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FE
NATIONAL COUNCIL OF EXAMINERS FOR ENGINEERING AND SURVEYING NCEES.ORG/EXAMS
This document is copyrighted by NCEES and must be reproduced
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Contact permissions@ncees.org for more information.
© September 2014, All rights reserved.
National Council of Examiners for Engineering and Surveying
FUNDAMENTALS OF ENGINEERING
SAMPLE
QUESTIONS
Only one thing is better
than being an engineer.
Being a P.E.
Clean water. Sound structures. Safe power. We are charged with preserving these
and many more fundamentals that protect the health, safety, and welfare of
the public. Earn your license, and join the national community of professionals
committed to excellence.
YOUR BOARD SETS THE BAR
Engineering licensure in the United States is regulated by licensing boards in each
state and territory. These boards set and maintain the standards that protect
the public they serve. As a result, licensing requirements and procedures vary
by jurisdiction, so stay in touch with your board (ncees.org/licensing-boards).
NCEES
NCEES is a national nonprofit organization made up of the U.S. engineering and
surveying licensing boards in all 50 states, U.S. territories, and the District of
Columbia. It develops and scores the exams used for engineering and surveying
licensure in the United States. It also promotes professional mobility through its
services for licensees and its member boards.
Licensure: what it takes
These are the general requirements for licensure in the United States.
Check with your licensing board for details specific to your jurisdiction.
EDUCATION
Earn your 4-year bachelor of science degree.
Make sure that your engineering program is EAC/ABET accredited.
EXAMINATIONS
Pass the FE exam.
Take the FE exam right before or after you graduate. It is administered year-round
at approved Pearson VUE test centers throughout the United States, the District
of Columbia, and U.S. territories. Registration is always open, so plan ahead.
Visit ncees.org/exams to review your state board’s policies and procedures.
Pass the exam, and become an E.I. (engineer intern) or E.I.T. (engineer-in-training).
Pass the PE exam.
This exam is offered in April and October, though some disciplines are offered only
annually. Registration opens 3–4 months ahead and closes 4–6 weeks before the
exam date. Some state licensing boards require you to gain experience before you
can take the PE exam. Access your state licensing board’s policies and procedures
at ncees.org/exams.
EXPERIENCE
Get 4 years of engineering experience.
This means progressive, acceptable, and verifiable work in the industry.
Some boards require your supervisors to be professional engineers.
Take the first step.
Take the FE.
The Fundamentals of Engineering, or FE, exam is the first exam required for licensure
as a P.E. (professional engineer). You’ll choose one of 7 freestanding, discipline-specific
exams:
•
•
•
•
Chemical
• Industrial
Civil• Mechanical
Electrical and Computer
• Other Disciplines
Environmental
If you’re not sure which exam discipline to choose, look through FE Sample Questions
to help you decide. Each section contains the exam specifications, or subject areas,
and 10 sample questions and solutions for each discipline.
When you’re ready to take your exam, go to ncees.org/FE-exam to register.
Once approved, you’ll schedule an appointment at an approved Pearson VUE
test center near you.
Add it together.
Licensure sets you apart.
Here’s how.
RECOGNITION
“P.E.” instantly says that you’re experienced, knowledgeable, and accountable.
GROWTH
Engineering positions at all levels of industry and government increasingly
require licensure.
AUTHORITY
As a P.E., you can consult in private practice. Without it, you don’t have the
same opportunities.
MOBILITY
Earning your P.E. license in one state allows you to more easily apply for licensure
in other states—a process known as comity licensure.
MONEY
Salary studies show that as a P.E., you can expect to earn significantly more
throughout your career.
FE EXAM
Q&A
WHAT’S THE FORMAT?
Each exam contains 110 multiple-choice questions and is administered via computer at
approved Pearson VUE test centers. A 6-hour appointment time includes a tutorial, the exam,
a break, and a survey. You’ll have 5 hours and 20 minutes to complete the actual exam.
WHAT DOES THE EXAM COVER?
The exam is designed for recent graduates and students who are close to finishing an
undergraduate engineering degree. There are 7 freestanding, discipline-specific FE exams.
The full exam specifications for each discipline are included in this book and are posted
online at ncees.org/FE-exam.
WHAT CAN I TAKE INTO THE EXAM ROOM?
The following items are allowed in the exam room: your ID, an NCEES-approved calculator, key
to your test center locker, reusable booklet provided by Pearson VUE, eyeglasses, light sweater
or jacket, and items included in the Pearson VUE Comfort Aid List. An electronic version of the
FE Reference Handbook is incorporated into the exam.
HOW CAN I PREPARE?
Purchase an NCEES FE computer-based practice exam, which provides the most realistic
exam-day simulation available (ncees.org/PracticeExams).
HOW DO I REGISTER?
Log in to your MyNCEES account, select the REGISTER button, and follow the onscreen
instructions. If you need to create a MyNCEES account, go to account.ncees.org.
HOW DO I SCHEDULE MY EXAM?
Once your completed registration is approved, you’ll receive an email notification that you’re
authorized to take the exam and are eligible to schedule your exam appointment. To schedule
your exam, log in to MyNCEES, select the SCHEDULE button, and follow the onscreen
instructions.
WHERE AND WHEN CAN I TAKE THE EXAM?
The FE is offered year round at approved Pearson VUE test centers.
WHERE CAN I LEARN MORE?
For more information, download the NCEES Examinee Guide or visit ncees.org/FE-exam.
You can also go to youtube.com/NCEESMedia to watch short instructional videos that explain
what to expect on exam day.
NCEES practice exams
We do the exams. You do the math.
Study with NCEES.
PURSUE EVERY ADVANTAGE
Why not study with NCEES? You’ll have the advantage of using a product that is
developed by the same people who create the exam that you are preparing to take.
No other study materials can give you that.
KNOW WHAT TO EXPECT
NCEES practice exams are an excellent tool for helping you determine what you
know—and what you don’t know—before taking the exam. The computer-based
practice exams
• Contain questions and solutions from past exams
• Simulate the real format, style, and level of difficulty
• Provide immediate feedback on performance in each topic area
FE COMPUTER-BASED PRACTICE EXAMS
Evaluate your readiness for the FE exam by testing your knowledge with the most
realistic computer-based simulation available. Each timed practice exam consists
of 50 questions and functions much the same as the actual exam. You will be given
2.5 hours to complete your exam. Solutions to the questions will show you how to
approach problems, and immediate feedback about your performance in each topic
area can help you focus your preparation.
PU
R
CH
N.
RA
T IO
10%
N
Chemical
Civil
Electrical and Computer
Environmental
Industrial
Mechanical
Other Disciplines
SAVE
W HE
•
•
•
•
•
•
•
$49.95 each
ST
Choose your discipline:
AS
ED
W IT H E X A M
RE
GI
If you purchase an FE computer-based practice
exam at the same time you register for an exam,
you’ll receive a 10 percent discount on the practice exam.
FE REFERENCE HANDBOOK
Reviewing the handbook before exam day will help you become familiar with the
charts, formulas, tables, and other reference information provided. Download the
PDF and practice using it to help you navigate easily on exam day.
• Print
• Download
$13.95
Free
Order at ncees.org/PracticeExams.
PROVE YOURSELF WITHOUT SAYING A WORD.
Standards matter. Character counts. Now more than ever, your P.E. can be the
competitive edge you need.
TABLE
OF CONTENTS
DISCIPLINE
Chemical
2
Civil
13
Electrical and Computer
24
Environmental
34
Industrial
44
Mechanical
54
Other Disciplines
63
CHEMICAL
Fundamentals of Engineering (FE)
CHEMICAL CBT Exam Specifications
Effective Beginning with the January 2014 Examinations
•
•
•
The FE exam is a computer-based test (CBT). It is closed book with an electronic reference.
Examinees have 6 hours to complete the exam, which contains 110 multiple-choice questions.
The 6-hour time also includes a tutorial, a break, and a brief survey at the conclusion.
The FE exam uses both the International System of Units (SI) and the US Customary System (USCS).
Knowledge 2
Number of Questions
1.
Mathematics A. Analytic geometry
B. Roots of equations
C. Calculus
D. Differential equations
8–12
2.
Probability and Statistics A. Probability distributions (e.g., discrete, continuous, normal, binomial)
B. Expected value (weighted average) in decision making
C. Hypothesis testing
D. Measures of central tendencies and dispersions (e.g., mean, mode,
standard deviation)
E. Estimation for a single mean (e.g., point, confidence intervals)
F. Regression and curve fitting
4–6
3.
Engineering Sciences A. Applications of vector analysis (e.g., statics)
B. Basic dynamics (e.g., friction, force, mass, acceleration, momentum)
C. Work, energy, and power (as applied to particles or rigid bodies)
D. Electricity and current and voltage laws (e.g., charge, energy, current,
voltage, power, Kirchhoff, Ohm)
4–6
4.
Computational Tools A. Numerical methods and concepts (e.g., convergence, tolerance)
B. Spreadsheets for chemical engineering calculations
C. Simulators
4–6
5.
Materials Science A. Chemical, electrical, mechanical, and physical properties
(e.g., effect of temperature, pressure, stress, strain)
B. Material types and compatibilities (e.g., engineered materials,
ferrous and nonferrous metals)
C. Corrosion mechanisms and control
4–6
6.
Chemistry A. Inorganic chemistry (e.g., molarity, normality, molality, acids, bases,
redox reactions, valence, solubility product, pH, pK, electrochemistry,
periodic table)
B. Organic chemistry (e.g., nomenclature, structure, qualitative and
quantitative analyses, balanced equations, reactions, synthesis, basic
biochemistry)
8–12
Fluid Mechanics/Dynamics A. Fluid properties
B. Dimensionless numbers (e.g., Reynolds number)
C. Mechanical energy balance (e.g., pipes, valves, fittings, pressure losses across
packed beds, pipe networks)
D. Bernoulli equation (hydrostatic pressure, velocity head)
E. Laminar and turbulent flow
F. Flow measurement (e.g., orifices, Venturi meters)
G. Pumps, turbines, and compressors
H. Compressible flow and non-Newtonian fluids
8–12
8.
Thermodynamics A. Thermodynamic properties (e.g. specific volume, internal energy, enthalpy,
entropy, free energy)
B. Properties data and phase diagrams (e.g. steam tables, psychrometric charts,
T-s, P-h, x-y, T-x-y)
C. Thermodynamic laws (e.g., 1st law, 2nd law)
D. Thermodynamic processes (e.g., isothermal, adiabatic, isentropic)
E. Cyclic processes and efficiency (e.g., power, refrigeration, heat pump)
F. Phase equilibrium (e.g., fugacity, activity coefficient)
G. Chemical equilibrium
H. Heats of reaction and mixing
8–12
9.
Material/Energy Balances A. Mass balance (steady and unsteady state)
B. Energy balance (steady and unsteady state)
C. Recycle/bypass processes
D. Reactive systems (e.g., combustion)
8–12
10. Heat Transfer A. Conductive heat transfer
B. Convective heat transfer (natural and forced)
C. Radiation heat transfer
D. Heat transfer coefficients (e.g., overall, local, fouling)
E. Heat transfer equipment, operation, and design (e.g., double pipe, shell and
tube, fouling, number of transfer units, log-mean temperature difference,
flow configuration)
8–12
11.
