules, Section 240.15 Rules of Professional ConductTo safeguard the health, safety, and welfare of the public and to maintain integrity and high standards of skill and practice inthe engineering and surveying professions, the rules of professional conduct provided in this section shall be binding uponevery licensee and on all firms authorized to offer or perform engineering or surveying services in this jurisdiction.A. Licensee’s Obligation to the Public1. Licensees shall be cognizant that their first and foremost responsibility is to safeguard the health, safety, andwelfare of the public when performing services for clients and employers.2. Licensees shall sign and seal only those plans, surveys, and other documents that conform to accepted engineeringand surveying standards and that safeguard the health, safety, and welfare of the public.3. Licensees shall notify their employer or client and such other authority as may be appropriate when theirprofessional judgment is overruled when the health, safety, or welfare of the public is endangered.4. Licensees shall, to the best of their knowledge, include all relevant and pertinent information in an objective andtruthful manner within all professional documents, statements, and testimony.5. Licensees shall express a professional opinion publicly only when it is founded upon an adequate knowledge of thefacts and a competent evaluation of the subject matter.4
Ethics and Professional Practice6. Licensees shall issue no statements, criticisms, or arguments on engineering and surveying matters that are inspiredor paid for by interested parties, unless they explicitly identify the interested parties on whose behalf they arespeaking and reveal any interest they have in the matters.7. Licensees shall not partner, practice, or offer to practice with any person or firm that they know is engaged infraudulent or dishonest business or professional practices.8. Licensees who have knowledge or reason to believe that any person or firm has violated any rules or laws applyingto the practice of engineering or surveying shall report it to the board, may report it to appropriate legal authorities,and shall cooperate with the board and those authorities as requested.9. Licensees shall not knowingly provide false or incomplete information regarding an applicant in obtaininglicensure.10. Licensees shall comply with the licensing laws and rules governing their professional practice in each of thejurisdictions in which they practice.B. Licensee’s Obligation to Employer and Clients1. Licensees shall undertake assignments only when qualified by education or experience in the specific technicalfields of engineering or surveying involved.2. Licensees shall not affix their signatures or seals to any plans or documents dealing with subject matter in whichthey lack competence, nor to any such plan or document not prepared under their responsible charge.3. Licensees may accept assignments and assume responsibility for coordination of an entire project if each technicalsegment is signed and sealed by the licensee responsible for preparation of that technical segment.4. Licensees shall not reveal facts, data, or information obtained in a professional capacity without the prior consentof the client, employer, or public body on which they serve except as authorized or required by law or rules.5. Licensees shall not solicit or accept gratuities, directly or indirectly, from contractors, their agents, or other partiesin connection with work for employers or clients.6. Licensees shall disclose to their employers or clients all known or potential conflicts of interest or othercircumstances that could influence or appear to influence their judgment or the quality of
FE Reference Handbook 10.0.1 This document may be printed from the . Second printing May 2020 Edition 10.0.1. iii Preface About the Handbook The Fundamentals of Engineering (FE) exam is computer-based, and the FE Reference Handbook is the only resource material you may use during the exam. Reviewing it before exam day will help you become .
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How to use this Handbook This Handbook is used to complement the rest of the course materials. For your easy reference and use, this Handbook is downloadable. This Handbook provides some basic information about the IPA system for English pronunciation in order to help you master phonetic transcription. This Handbook includes the following sections:
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The Fundamentals of Engineering (FE) Supplied-Reference Handbook is the only reference material allowed in the FE examination. Many examinees find that it is helpful to review this book before exam day to become familiar with the reference material it contains. If you have purchased or downloaded the Reference Handbook
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