8–12
Mass Transfer and Separation A. Molecular diffusion (e.g., steady and unsteady state, physical property estimation)
B. Convective mass transfer (e.g., mass transfer coefficient, eddy diffusion)
C. Separation systems (e.g., distillation, absorption, extraction, membrane processes)
D. Equilibrium stage methods (e.g., graphical methods, McCabe-Thiele, efficiency)
E. Continuous contact methods (e.g., number of transfer units, height equivalent to a
theoretical plate, height of transfer unit, number of theoretical plates)
F. Humidification and drying
CHEMICAL
7.
3
CHEMICAL
4
12. Chemical Reaction Engineering A. Reaction rates and order
B. Rate constant (e.g., Arrhenius function)
C. Conversion, yield, and selectivity
D. Type of reactions (e.g., series, parallel, forward, reverse, homogeneous,
heterogeneous, catalysis, biocatalysis)
E. Reactor types (e.g., batch, semibatch, continuous stirred tank, plug flow,
gas phase, liquid phase)
8–12
13. Process Design and Economics A. Process flow diagrams and piping and instrumentation diagrams
B. Equipment selection (e.g., sizing and scale-up)
C. Cost estimation
D. Comparison of economic alternatives (e.g., net present value,
discounted cash flow, rate of return, expected value and risk)
E. Process design and optimization (e.g., sustainability, efficiency,
green engineering, inherently safer design, evaluation of specifications)
8–12
14. Process Control A. Dynamics (e.g., time constants and 2nd order, underdamped, and
transfer functions)
B. Control strategies (e.g., feedback, feed-forward, cascade, ratio, and PID)
C. Control loop design and hardware (e.g., matching measured and manipulated
variables, sensors, control valves, and conceptual process control)
5–8
15. Safety, Health, and Environment A. Hazardous properties of materials (e.g., corrosivity, flammability,
toxicity, reactivity, handling and storage), including MSDS
B. Industrial hygiene (e.g., noise, PPE, ergonomics)
C. Process safety and hazard analysis [e.g., layer of protection analysis,
hazard and operability studies (HazOps), fault-tree analysis or event tree]
D. Overpressure and underpressure protection (e.g., relief, redundant control,
intrinsically safe)
E. Waste minimization, waste treatment, and regulation (e.g., air, water, solids,
RCRA, CWA, EPA, OSHA)
5–8
16. Ethics and Professional Practice A. Codes of ethics (professional and technical societies)
B. Agreements and contracts
C. Ethical and legal considerations
D. Professional liability
E. Public protection issues (e.g., licensing boards)
2–3
2.
3.
CHEMICAL
1.
The only point of inflection on the curve representing the equation y = x3 + x2 – 3 is at:
A.
2
x=- 3
B.
1
x=- 3
C.
x=0
D.
1
x= 3
Which of the following occurs in the reaction Cu+2 + Zn → Cu + Zn+2?
A.
Only copper is oxidized.
B.
Only zinc is oxidized.
C.
Both copper and zinc are oxidized.
D.
Neither copper nor zinc is oxidized.
The pressure of 100 kg of nitrogen (N2) at 70°C in a 100-m3 tank is most nearly:
A.
2,850 kPa
B.
102 kPa
C.
20 kPa
D.
102 mPa
5
CHEMICAL
4.
Hydrogen (H2) and oxygen (O2) are reacted in a fuel cell to produce energy. The product
of the reaction is water, and any excess gases are vented after the fuel cell, as shown in
the figure below. The hydrogen and oxygen tanks are maintained at the same temperature
and pressure, and they feed at the same volumetric flow rate. The reaction goes to 60%
completion in the fuel cell (hydrogen basis).
If all of the unreacted hydrogen and a portion of the unreacted oxygen are recycled, then
the molar ratio of oxygen in the vent to oxygen in the fresh feed is most nearly:
RECYCLE
H2
FUEL
CELL
SEPARATOR
O2
H2O
6
A.
0.00
B.
0.50
C.
0.58
D.
0.82
VENT
CHEMICAL
5.
The following figure is the solution of a binary distillation tower design using the
McCabe-Thiele method. The equilibrium curve shown is for Component A. Component A
is separated from B in the distillation column to produce a distillate that is 97 mole% A.
The feed rate to the tower is 100 kmol/hr. The tower includes a partial reboiler and total
condenser. The bottoms flow rate (kmol/hr) is most nearly:
1.0
9
8
0.8
7
MOLE FRACTION A, VAPOR
6
0.6
5
4
0.4
3
2
0.2
1
0.0
0.0
0.2
0.4
0.6
0.8
1.0
MOLE FRACTION A, LIQUID
A.
3.0
B.
42.6
C.
53.8
D.
97.0
7
CHEMICAL
6.
Operating conditions for a plug-flow reactor for the elementary liquid-phase reaction
A + B → R are as follows:
CAO = 0.10 kmol/m3
CB = 0.10 kmol/m3
V = 0.50 m3
q = 0.20 m3/min
CA (at exit) = 0.40 kmol/m3
The space time (min) for this reactor is most nearly:
A.
0.25
B.
0.40
C.
2.0
D.
2.5
7.
If $500 is invested at an annual interest rate of 8% per year, its future worth at the end of
30 years will be most nearly:
8
A.
$1,200
B.
$1,700
C.
$5,031
D.
$15,000
9.
CHEMICAL
8.
The volume (L) of 1 mol of H2O at 546 K and 1.00 atm pressure is most nearly:
A.
11.2
B.
14.9
C.
22.4
D.
44.8
A chemical plant has a waste stream containing 5% by weight HCl flowing at the rate of
1,000 L/min. Before it can be discharged, it must be neutralized with NaOH. A solution
of NaOH at a strength of 1% by weight is available. Molecular weights are as follows:
NaCl = 58.4
HCl
= 36.5
NaOH = 39.9
The specific gravity of the solutions may be assumed to be 1.0. The required flow rate
(L/min) of the NaOH stream is most nearly:
10.
A.
8,900
B.
5,500
C.
4,570
D.
220
As a professional engineer originally licensed 30 years ago, you are asked to evaluate
a newly developed computerized control system for a public transportation system.
You may accept this project if:
A.
B.
you are competent in the area of modern control systems
you do not live in the jurisdiction where the transportation system is being
installed
C.
your original area of specialization was in transportation systems
D.
you have regularly attended meetings of a professional engineering society
9
CHEMICAL
Solutions
Solutions
1.
f(x) = x3 + x2 – 3
Inflection point occurs when f "(x) = 0
Inflection point occurs when f "(x) = 0
1.
f(x) = x3 +2 x2 – 3
f '(x) = 3x + 2x
f '(x) = 3x2 + 2x
f "(x) = 6x + 2
f "(x) = 6x + 2
Set equal to zero
Set equal to zero
6x + 2 = 0
6x + 2 = 0
x = –1/3
x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
THE CORRECT ANSWER IS: B
THE CORRECT ANSWER IS: B
2.
2.
Oxidation is defined as the loss of electrons. In this case, Cu+2 → Cu, which gains two
+2 → Cu, which gains two electrons,
Oxidation
is defined
+2 loss of electrons. In this case, Cu
electrons, and
Zn → as
Znthe
, which loses two electrons. Therefore,
only zinc is oxidized.
and Zn → Zn+2, which loses two electrons. Therefore, only zinc is oxidized.
THE CORRECT ANSWER IS: B
THE CORRECT ANSWER IS: B
3.
3.
Use the ideal gas formula:
Use the ideal gas formula:
PV = mRT
mRT
P= V
8, 314 J kmol
J
R = kmole·K 28 kg = 297 kg·K
P=
J
(100 kg) b 297 kg·K l (343 K)
100 m3
= 102, 000 J 3
m
= 102, 000 N·m
m3
= 102, 000 N2
m
= 102 kPa
THE CORRECT ANSWER IS: B
10
6
Solutions
22
222
222
2
2
CHEMICAL
4.4.
4.
Solutions
Solutions
Solutions
1/2OO →
→
O
Balanced
Balancedequation:
equation:HH ++1/2
→HH
HO
O
Balanced
equation: H
PPOOOHand
and
VVHHH ==VVOOO and
===TTOTOO
and
Feed
characteristics:
since
PPHHHO==2=P→
and
andTTT
Feed
characteristics:
since
2 + 1/2
2O V
HHH
222
222
22
22 2
22 2
2 22
Feed characteristics:
since
PH = PO and VH = VO and TH = TO
Therefore,
from
Therefore,
fromideal
idealgas
gaslaw:
law:
2
2
2
2
Therefore, from ideal gas law:
RTHH no nHo H
HH PPHH VoVHo H ==no nHo H RT
Ratio
RatioOO2 2== 2 2 o o 2 2 2 2 2 2==no no 2 2==1.0
1.0
no nOonoO2H2RT
RT
RT2H22 nOo OH2 22
H2 22 PPPOHO222VV2H2=2==
2 OO
=
=1.0
Ratio O =
PO2 Vo 2 = no O2 RTO2 no O2
2
Using
mole
feed,
and
all
the
would
feed,
and
atmaximum
maximum
H2 2recycle,
recycle,
allhydrogen
thehydrogen
hydrogen
wouldbe
be
Usingbasis
basisof
of11mole
moleHHH
basis
of
ininin
feed,
and
at at
maximum
H2 H
recycle,
all the
would
22 2
consumed:
consumed:
be
consumed:
Using
basis of 1 mole H2 in feed, and at maximum H2 recycle, all the hydrogen would be
Balance
→HH
H22O
O
Balanceequation:
equation:HH2 22++1/2
consumed:
1/2OO222→
→
2O
Balance equation: H2 + 1/2 O2 → H2O
OO2 2OUT
0.5mole
mole==
OUT 0.5
==1.0
Ratio
0.5
Ratio OO
0.5
mole
1.0
mole
IN
O222IN
0.5
mole
OUT
= 1.0 mole = 0.5
Ratio O
2 IN
THE
THECORRECT
CORRECTANSWER
ANSWERIS:
IS:BB
THE CORRECT ANSWER IS: B
5.5.
5.
5.
6.6.
6.
Feed
Feed
bottoms
distillate
100kg/hr
=bottoms
+distillate
=100kg/hr
Feed==
bottoms++
distillate==
100kg/hr
=diagram,
+ distillate
=of
Feed diagram,
bottoms
100kg/hr
mole
fraction
From
mole
fraction
of
the
feed
47%.
From
diagram,
mole
fraction
ofAA
Ainin
inthe
thefeed
feedisis
is47%.
47%.
From
diagram,
mole
fraction
of
A
in
the
feed
is
47%.
From
Balance
Balance
on
gives
Balanceon
onAA
Agives
gives
Balance
A++
gives
47
000.04
..on
..04
47
97
=000.97
+
47==
97DD
D
04BB
B
=
+
.
.
47
0
97
D
0
04
since
since
100
=100
-DD
sinceBB
B==
100-D B
43
since
B =43
100
D
43==-46
then
then
=93
= 46
D==
46.2..22
thenDD
93
93
43
=100
=46
46.2 53
then D
and
and
93-=100
-46
= 53
andBB
B==
100
46.2..22==
53.8..88
and B = 100 - 46.2 = 53.8
THE
THECORRECT
CORRECTANSWER
ANSWERIS:
IS:CC
THE CORRECT ANSWER IS: C
THE CORRECT ANSWER IS: C
VV
0.50
0.50mm3 3
==2.5
xx==qq==
2.5min
min
3
mm3 3/min
0.20
/min
V 0.20
0.50
m
=
x
=q=
=
= 2.5 min
x=
0.20 m3 /min
THE
THECORRECT
CORRECTANSWER
ANSWERIS:
IS:DD
THE CORRECT ANSWER IS: D
77
7
11
CHEMICAL
Solutions
F
7.
0
1
2
3
30
500
i = 8%
F = 500(F/P, 8%, 30)
= 500 (10.0627)
= $5,031
THE CORRECT ANSWER IS: C
8.
Pv = nRT
(1)(v) = (1)(0.08206)(546)
v = 44.8 L
THE CORRECT ANSWER IS: D
9.
1, 000
1.00 kg 5 kg HCl
kmol HCl
L
×
× L ×
100 kg
36.5 kg HCl
min
= F×
1.00 kg 1kg NaOH
kmol NaOH
L × 100 kg × 39.9 kg NaOH
F = 5, 466 L/min
THE CORRECT ANSWER IS: B
10.
Refer to the NCEES Rules of Professional Conduct.
THE CORRECT ANSWER IS: A
12
Fundamentals of Engineering (FE)
CIVIL CBT Exam Specifications
Effective Beginning with the January 2014 Examinations
•
•
Knowledge CIVIL
•
The FE exam is a computer-based test (CBT). It is closed book with an electronic reference.
Examinees have 6 hours to complete the exam, which contains 110 multiple-choice questions.
The 6-hour time also includes a tutorial, a break, and a brief survey at the conclusion.
The FE exam uses both the International System of Units (SI) and the US Customary System (USCS).
Number of Questions
1.
Mathematics A. Analytic geometry
B. Calculus
C. Roots of equations
D. Vector analysis
7–11
2.
Probability and Statistics A. Measures of central tendencies and dispersions (e.g., mean, mode,
standard deviation)
B. Estimation for a single mean (e.g., point, confidence intervals)
C. Regression and curve fitting
D. Expected value (weighted average) in decision making
4–6
3.
Computational Tools A. Spreadsheet computations
B. Structured programming (e.g., if-then, loops, macros)
4–6
4.
Ethics and Professional Practice
A. Codes of ethics (professional and technical societies)
B. Professional liability
C. Licensure
D. Sustainability and sustainable design
E. Professional skills (e.g., public policy, management, and business)
F. Contracts and contract law
4–6
5.
Engineering Economics A. Discounted cash flow (e.g., equivalence, PW, equivalent annual worth,
FW, rate of return)
B. Cost (e.g., incremental, average, sunk, estimating)
C. Analyses (e.g., breakeven, benefit-cost, life cycle)
D. Uncertainty (e.g., expected value and risk)
4–6
6.
Statics
A. Resultants of force systems
B. Equivalents of force systems
C. Equilibrium of rigid bodies
D. Frames and trusses
E. Centroid of area
F. Area moments of inertia
G. Static friction
7–11
13
CIVIL
14
7.
Dynamics
A. Kinematics (e.g., particles and rigid bodies)
B. Mass moments of inertia
C. Force acceleration (e.g., particles and rigid bodies)
D. Impulse momentum (e.g., particles and rigid bodies)
E. Work, energy, and power (e.g., particles and rigid bodies)
4–6
8.
Mechanics of Materials A. Shear and moment diagrams
B. Stresses and strains (e.g., axial, torsion, bending, shear, thermal)
C. Deformations (e.g., axial, torsion, bending, thermal)
D. Combined stresses
E. Principal stresses
F. Mohr’s circle
G. Column analysis (e.g., buckling, boundary conditions)
H. Composite sections
I. Elastic and plastic deformations
J. Stress-strain diagrams
7–11
9.
Materials
A. Mix design (e.g., concrete and asphalt)
B. Test methods and specifications (e.g., steel, concrete, aggregates, asphalt, wood)
C. Physical and mechanical properties of concrete, ferrous and nonferrous metals,
masonry, wood, engineered materials (e.g., FRP, laminated lumber, wood/plastic
composites), and asphalt
4–6
10. Fluid Mechanics A. Flow measurement
B. Fluid properties
C. Fluid statics
D. Energy, impulse, and momentum equations
4–6
11.
8–12
Hydraulics and Hydrologic Systems A. Basic hydrology (e.g., infiltration, rainfall, runoff, detention, flood flows,
watersheds)
B. Basic hydraulics (e.g., Manning equation, Bernoulli theorem, open-channel
flow, pipe flow)
C. Pumping systems (water and wastewater)
D. Water distribution systems
E. Reservoirs (e.g., dams, routing, spillways)
F. Groundwater (e.g., flow, wells, drawdown)
G. Storm sewer collection systems
Structural Analysis
A. Analysis of forces in statically determinant beams, trusses, and frames
B. Deflection of statically determinant beams, trusses, and frames
C. Structural determinacy and stability analysis of beams, trusses, and frames
D. Loads and load paths (e.g., dead, live, lateral, influence lines and moving
loads, tributary areas)
E. Elementary statically indeterminate structures
6–9
13.
Structural Design
A. Design of steel components (e.g., codes and design philosophies, beams,
columns, beam-columns, tension members, connections)
B. Design of reinforced concrete components (e.g., codes and design
philosophies, beams, slabs, columns, walls, footings)
6–9
14.
Geotechnical Engineering A. Geology
B. Index properties and soil classifications
C. Phase relations (air-water-solid)
D. Laboratory and field tests
E. Effective stress (buoyancy)
F. Stability of retaining walls (e.g., active pressure/passive pressure)
G. Shear strength
H. Bearing capacity (cohesive and noncohesive)
I. Foundation types (e.g., spread footings, deep foundations, wall
footings, mats)
J. Consolidation and differential settlement
K. Seepage/flow nets
L. Slope stability (e.g., fills, embankments, cuts, dams)
M. Soil stabilization (e.g., chemical additives, geosynthetics)
N. Drainage systems
O. Erosion control
9–14
15.
Transportation Engineering A. Geometric design of streets and highways
B. Geometric design of intersections
C. Pavement system design (e.g., thickness, subgrade, drainage, rehabilitation)
D. Traffic safety
E. Traffic capacity
F. Traffic flow theory
G. Traffic control devices
H. Transportation planning (e.g., travel forecast modeling)
8–12
CIVIL
12.
15
CIVIL
16
16. Environmental Engineering A. Water quality (ground and surface)
B. Basic tests (e.g. water, wastewater, air)
C. Environmental regulations
D. Water supply and treatment
E. Wastewater collection and treatment
6–9
17. Construction
A. Construction documents
B. Procurement methods (e.g., competitive bid, qualifications-based)
C. Project delivery methods (e.g., design-bid-build, design build, construction
management, multiple prime)
D. Construction operations and methods (e.g., lifting, rigging, dewatering
and pumping, equipment production, productivity analysis and improvement,
temporary erosion control)
E. Project scheduling (e.g., CPM, allocation of resources)
F. Project management (e.g., owner/contractor/client relations)
G. Construction safety
H. Construction estimating
4–6
18. Surveying
A. Angles, distances, and trigonometry
B. Area computations
C. Earthwork and volume computations
D. Closure
E. Coordinate systems (e.g., state plane, latitude/longitude)
F. Leveling (e.g., differential, elevations, percent grades)
4–6
1.
A.
2
x=- 3
B.
1
x=- 3
C.
x=0
D.
1
x= 3
CIVIL
2.
The only point of inflection on the curve representing the equation y = x3 + x2 – 3 is at:
As a professional engineer originally licensed 30 years ago, you are asked to evaluate
a newly developed computerized control system for a public transportation system.
You may accept this project if:
A.
B.
you are competent in the area of modern control systems
you do not live in the jurisdiction where the transportation system is being
installed
C.
your original area of specialization was in transportation systems
D.
you have regularly attended meetings of a professional engineering society
3.
If $500 is invested at an annual interest rate of 8% per year, its future worth at the end
of 30 years will be most nearly:
A.
$1,200
B.
$1,700
C.
$5,031
D.
$15,000
17
4.
The following preliminary concrete mix has been designed assuming that the aggregates
are in oven-dry condition.
CIVIL
Water = 305 lb/yd3
Cement = 693 lb/yd3
Coarse aggregate (SSD) = 1,674 lb/yd3
Fine aggregate (SSD) = 1,100 lb/yd3
The properties of the aggregates are:
Coarse
Aggregate
Fine
Aggregate
Absorption (moisture content at SSD)
0.5%
0.7%
Moisture content as used in mix
2.0%
6.0%
Property
The amount of water (lb/yd3) that would be used in the final mix is most nearly:
5.
18
A.
206
B.
222
C.
305
D.
388
A 20-acre parcel of land has a rainfall intensity of 1.5 in./hr and a rational method runoff
coefficient (C) of 0.10. The flow rate (cfs) for this site is most nearly:
A.
3.0
B.
5.0
C.
7.5
D.
9.0
6.
Beam AB has a distributed load as shown and supports at A and B. If the weight of the
beam is negligible, the force RB (kN) is most nearly:
3m
3m
CIVIL
8 kN/m
A
B
RA
7.
A.
24
B.
12
C.
10
D.
8
RB
Which of the following is true of a normally consolidated clay?
A.
It will not settle further under present loading conditions.
B.
It appears to have been subjected to previous desiccation or drying.
C.
It will settle an additional amount if the water table rises.
D.
It appears to have been subjected to greater loading condition.
19
8.
A horizontal circular curve has the following data:
I = 40°50'
R = 600.00
Station of PI = 20+00.00
CIVIL
The station of the PT is most nearly:
9.
10.
20
A.
22+00.76
B.
22+04.27
C.
22+23.34
D.
22+32.34
A municipal wastewater treatment plant is processing a waste flow with a 5-day BOD of
200 mg/L at 20°C. If the BOD rate constant k1 (base e) at 20°C is 0.23 day–1, the ultimate
BOD (mg/L) of the raw wastewater at 20°C is most nearly:
A.
133
B.
233
C.
293
D.
420
A loader has a full-bucket capacity of 3 yd3, and the average time required to place one
bucketload of soil into a truck is 1 min. The loader is supported by four trucks with
a volume of 15 yd3 each and a cycle time of 12 min plus the time to load the truck.
The ideal productivity (yd3/hr) of this system is most nearly:
A.
180
B.
212
C.
277
D.
300
Solutions
1.
f(x) = x3 + x2 – 3
Inflection point occurs when f "(x) = 0
f '(x) = 3x2 + 2x
f "(x) = 6x + 2
Set equal to zero
CIVIL
6x + 2 = 0
x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
THE CORRECT ANSWER IS: B
2.
Refer to the NCEES Rules of Professional Conduct.
THE CORRECT ANSWER IS: A
F
3.
0
1
2
3
30
500
i = 8%
F = 500(F/P, 8%, 30)
= 500 (10.0627)
= $5,031
THE CORRECT ANSWER IS: C
4.
The moisture content of each aggregate includes: (1) water that would be needed to bring
aggregates to SSD condition (the absorbed water) and (2) the excess water that is free to
add to the mix water. Since the as-used moisture content is greater than the absorption for
each aggregate, each aggregate contributes the excess water to the mix, thus reducing the
water that must be added to the mix. The water added to the mix is the water computed for
oven-dry aggregates (305 lb/yd3) plus the excess water in each aggregate.
Final water = 305 – [(2.0% – 0.5%)/100] × 1,674 – [(6.0% – 0.7%)/100] × 1,100 = 221.6 lb/yd3
THE CORRECT ANSWER IS: B
21
Solutions
Solutions
5.
Use the rational formula.
5.
Use the rational formula.
Q = CIA
Q
in./hr)(20 acres) = 3.0 cfs
Q=
= (0.10)(1.5
CIA
CIVIL
Q = (0.10)(1.5 in./hr)(20 acres) = 3.0 cfs
THE CORRECT ANSWER IS: A
THE CORRECT ANSWER IS: A
6.
6.
The triangular force distribution can be replaced with a concentrated force F acting
through
the centroid
of the triangle.
magnitude
of aFconcentrated
is numerically
equal
to the through the
The triangular
force distribution
canThe
be replaced
with
force
F acting
area
of
the
triangle.
centroid of the triangle. The magnitude of F is numerically equal to the area of the triangle.
F
F = 1/2(3m)(8 kN/m)
F = 12 kN/m
5m
F
5m
ΣMAA == 00
ΣMAA == (6m)(R
(6m)(RBB)) −− (5m)(12
(5m)(12 kN/m)
kN/m)
(6m)(RBB)) −− (5m)(12
(5m)(12 kN/m)
kN/m) == 00
6m
6RBB == (5m)(12
(5m)(12 kN/m)
kN/m)
6RBB== 60
60 kN
kN
RA
RA
RBB == 10
10 kN
kN
6m
RB
RB
THE CORRECT ANSWER IS: C
7.
A normally consolidated clay will not settle further under present loading conditions.
THE CORRECT ANSWER IS: A
8.
40.8333°
I
= 223.34
T = R tan ` 2 j = 600 × tan
2
r
r
L = RI 180 = 600 × 40.8333°× 180 = 427.61
PC = PI - T = 20 + 00.00 - 223.34 = 17 + 76.66
PT = PC + L = 17 + 76.66 + 427.61 = 22 + 04.27
THE CORRECT ANSWER IS: B
22
6
Solutions
Solutions
9.
BOD5 = 200 mg/L
∴ t = 5 days
k1 = 0.23 day−1
BODt = BODult (1 − e−k1t)
CIVIL
200 mg/L = BODult (1 − e−0.23 × 5)
BODult = 200/(1 − e−1.15)
BODult = 292.7 mg/L
THE CORRECT ANSWER IS: C
10.
Time to load one truck = 15 yd3/3 yd3/min
= 5 min
Four trucks are available.
Cycle time for one truck = 5 min loading plus 12 min to travel, dump, and return = 17 min.
Loading time for four trucks = 4 × 5 = 20 min.
Therefore, an empty truck is always available to load.
yd3
60 min/hr
Ideal production capacity = a 5 min/truck kc15 truck m
yd3
= 180 hr
THE CORRECT ANSWER IS: A
7
23
Fundamentals of Engineering (FE)
ELECTRICAL AND COMPUTER CBT Exam Specifications
Effective Beginning with the January 2014 Examinations
•
•
•
The FE exam is a computer-based test (CBT). It is closed book with an electronic reference.
Examinees have 6 hours to complete the exam, which contains 110 multiple-choice questions.
The 6-hour time also includes a tutorial, a break, and a brief survey at the conclusion.
The FE exam uses both the International System of Units (SI) and the US Customary System (USCS).
ELECTRICAL &
COMPUTER
Knowledge 24
Number of Questions
1.
Mathematics A. Algebra and trigonometry
B. Complex numbers
C. Discrete mathematics
D. Analytic geometry
E. Calculus
F. Differential equations
G. Linear algebra
H. Vector analysis
11–17
2.
Probability and Statistics A. Measures of central tendencies and dispersions (e.g., mean, mode,
standard deviation)
B. Probability distributions (e.g., discrete, continuous, normal, binomial)
C. Expected value (weighted average) in decision making
D. Estimation for a single mean (e.g., point, confidence intervals,
conditional probability)
4–6
3.
Ethics and Professional Practice A. Codes of ethics (professional and technical societies)
B. NCEES Model Law and Model Rules
C. Intellectual property (e.g., copyright, trade secrets, patents)
3–5
4.
Engineering Economics A. Time value of money (e.g., present value, future value, annuities)
B. Cost estimation
C. Risk identification
D. Analysis (e.g., cost-benefit, trade-off, breakeven)
3–5
5.
Properties of Electrical Materials A. Chemical (e.g., corrosion, ions, diffusion)
B. Electrical (e.g., conductivity, resistivity, permittivity, magnetic permeability)
C. Mechanical (e.g., piezoelectric, strength)
D. Thermal (e.g., conductivity, expansion)
4–6
6.
Engineering Sciences
A. Work, energy, power, heat
B. Charge, energy, current, voltage, power
C. Forces (e.g., between charges, on conductors)
D. Work done in moving a charge in an electric field (relationship between
voltage and work)
6–9
E.
F.
7.
Capacitance
Inductance
10–15
8. Linear Systems
A. Frequency/transient response
B. Resonance
C. Laplace transforms
D. Transfer functions
E. 2-port theory
5–8
9. Signal Processing A. Convolution (continuous and discrete)
B. Difference equations
C. Z-transforms
D. Sampling (e.g., aliasing, Nyquist theorem)
E. Analog filters
F. Digital filters
5–8
10. Electronics
A. Solid-state fundamentals (e.g., tunneling, diffusion/drift current, energy
bands, doping bands, p-n theory)
B. Discrete devices (diodes, transistors, BJT, CMOS) and models and their
performance
C. Bias circuits
D. Amplifiers (e.g., single-stage/common emitter, differential)
E. Operational amplifiers (ideal, non-ideal)
F. Instrumentation (e.g., measurements, data acquisition, transducers)
G. Power electronics
7–11
11. Power
A. Single phase and three phase
B. Transmission and distribution
C. Voltage regulation
D. Transformers
E. Motors and generators
F. Power factor (pf)
8–12
12. Electromagnetics
A. Maxwell equations
B. Electrostatics/magnetostatics (e.g., measurement of spatial
relationships, vector analysis)
C. Wave propagation
ELECTRICAL &
COMPUTER
Circuit Analysis (DC and AC Steady State) A. KCL, KVL
B. Series/parallel equivalent circuits
C. Thevenin and Norton theorems
D. Node and loop analysis
E. Waveform analysis (e.g., RMS, average, frequency, phase, wavelength)
F. Phasors
G. Impedance
5–8
25
ELECTRICAL &
COMPUTER
D.Transmission lines (high frequency)
E.Electromagnetic compatibility
26
13.
Control Systems
A. Block diagrams (feed-forward, feedback)
B. Bode plots
C. Closed-loop and open-loop response
D. Controller performance (gain, PID), steady-state errors
E. Root locus
F. Stability
G. State variables
6–9
14.
Communications
A. Basic modulation/demodulation concepts (e.g., AM, FM, PCM)
B. Fourier transforms/Fourier series
C. Multiplexing (e.g., time division, frequency division)
D.Digital communications
5–8
15.
Computer Networks
A. Routing and switching
B. Network topologies/frameworks/models
C. Local area networks
3–5
16.
Digital Systems
A. Number systems
B. Boolean logic
C. Logic gates and circuits
D. Logic minimization (e.g., SOP, POS, Karnaugh maps)
E. Flip-flops and counters
F. Programmable logic devices and gate arrays
G. State machine design
H. Data path/controller design
I. Timing (diagrams, asynchronous inputs, races, hazards)
7–11
17.
Computer Systems
A. Architecture (e.g., pipelining, cache memory)
B. Microprocessors
C. Memory technology and systems
D. Interfacing
4–6
18.
Software Development
A. Algorithms
B. Data structures
C. Software design methods (structured, object-oriented)
D. Software implementation (e.g., procedural, scripting languages)
E. Software testing
4–6
1.
A.
2
x=- 3
B.
1
x=- 3
C.
x=0
D.
1
x= 3
ELECTRICAL &
COMPUTER
2.
The only point of inflection on the curve representing the equation y = x3 + x2 – 3 is at:
As a professional engineer originally licensed 30 years ago, you are asked to evaluate
a newly developed computerized control system for a public transportation system.
You may accept this project if:
A.
B.
you are competent in the area of modern control systems
you do not live in the jurisdiction where the transportation system is being
installed
C.
your original area of specialization was in transportation systems
D.
you have regularly attended meetings of a professional engineering society
3.
If $500 is invested at an annual interest rate of 8% per year, its future worth at the end
of 30 years will be most nearly:
A.
$1,200
B.
$1,700
C.
$5,031
D.
$15,000
27
4.
In the circuit shown, voltage VO (V) is most nearly:
VO
+
19.5
B.
18.5
C.
16.5
D.
3.0
+
6V
6Ω
The following electronic system is designed to process measurements from an
accelerometer that produces the input voltage signal v1(t).
0.1 µF
120 kΩ
+
−
40 kΩ
v2(t)
−
+
−
+
v1(t)
10 kΩ
10 kΩ
+
−
5.
A.
6Ω
+
ELECTRICAL &
COMPUTER
36 V
3Ω
v3(t)
−
For a practical measurement situation, the signal v2 is periodic and can be characterized
by the Fourier series:
v2(t) = 1.6 sin (1,000t) + 0.8 sin (2,000t) + 0.4 sin (3,000t) + ....
The amplitude (volts) of the fundamental component in v3(t) is most nearly:
28
A.
1.6
B.
1.13
C.
0.56
D.
0.3
6.
The figure below shows a circuit with an n-channel enhancement mode MOSFET
transistor.
+15 V
R iDRAIN
+5 V
ELECTRICAL &
COMPUTER
vDRAIN
In the FET triode region:
iDRAIN = K[2(vGS – Vt)vDS – vDS2]
In the FET saturation region:
iDRAIN = K(vGS – Vt)2
The FET operates in saturation for vDS ≥ vGS – Vt.
Assume that K = 0.5 mA/V2 and Vt = 1 V.
If vDRAIN = 2 V, the value of R (kΩ) is most nearly:
7.
A.
1.63
B.
2.17
C.
2.50
D.
3.42
An industrial plant load is rated at 2.8 MVA at 0.7 pf lagging. If a capacitor bank rated at
3 MVA is added to the load, the new overall power factor of the system is most nearly:
A.
0.9 leading
B.
0.9 lagging
C.
0.6 leading
D.
0.6 lagging
29
8.
The following Routh array has been constructed for a simple control system
with a gain of K in the feedback path.
s4
s3
s2
s1
s0
1
12
42K
7
10 + 14K
74 – 14K
42K
2
196K – 602K – 740
42K
ELECTRICAL &
COMPUTER
The denominator of the closed-loop system transfer function is:
9.
10.
30
A.
s3 + 7s2 + 12s + 10
B.
s4 + 7s3 + 12s2 + 10s
C.
s4 + 7s3 + 12s2 + (10 + 14K)s + 42K
D.
not defined from the Routh array
Which of the following is true of the electric field intensity about an isolated
point charge?
A.
It varies directly as the distance to the charge.
B.
It varies inversely as the distance to the charge.
C.
It varies directly as the square of the distance to the charge.
D.
It varies inversely as the square of the distance to the charge.
The binary number 1011 corresponds to the decimal number:
A.
3
B.
10
C.
11
D.
15
Solutions
Solutions
f(x) = x3 + x2 – 3
Inflection point occurs when f "(x) = 0
f(x) = x3 +2 x2 – 3
Inflection point occurs when f "(x) = 0
f '(x) = 3x + 2x
f '(x) = 3x2 + 2x
f "(x) = 6x + 2
fSet
"(x)equal
= 6xto+ zero
2
Set equal to zero
6x + 2 = 0
6x + 2 = 0
x = –1/3
x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
THE CORRECT ANSWER IS: B
THE CORRECT ANSWER IS: B
2.
2.
Refer to the NCEES Rules of Professional Conduct.
Refer to the NCEES Rules of Professional Conduct.
THE CORRECT ANSWER IS: A
THE CORRECT ANSWER IS: A
3.
3.
0
0
1
1
2
2
3
3
ELECTRICAL &
COMPUTER
1.
1.
F
F
30
30
500
500
i = 8%
i = 8%
F
F
= 500(F/P, 8%, 30)
= 500(F/P, 8%, 30)
= 500 (10.0627)
= 500 (10.0627)
= $5,031
= $5,031
THE CORRECT ANSWER IS: C
THE CORRECT ANSWER IS: C
4.
4.
Apply KCL to the node marked VO:
Apply KCL to the node marked VO
:
1
1
1
3 ^VO - 36h + 6 VO + 6 ^VO - 6h = 0 ( VO = 19.5 V
THE CORRECT ANSWER IS: A
THE CORRECT ANSWER IS: A
31
5
Solutions
ELECTRICAL &
COMPUTER
5.
5.
5.
5.
5.
Solutions
The second stage of the circuit is an inverting
amplifier with a gain A given by:
Solutions
The second stage of the circuit is an inverting
amplifier with a gain A22 given by:
Solutions
Solutions
The second
stage of the circuit is an inverting amplifier with a gain A2 given by:
Z Fstage
10with
kX aagain
1 h
The
second
stage
ofthe
the
circuit
isan
inverting
amplifier
with
gainAA22given
givenby:
by:
The
of
amplifier
^ inverting
= 10 kis
A2 =second
Z Fcircuit
;an
where
X
j~1C = 1 + j~ ^10 k10
10ZkFX
X ×k0X.1nF×10 -6h
A2 = - ZZFF where Z F = 10 kX ; ^ j1~
10
1 Chhh = 1 + j~ ^10 k10
k×kX
10 kX where
X
0X.1giving
nF×10---666h
=
A22==frequency
ZFF==10
10kkX
where
X;;^^component
-- 10
=
A
Z
The
of
the
fundamental
is
1,000
rad/s,
X of the fundamental component
jj~~CC 11++jisj~~1,000
^10kkX
10 kkX
^10
Xrad/s,
10 hh
××00..11nn
FF××10
The frequency
giving
The frequency of10the
fundamental
component
is
1,000
rad/s,
giving
, 000
10 kX of
The
frequency
the
fundamental
component
1,000
rad/s,giving
giving
The
fundamental
component
- 45crad/s,
=ofthe
Z F =frequency
+ - 45c and
A2 = 0.707isis
+1,000
^110
+ kjhXX 10, 000
2
= 10,,000
Z F = 10kkX
+ - 45c and A2 = 0.707 + - 45c
000
+ jhX
1the
X ==10
2 of+
ZFF== ^10
+the
45
andAA22==00..707
707+
+--45
45cc of v (t) = 1.6 V, the amplitude of the
--45
Z
ccand
Since
amplitude
fundamental
component
2
^1++jhjhX
X
^1
22
(t) = 1.6 × 0.707
= 1.13 V.of v2(t) = 1.6 V, the amplitude of the
fundamental
component
Since the amplitude
of in
thev3fundamental
component
Since the
the
of
component
of of
vof
(t) =(t)1.6
theV,
of the of
Since
the amplitude
amplitude
ofthe
thefundamental
fundamental
component
1.6
V,amplitude
the amplitude
amplitude
of the
the
Since
amplitude
of
the
component
==V,
1.6
the
2 vv22(t)
(t) = 1.6 × 0.707
= 1.13 V.
fundamental
component
in
vfundamental
3(t)
fundamental
component
in
v
=
1.6
×
0.707
=
1.13
V.
= 1.6
fundamental
component
in v333(t)IS:
THE CORRECT
ANSWER
B × 0.707 = 1.13 V.
THE CORRECT ANSWER IS: B
THECORRECT
CORRECTANSWER
ANSWERIS:
IS:BB
THE
6.
6.
6.
6.
vDS = 2 V
vDS –= V2 V
=5–1=4V
GS ==22tV
V
vvvDS
DS
DS
= 4 Vtransistor operates in the triode region.
vGS <– vVt = –5 V– ,1so
DS ––VVGS
t11==4the
=
5
–
=
5
–
4VV
vvvGS
GS
ttt
GS
– V[2(4)(2)
operates in the triode region.
DS < vGS
t, so the –transistor
=
0.5
4] = 6 mA
ivvvDRAIN
<
–
V
,
so
the
transistor
operates
inin
<
v
–
V
,
so
the
transistor
operates
inthe
thetriode
trioderegion.
region.
v
–
V
,
so
the
transistor
operates
the
triode
region.
DS
GS
DS
GS t tt
GS
iDS
DRAIN = 0.5 [2(4)(2) – 4] = 6 mA
0.5[2(4)(2)
[2(4)(2)–––4]4]
4]===666mA
mA
==0.5
[2(4)(2)
mA
iiDRAIN
15=20.5
DRAIN
= 6 = 2.17 kX
RDRAIN
15 - 2
R =15
15-6-22 = 2.17 kX
= 2.17 kX
R== CORRECT
X
R
THE
IS: B
66 = 2.17 kANSWER
THE CORRECT ANSWER IS: B
THECORRECT
CORRECTANSWER
ANSWERIS:
IS:BB
THE
7.
7.
7.
7.
PL = 2.8 (0.7) = 1.96 MW
(0.7)
= –1
1.96
MW
PL = 2.8
2.8(0.7)
sin[cos
0.7]
= 2 Mvar
PLLLL===2.8
2.8
(0.7)
1.96
MW
== 1.96
MW
PQ
–1
0.7] = 2MVA
Mvar
QL==P2.8+sin[cos
jQL =–1
1.96
S
–1
–1
L sin[cos
0.7]+==j2
Mvar
QLLLL =
= 2.8
2.8
sin[cos
0.7]
22Mvar
Q
= 1.96
+ j2+MVA
SL = PL + jQ=L(1.96
+++j2)
(–j3) = 1.96 – j1 = 2.2 ∠–27° MVA
jQLLL===1.96
1.96
+j2
j2MVA
MVA
SLLL===SPPLLLL+++SC
jQ
1.96
j2
MVA
SS
+ leading
j2) + (–j3) = 1.96 – j1 = 2.2 ∠–27° MVA
S = SL + SC = (1.96
= 0.89
(1.96
j2)++(–j3)
(–j3)==1.96
1.96––j1
j1==2.2 ∠–27°
2.2 ∠–27°
∠–27°MVA
MVA
S===SScos(–27°)
++ SSCCC==(1.96
++j2)
2.2
Spf
LL
L
pf = cos(–27°) = 0.89 leading
pf==cos(–27°)
cos(–27°)==0.89
0.89leading
leading
pf
THE CORRECT ANSWER IS: A
THE CORRECT ANSWER IS: A
THECORRECT
CORRECTANSWER
ANSWERIS:
IS:AA
THE
32
6
6
Solutions
8.From the given array, this is a fourth-order
system. The denominator of the system
Solutions
is of the form:
8.
From the given array, this is a fourth-order system. The denominator of the system is of the
form:
a4s4 + a3s3 + a2s2 + a1s + a0
a4s4 + a3s3 + a2s2 + a1s + a0
The Routh
array is formed by:
The Routh
an arrayan−2
an−4by:
is formed
ann−1
...
...
...
...
...
...
...
...
...
...
...
abn−3
2
abn−5
3
bc33
...
c1
c2
c3
...
bc22
...
...
...
ELECTRICAL &
COMPUTER
where
an−4
n−5
...
abn−1
1
bc11
an−2
n−3
...
where
- an an - 3
a a
a b -a b
b1 = n - 1 n a- 2
c1 = n - 3 1 b n - 1 2
n- 1
1
an - 1 an - 2 - an an - 3
an - 3 b1 - an - 1 b2
a
b
a
a
a
a
b1 = n - 1 na- 4
n n - 5 c1 = n - 5 1b an - 1 b3
n-1
c2 =
b2 =
an - 1
b11
an - 5 b1 - an - 1 b3
an - 1 an - 4 - an an - 5
b2 =
c2 =
an - 1
b1
Substituting from the given Routh array yields the denominator polynomial:
Substituting from the given Routh array yields the denominator polynomial:
s4 + 7s3 + 12s2 + (10 + 14K)s + 42K
s4 + 7s3 + 12s2 + (10 + 14K)s + 42K
THE CORRECT ANSWER IS: C
THE CORRECT ANSWER IS: C
9.
9.
The formula for electric field intensity can be found in Electrostatic Fields in the
Electrical
andfor
Computer
Engineering
the FE
Reference Handbook.
ThisElectrical
The
formula
electric field
intensitysection
can be of
found
in Electrostatic
Fields in the
formula
is
and
Computer
Engineering section of the FE Reference Handbook. This formula is
E=
Q1
a
4rfr 2 r12
is in
in the
the denominator,
denominator, E
E varies
varies inversely
inversely as
as the
the square
square of
of the
where r is the distance. Since r22 is
the distance
to charge.
the charge.
distance
to the
THE CORRECT ANSWER IS: D
10.
1011 = (1 # 23) + (0 # 2 2) + (1 # 21) + (1 # 20)
= 8 + 0 + 2 +1
= 11
THE
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: C
C
33
7
Fundamentals of Engineering (FE)
ENVIRONMENTAL CBT Exam Specifications
Effective Beginning with the January 2014 Examinations
•
•
•
The FE exam is a computer-based test (CBT). It is closed book with an electronic reference.
Examinees have 6 hours to complete the exam, which contains 110 multiple-choice questions.
The 6-hour time also includes a tutorial, a break, and a brief survey at the conclusion.
The FE exam uses both the International System of Units (SI) and the US Customary System (USCS).
ENVIRONMENTAL
Knowledge 34
Number of Questions
1.
Mathematics A. Analytic geometry
B. Numerical methods
C. Roots of equations
D. Calculus
E. Differential equations
4–6
2.
Probability and Statistics A. Measures of central tendencies and dispersions (e.g., mean, mode,
standard deviation)
B. Probability distributions (e.g., discrete, continuous, normal, binomial)
C. Estimation (point, confidence intervals) for a single mean
D. Regression and curve fitting
E. Expected value (weighted average) in decision making
F. Hypothesis testing
3–5
3.
Ethics and Professional Practice A. Codes of ethics (professional and technical societies)
B. Agreements and contracts
C. Ethical and legal considerations
D. Professional liability
E. Public protection issues (e.g., licensing boards)
F. Regulations (e.g., water, wastewater, air, solid/hazardous waste,
groundwater/soils)
5–8
4.
Engineering Economics A. Discounted cash flow (e.g., life cycle, equivalence, PW, equivalent annual
worth, FW, rate of return)
B. Cost (e.g., incremental, average, sunk, estimating)
C. Analyses (e.g., breakeven, benefit-cost)
D. Uncertainty (expected value and risk)
4–6
5.
Materials Science
A. Properties (e.g., chemical, electrical, mechanical, physical)
B. Corrosion mechanisms and controls
C. Material selection and compatibility
3–5
6. Environmental Science and Chemistry A. Reactions (e.g., equilibrium, acid base, oxidation-reduction, precipitation)
B. Stoichiometry
C. Kinetics (chemical, microbiological)
D. Organic chemistry (e.g., nomenclature, functional group reactions)
E. Ecology (e.g., Streeter-Phelps, fluviology, limnology, eutrophication)
F. Multimedia equilibrium partitioning (e.g., Henry’s law, octonal partitioning
coefficient)
11–17
7.
5–8
Risk Assessment
A. Dose-response toxicity (carcinogen, noncarcinogen)
B. Exposure routes
9–14
9. Thermodynamics
A. Thermodynamic laws (e.g., 1st law, 2nd law)
B. Energy, heat, and work
C. Ideal gases
D. Mixture of nonreacting gases
E. Heat transfer
3–5
10. Water Resources
A. Demand calculations
B. Population estimations
C. Runoff calculations (e.g., land use, land cover, time of concentration, duration,
intensity, frequency)
D. Reservoir sizing
E. Routing (e.g., channel, reservoir)
F. Water quality and modeling (e.g., erosion, channel stability, stormwater quality
management)
10–15
11. Water and Wastewater
A. Water and wastewater characteristics
B. Mass and energy balances
C. Conventional water treatment processes (e.g., clarification, disinfection, filtration,
flocculation, softening, rapid mix)
D. Conventional wastewater treatment processes (e.g., activated sludge, decentralized
wastewater systems, fixed-film system, disinfection, flow equalization, headworks,
lagoons)
E. Alternative treatment process (e.g., conservation and reuse, membranes, nutrient
removal, ion exchange, activated carbon, air stripping)
F. Sludge treatment and handling (e.g., land application, sludge digestion, sludge
dewatering)
14–21
ENVIRONMENTAL
8. Fluid Mechanics A. Fluid statics
B. Closed conduits (e.g., Darcy-Weisbach, Hazen-Williams, Moody)
C. Open channel (Manning)
D. Pumps (e.g., power, operating point, parallel and series)
E. Flow measurement (e.g., weirs, orifices, flowmeters)
F. Blowers (e.g., power, operating point, parallel, and series)
35
ENVIRONMENTAL
36
12.
Air Quality
10–15
A. Chemical principles (e.g., ideal gas, mole fractions, stoichiometry,
Henry’s law)
B. Mass balances
C. Emissions (factors, rates)
D. Atmospheric sciences (e.g., stability classes, dispersion modeling, lapse rates)
E. Gas handling and treatment technologies (e.g., hoods, ducts, coolers,
biofiltration, scrubbers, adsorbers, incineration)
F. Particle handling and treatment technologies (e.g., baghouses, cyclones,
electrostatic precipitators, settling velocity)
13.
Solid and Hazardous Waste
A. Composting
B. Mass balances
C. Compatibility
D. Landfilling (e.g., siting, design, leachate, material and energy recovery)
E. Site characterization and remediation
F. Hazardous waste treatment (e.g., physical, chemical, thermal)
G. Radioactive waste treatment and disposal
10–15
14.
Groundwater and Soils
A. Basic hydrogeology (e.g., aquifers, permeability, water table, hydraulic
conductivity, saturation, soil characteristics)
B. Drawdown (e.g., Jacob, Theis, Thiem)
C. Groundwater flow (e.g., Darcy’s law, specific capacity, velocity, gradient)
D. Soil and groundwater remediation
9–14
1.
2.
The only point of inflection on the curve representing the equation y = x3 + x2 – 3 is at:
A.
2
x=- 3
B.
1
x=- 3
C.
x=0
D.
1
x= 3
A.
B.
ENVIRONMENTAL
As a professional engineer originally licensed 30 years ago, you are asked to evaluate
a newly developed computerized control system for a public transportation system.
You may accept this project if:
you are competent in the area of modern control systems
you do not live in the jurisdiction where the transportation system is being
installed
C.
your original area of specialization was in transportation systems
D.
you have regularly attended meetings of a professional engineering society
3.
If $500 is invested at an annual interest rate of 8% per year, its future worth at the end
of 30 years will be most nearly:
A.
$1,200
B.
$1,700
C.
$5,031
D.
$15,000
37
4.
ENVIRONMENTAL
5.
6.
38
A gas mixture at 25°C and 1 atm contains 100 mg/L of H2S. The partial pressure (atm)
exerted by the H2S is most nearly:
A.
0.0029
B.
0.0056
C.
0.072
D.
0.14
Which of the following is associated with the corrosion of sanitary sewers?
A.
H2S
B.
BOD
C.
Fats, oils, grease (FOG)
D.
NH3
A pump is used to deliver water from a lake to an elevated storage tank. The pipe network
consists of 1,800 ft (equivalent length) of 8-in. pipe (Hazen-Williams roughness
coefficient = 120). Ignore minor losses. The pump discharge rate is 600 gpm.
The friction loss (ft) is most nearly:
A.
15
B.
33
C.
106
D.
135
7.
A community has experienced the following exponential growth in population and
water consumption.
Year
Population
Water
Consumption
(MGD)
1990
2000
45,000
61,000
6.30
9.45
If the rate of expected population growth remains equal to the observed growth rate in
the 1990s, but the per capita water consumption rate stabilizes at 160 gpd, the projected
water demand (MGD) in 2010 is most nearly:
12.3
B.
12.6
C.
13.2
D.
14.2
ENVIRONMENTAL
A.
8.
For coal-fired steam electric power plants, control of SOx emissions is most commonly
achieved by:
9.
A.
lime scrubbing
B.
catalytic conversion
C.
electrostatic precipitation
D.
carbon adsorption
A community generates 50,000 lb/day of solid waste that is disposed of in a sanitary
landfill. The mass ratio of refuse to cover is 3 to 1. The in-place density of the fill
(refuse plus cover) is 1,000 lb/yd3. The necessary volume (yd3) of fill (refuse plus cover)
for a 10-year operation period is most nearly:
A.
730,000
B.
243,000
C.
183,000
D.
61,000
39
ENVIRONMENTAL
10.
40
Two monitoring wells were constructed in an unconfined aquifer. The wells are separated
by a distance of 250 ft. The water surface elevations in the up-gradient and down-gradient
wells were 101.00 ft and 100.85 ft, respectively. The aquifer hydraulic conductivity is
5 ft/day. The fluid velocity (ft/day) in the aquifer is most nearly:
A.
0.0006
B.
0.003
C.
0.75
D.
5
Solutions
1.
f(x) = x3 + x2 – 3
Inflection point occurs when f "(x) = 0
f '(x) = 3x2 + 2x
f "(x) = 6x + 2
Set equal to zero
6x + 2 = 0
x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
THE CORRECT ANSWER IS: B
2.
Refer to the NCEES Rules of Professional Conduct.
ENVIRONMENTAL
THE CORRECT ANSWER IS: A
F
3.
0
1
2
3
30
500
i = 8%
F = 500(F/P, 8%, 30)
= 500 (10.0627)
= $5,031
THE CORRECT ANSWER IS: C
41
Solutions
4.
4.
Solutions
Solutions
MW H22SS == 34
34 g/mol
g/mol
MW H2S = 34 g/mol
100 mg
1g
Moles H 2 S = b 34g/mol
100 mg lb 1 g l = 0.0029 mol H 2 S
Moles H 2 S = b 34g/mol lb1, 000 mg l = 0.0029 mol H 2 S
1, 000 mg
Using PV = nRT, the volume of H 2 S =
Using PV = nRT, the volume of H 2 S =
catm lb
b0.0029 mollb0.08206 L
Kl
Lcatm
mol
cK lb298
nRT
b
b
l
298
Kl = 0.072 L
0.0029
mol
0.08206
=
=
V nRT
c
mol
K
P
1 atm
= 0.072 L
V= P =
1 atm
volume of gas
Partial pressure = volume of gas
Partial pressure = volume of air
volume of air
0.072 L =
0.072
1L L = 0.072
0.072
1L
ENVIRONMENTAL
THE CORRECT
CORRECT ANSWER IS:
IS: C
THE
THE CORRECT ANSWER
ANSWER IS: C
C
5.
5.
5.
H2SS is
is the primary
primary product produced
produced under conditions
conditions that can
can cause corrosion.
corrosion.
H
H22S is the
the primary product
product produced under
under conditions that
that can cause
cause corrosion.
THE CORRECT ANSWER IS: A
THE
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: A
A
6.
6.
0.54
0.63
0.54
V = k1 CR0.63
0.63 S 0.54 = k1 CR 0.63 (h f /L) 0.54
V = k1 CR S = k11.85
CR (h f /L)
V
` h f = L ; V 0.63 E1.85
` h f = L ; k1 CR 0.63 E
k1 CR
k1 = 1.318
k1 = 1.318
L = 1, 800 ft
L = 1, 800 ft
600 gal/min
Q
= 3.830 ft/sec
V= Q=
600 gal/min
3
V = A = (7.48 gal/ft 3) (60 sec/min) (r (8/12 ft) 22 /4) = 3.830 ft/sec
A
C = 120 (7.48 gal/ft ) (60 sec/min) (r (8/12 ft) /4)
C = 120
R = D/4 = (8/12 ft) /4 = 0.1667 ft
R = D/4 = (8/12 ft) /4 = 0.1667 ft
1.85
3.830
1.85 = 14.9 ft
h f = 1, 800 ;
E
3.830
= 14.9 ft
h f = 1, 800 ; (1.318) (120) (0.1667) 0.63
E
(1.318) (120) (0.1667) 0.63
THE CORRECT ANSWER IS: A
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: A
A
THE
42
6
6
Solutions
7.
7.
7.
Solutions
Solutions
Annual population
population growth:
growth:
Annual
Annual population
growth:
1/10
61, 000
000 1/10
61,
n1/10 = 1.0309 _3.09% i
= dd 61,
=
45, 000
000 nn = 1.0309 _3.09% i
45,
d
=
= 1.0309 _3.09% i
45, 000
10
10 = 82,689
Projected population
population in
in 2010
2010 =
= (61,000)(1.0309)
(61,000)(1.0309)10
== 82,689
Projected
82,689
10 = 82,689
Projected population in 2010 −6
=
(61,000)(1.0309)
−6
−6
Mgal/gal)==
=13.2
13.2MGD
MGD
Flow =
= (82,689)(160
(82,689)(160 gpd)(10
gpd)(10 Mgal/gal)
Mgal/gal)
13.2
MGD
Flow
Flow = (82,689)(160 gpd)(10−6 Mgal/gal) = 13.2 MGD
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: C
C
THE
THE CORRECT ANSWER IS: C
8.
SOxx is
is removed
removed by
by liquid
liquid scrubbing
scrubbing at
at aa high
high pH.
pH. Lime
Lime may
may be
be added
added to
to raise
raise the
the pH.
pH.
8.SO
8.
SO
x
8.
SOx is removed by liquid scrubbing at a high pH. Lime may be added to raise the pH.
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: A
A
THE
THE CORRECT ANSWER IS: A
Determine mass
mass of
of cover.
cover.
Determine
Determine mass of cover.
1 lb
lb cover
cover h
= ^^50,
= 16,
16, 667
667 lb
lb
Cover =
50, 000
000 lb
lb refuse)
refuse)^^ 31 lb
Cover
r
efuse h =
1
rcover
efuse
h = 16, 667 lb
Cover = ^50, 000 lb refuse) ^33 lb
lb refuse
Total mass
mass fill
fill ^^10
10-- year
year life
lifehh
Total
Total mass fill ^10 - year lifeh
# 10
= ^^50,
+ 16,
= 2.433
Fill =
50, 000
000 lb/
lb/dday
ay refuse
refuse +
16, 667
667 lb
lb//day
day cover
365 days/yr
days/yrhh^^10
10 yr
yrhh =
2.433 #
1088 lb
lb
coverhh^^365
Fill
8
#
^
h
^
h
^
h
Fill = 50, 000 lb/day 88refuse + 16, 667 lb/day cover 365 days/yr 10 yr = 2.433 10 lb
2.433 ×10 lb
= 2.433 ×10 8 lb
= 243, 000 yd33
Volume
Volume =
33 = 243, 000 yd
1,
000
lb/yd
2.433
×10
lb
Volume = 1, 000 lb/yd 3 = 243, 000 yd3
1, 000 lb/yd
THE
CORRECT
ANSWER IS:
IS: B
B
THE CORRECT ANSWER
THE CORRECT ANSWER IS: B
10.
10.
10.
Darcy’s
Equation
Darcy’s
Darcy’s Equation
Equation
Darcy’s Equation
Q=
= (KA)(dh/dx)
(KA)(dh/dx)
Q
Q = (KA)(dh/dx)
V=
= Q/A
Q/A =
=K
K Δh/Δx
Δh/Δx
V
V = Q/A = K Δh/Δx
K=
= 55 ft/day
ft/day
K
K = 5 ft/day
Δh =
= 101.00
101.00 ft
ft −
− 100.85
100.85 ft
ft =
= 0.15
0.15 ft
ft
Δh
Δh = 101.00 ft − 100.85 ft = 0.15 ft
Δx =
= 250
250 ft
ft
Δx
Δx = 250 ft
^ 0.15 ft
ft hh
= ^^55 ft/day
= 0.003 ft/day
V=
ft/day hh ^^0.15
V
0.15
250 ftfthh = 0.003 ft/day
V = ^ 5 ft/day h ^ 250 ft h = 0.003 ft/day
^ 250 ft h
ENVIRONMENTAL
9.
9.
9.
THE CORRECT
CORRECT ANSWER IS:
IS: B
THE
THE CORRECT ANSWER
ANSWER IS: B
B
THE CORRECT ANSWER IS: B
77
7
43
Fundamentals of Engineering (FE)
INDUSTRIAL CBT Exam Specifications
Effective Beginning with the January 2014 Examinations
•
•
•
The FE exam is a computer-based test (CBT). It is closed book with an electronic reference.
Examinees have 6 hours to complete the exam, which contains 110 multiple-choice questions.
The 6-hour time also includes a tutorial, a break, and a brief survey at the conclusion.
The FE exam uses both the International System of Units (SI) and the US Customary System (USCS).
OTHER
INDUSTRIAL
Knowledge 44
Number of Questions
1.
Mathematics A. Analytic geometry
B. Calculus
C. Matrix operations
D. Vector analysis
E. Linear algebra
6–9
2.
Engineering Sciences
A. Work, energy, power
B. Material properties and selection
C. Charge, energy, current, voltage, and power
5–8
3.
Ethics and Professional Practice A. Codes of ethics and licensure
B. Agreements and contracts
C. Professional, ethical, and legal responsibility
D. Public protection and regulatory issues
5–8
4.
Engineering Economics A. Discounted cash flows (PW, EAC, FW, IRR, amortization)
B. Types and breakdown of costs (e.g., fixed, variable, direct and indirect labor)
C. Cost analyses (e.g., benefit-cost, breakeven, minimum cost, overhead)
D. Accounting (financial statements and overhead cost allocation)
E. Cost estimation
F. Depreciation and taxes
G. Capital budgeting
10–15
5.
Probability and Statistics
A. Combinatorics (e.g., combinations, permutations)
B. Probability distributions (e.g., normal, binomial, empirical)
C. Conditional probabilities
D. Sampling distributions, sample sizes, and statistics (e.g., central tendency,
dispersion)
E. Estimation (e.g., point, confidence intervals)
F. Hypothesis testing
G. Regression (linear, multiple)
H. System reliability (e.g., single components, parallel and series systems)
I. Design of experiments (e.g., ANOVA, factorial designs)
10–15
Modeling and Computations A. Algorithm and logic development (e.g., flow charts, pseudocode)
B. Databases (e.g., types, information content, relational)
C. Decision theory (e.g., uncertainty, risk, utility, decision trees)
D. Optimization modeling (e.g., decision variables, objective functions,
and constraints)
E. Linear programming (e.g., formulation, primal, dual, graphical solutions)
F. Mathematical programming (e.g., network, integer, dynamic, transportation,
assignment)
G. Stochastic models (e.g., queuing, Markov, reliability)
H. Simulation
8–12
7.
Industrial Management
A. Principles (e.g., planning, organizing, motivational theory)
B. Tools of management (e.g., MBO, reengineering, organizational structure)
C. Project management (e.g., scheduling, PERT, CPM)
D. Productivity measures
8–12
8. Manufacturing, Production, and Service Systems
A. Manufacturing processes
B. Manufacturing systems (e.g., cellular, group technology, flexible)
C. Process design (e.g., resources, equipment selection, line balancing)
D. Inventory analysis (e.g., EOQ, safety stock)
E. Forecasting
F. Scheduling (e.g., sequencing, cycle time, material control)
G. Aggregate planning
H. Production planning (e.g., JIT, MRP, ERP)
I. Lean enterprises
J. Automation concepts (e.g., robotics, CIM)
K. Sustainable manufacturing (e.g., energy efficiency, waste reduction)
L. Value engineering
8–12
9.
Facilities and Logistics
A. Flow measurements and analysis (e.g., from/to charts, flow planning)
B. Layouts (e.g., types, distance metrics, planning, evaluation)
C. Location analysis (e.g., single- and multiple-facility location, warehouses)
D. Process capacity analysis (e.g., number of machines and people, trade-offs)
E. Material handling capacity analysis
F. Supply chain management and design
8–12
10. Human Factors, Ergonomics, and Safety
A. Hazard identification and risk assessment
B. Environmental stress assessment (e.g., noise, vibrations, heat)
C. Industrial hygiene
D. Design for usability (e.g., tasks, tools, displays, controls, user interfaces)
E. Anthropometry
F. Biomechanics
G. Cumulative trauma disorders (e.g., low back injuries, carpal tunnel syndrome)
H. Systems safety
I. Cognitive engineering (e.g., information processing, situation awareness, human
error, mental models)
8–12
INDUSTRIAL
6.
45
OTHER
INDUSTRIAL
46
11.
Work Design
A. Methods analysis (e.g., charting, workstation design, motion economy)
B. Time study (e.g., time standards, allowances)
C. Predetermined time standard systems (e.g., MOST, MTM)
D. Work sampling
E. Learning curves
8–12
12.
Quality
A. Six sigma
B. Management and planning tools (e.g., fishbone, Pareto, QFD, TQM)
C. Control charts
D. Process capability and specifications
E. Sampling plans
F. Design of experiments for quality improvement
G. Reliability engineering
8–12
13.
Systems Engineering
A. Requirements analysis
B. System design
C. Human systems integration
D. Functional analysis and allocation
E. Configuration management
F. Risk management
G. Verification and assurance
H. System life-cycle engineering
8–12
1.
2.
The only point of inflection on the curve representing the equation y = x3 + x2 – 3 is at:
A.
2
x=- 3
B.
1
x=- 3
C.
x=0
D.
1
x= 3
As a professional engineer originally licensed 30 years ago, you are asked to evaluate
a newly developed computerized control system for a public transportation system.
You may accept this project if:
A.
B.
you are competent in the area of modern control systems
you do not live in the jurisdiction where the transportation system is being
installed
your original area of specialization was in transportation systems
D.
you have regularly attended meetings of a professional engineering society
INDUSTRIAL
C.
3.
If $500 is invested at an annual interest rate of 8% per year, its future worth at the end
of 30 years will be most nearly:
A.
$1,200
B.
$1,700
C.
$5,031
D.
$15,000
47
4.
5.
Suppose the lengths of telephone calls form a normal distribution with a mean length
of 8.0 min and a standard deviation of 2.5 min. The probability that a telephone call
selected at random will last more than 15.5 min is most nearly:
A.
0.0013
B.
0.0026
C.
0.2600
D.
0.9987
The project network below shows activity durations in weeks. There is a likelihood
that Activity D cannot start until the end of Week 3. In this context, the earliest that
the project can be completed is the end of Week:
B:3
A:6
E:2
C:5
G:8
OTHER
INDUSTRIAL
D:3
6.
A.
15
B.
17
C.
18
D.
43
F:6
I:1
H:3
The following process creates 10,000 good units per year.
A
B
C
The scrap rate of Process C is 20%. Process B has a scrap rate of 10%. To ensure that the
raw material input to the system at Process A is limited to 18,519 or less, the maximum
allowable scrap rate for Process A is most nearly:
48
A.
10%
B.
20%
C.
25%
D.
75%
7.
A warehouse services thirty 53-ft trailers per 8-hr shift using forklifts. The typical 53-ft
trailer holds 26 pallets. The warehouse receives in the first half of the shift and ships in
the second half of the shift. The work standard for forklift operations is listed below:
Load/unload pallet from trailer
Move from dock to warehouse or warehouse to dock
Load/unload pallet from rack
Move within warehouse
45 sec
120 sec
30 sec
60 sec
The number of forklifts needed to process all the pallets is most nearly:
A.
7
B.
9
C.
10
D.
11
A.
1.5 × 107
B.
1.5 × 104
C.
1.0 × 10–3
D.
6.7 × 10–8
INDUSTRIAL
8.
Polychlorinated-biphenyls (PCBs) and 2, 3, 7, 8-TCDD (dioxin) are both considered
lethal in sufficient concentration. The ratio of the rates of the median lethal single dose
of PCB and the median lethal single dose of dioxin that is expected to kill 50% of a group
of test animals is most nearly:
49
9.
An industrial engineer conducted a time study of an assembly operation with the times
given below.
Observation
Time
Observation
Time
1
3.10
6
3.15
2
3.05
7
3.12
3
3.10
8
3.08
4
3.08
9
3.05
5
3.12
10
3.10
The engineer gave a performance rating of 115. The allowance factor is 10% of job time.
The standard time for this operation is most nearly:
OTHER
INDUSTRIAL
10.
50
A.
2.96
B.
3.20
C.
3.56
D.
3.92
Which of the following is true for process capability?
A.
Cpk normally is greater than Cp.
B.
If the process is not centered, then Cpk equals Cp.
C.
Cp measures potential performance if the process is centered.
D.
Cpk is normally negative.
Solutions
1.
f(x) = x3 + x2 – 3
Inflection point occurs when f "(x) = 0
f '(x) = 3x2 + 2x
f "(x) = 6x + 2
Set equal to zero
6x + 2 = 0
x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
THE CORRECT ANSWER IS: B
2.
Refer to the NCEES Rules of Professional Conduct.
THE CORRECT ANSWER IS: A
3.
F
0
1
2
3
30
INDUSTRIAL
500
i = 8%
F = 500(F/P, 8%, 30)
= 500 (10.0627)
= $5,031
THE CORRECT ANSWER IS: C
4.
8 – 15.5 = 7.5
7.5
2.5 = 3 standard deviations
From the Unit Normal Distribution table, for x = 3, R(x) = 0.0013
THE CORRECT ANSWER IS: A
51
Solutions
5.
5.
Solutions
The diagram with early start, late start, early finish, and late finish times is as follows:
The diagram with early start, late start, early finish, and late finish times is as follows:
B: 66 66
F: 99 99
B: 9 9
NOTATION
F: 15 15
9 9
NOTATION
15 15
0
0
A: 0 0
LS
A: 6 6
Activity: ES
ES LS
E: 55 77
6 6 C: 0 1
Activity: EF
LF
E: 7 9
EF LF
C: 50 61
7 9
14
5 6
ES: earliest start
I: 13
13 14
ES: earliest start
I:
14
15
EF: earliest finish
14 15
G: 55 66
EF: earliest finish
G: 13 14
LS: latest start
13 14
0
8
LS: latest start
D: 0 8
LF: latest finish
3
11
D: 3 11
LF:
latest finish
H: 3 11
3 11
H: 6 14
6 14
The
Activity D
D has
has slack
slack of
of 88 weeks,
weeks, so
so starting
starting Activity
Activity D
D at the end of
The critical
critical path
path is
is A–B–F.
A–B–F. Activity
at
the end
of not
Week
3 will
affect thedate.
completion
date.
Therefore,
A–B–F
will
still path with
Week
3 will
affect
thenot
completion
Therefore,
A–B–F
will still
be the
critical
be
the critical
path with a time of 15 weeks.
a time
of 15 weeks.
THE
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: A
A
6.
Input to Process C = 10,000/0.8 = 12,500 units
Scrap rate of Process B = 10%
OTHER
INDUSTRIAL
So, input to Process B = 12,500/0.9 = 13,889 units
So,
13, 889
# 18, 519
(1 - x)
(1 - x)
1
$
13, 889 18, 519
(1 - x) $ 0.75
- x $ - 0.25
x # 0.25
THE CORRECT ANSWER IS: C
7.
Time to process 1 pallet = 45 + 120 + 60 + 30 + 120 = 375 sec, or 6.25 min
Pallets processed/shift = 30 × 26 = 780
780 × 6.25
= 81.25 hr
Pallet processing time =
60
81.25 hr
= 10.15
8 hr/forklift
52
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: C
C
THE
6
Solutions
Solutions
8.LD
8.
LD50
PCB==15,000
15,000
50PCB
LD50
dioxin==0.001
0.001
50dioxin
15, 000
Ratio = 0.001 = 1.5 # 107
THE CORRECT ANSWER IS: A
9.
Observed time = Σt/n = 30.95/10 = 3.095
Normal time = OT × PR = 3.095 × 1.15 = 3.559
Standard time = NT + AF = 3.559 × 1.1 = 3.915
THE CORRECT ANSWER IS: D
10.
10.
Cp indicates
indicates how
how well
well the
the process
process can
can perform
perform ifif itit is
is "centered"
"centered" in
in the
the specification
specification band.
band.
C
p
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: C
C
THE
INDUSTRIAL
7
53
Fundamentals of Engineering (FE)
MECHANICAL CBT Exam Specifications
Effective Beginning with the January 2014 Examinations
•
•
•
The FE exam is a computer-based test (CBT). It is closed book with an electronic reference.
Examinees have 6 hours to complete the exam, which contains 110 multiple-choice questions.
The 6-hour time also includes a tutorial, a break, and a brief survey at the conclusion.
The FE exam uses both the International System of Units (SI) and the US Customary System (USCS).
MECHANICAL
Knowledge 54
Number of Questions
1.
Mathematics A. Analytic geometry
B. Calculus
C. Linear algebra
D. Vector analysis
E. Differential equations
F. Numerical methods
6–9
2.
Probability and Statistics A. Probability distributions
B. Regression and curve fitting
4–6
3.
Computational Tools A. Spreadsheets
B. Flow charts
3–5
4.
Ethics and Professional Practice A. Codes of ethics
B. Agreements and contracts
C. Ethical and legal considerations
D. Professional liability
E. Public health, safety, and welfare
3–5
5.
Engineering Economics
A. Time value of money
B. Cost, including incremental, average, sunk, and estimating
C. Economic analyses
D. Depreciation
3–5
6.
Electricity and Magnetism A. Charge, current, voltage, power, and energy
B. Current and voltage laws (Kirchhoff, Ohm)
C. Equivalent circuits (series, parallel)
D. AC circuits
E. Motors and generators
3–5
7.
Statics
A. Resultants of force systems
B. Concurrent force systems
C. Equilibrium of rigid bodies
D. Frames and trusses
8–12
E. Centroids
F. Moments of inertia
G. Static friction
9–14
9. Mechanics of Materials
A. Shear and moment diagrams
B. Stress types (axial, bending, torsion, shear)
C. Stress transformations
D. Mohr’s circle
E. Stress and strain caused by axial loads
F. Stress and strain caused by bending loads
G. Stress and strain caused by torsion
H. Stress and strain caused by shear
I. Combined loading
J. Deformations
K. Columns
8–12
10. Material Properties and Processing
A. Properties, including chemical, electrical, mechanical, physical, and thermal
B. Stress-strain diagrams
C. Engineered materials
D. Ferrous metals
E. Nonferrous metals
F. Manufacturing processes
G. Phase diagrams
H. Phase transformation, equilibrium, and heat treating
I. Materials selection
J. Surface conditions
K. Corrosion mechanisms and control
L. Thermal failure
M. Ductile or brittle behavior
N. Fatigue
O. Crack propagation
8–12
11. Fluid Mechanics
A. Fluid properties
B. Fluid statics
C. Energy, impulse, and momentum
D. Internal flow
9–14
MECHANICAL
8. Dynamics, Kinematics, and Vibrations
A. Kinematics of particles
B. Kinetic friction
C. Newton’s second law for particles
D. Work-energy of particles
E. Impulse-momentum of particles
F. Kinematics of rigid bodies
G. Kinematics of mechanisms
H. Newton’s second law for rigid bodies
I. Work-energy of rigid bodies
J. Impulse-momentum of rigid bodies
K. Free and forced vibrations
55
MECHANICAL
E.
F.
G.
H.
I.
J.
56
External flow
Incompressible flow
Compressible flow
Power and efficiency
Performance curves
Scaling laws for fans, pumps, and compressors
12.
Thermodynamics
A. Properties of ideal gases and pure substances
B. Energy transfers
C. Laws of thermodynamics
D. Processes
E. Performance of components
F. Power cycles, thermal efficiency, and enhancements
G. Refrigeration and heat pump cycles and coefficients of performance
H. Nonreacting mixtures of gases
I. Psychrometrics
J. Heating, ventilating, and air-conditioning (HVAC) processes
K. Combustion and combustion products
13–20
13.
Heat Transfer
A. Conduction
B. Convection
C. Radiation
D. Thermal resistance
E. Transient processes
F. Heat exchangers
G. Boiling and condensation
9–14
14.
Measurements, Instrumentation, and Controls
A. Sensors
B. Block diagrams
C. System response
D. Measurement uncertainty
5–8
15.
Mechanical Design and Analysis A. Stress analysis of machine elements
B. Failure theories and analysis
C. Deformation and stiffness
D. Springs
E. Pressure vessels
F. Beams
G. Piping
H. Bearings
I. Power screws
J. Power transmission
K. Joining methods
L. Manufacturability
M. Quality and reliability
N. Hydraulic components
O. Pneumatic components
P. Electromechanical components
9–14
1.
2.
The only point of inflection on the curve representing the equation y = x3 + x2 – 3 is at:
A.
2
x=- 3
B.
1
x=- 3
C.
x=0
D.
1
x= 3
As a professional engineer originally licensed 30 years ago, you are asked to evaluate
a newly developed computerized control system for a public transportation system.
You may accept this project if:
A.
B.
you are competent in the area of modern control systems
you do not live in the jurisdiction where the transportation system is being
installed
C.
your original area of specialization was in transportation systems
D.
you have regularly attended meetings of a professional engineering society
If $500 is invested at an annual interest rate of 8% per year, its future worth at the end
of 30 years will be most nearly:
A.
$1,200
B.
$1,700
C.
$5,031
D.
$15,000
MECHANICAL
3.
57
4.
A pulley is driven by a belt as shown in the figure below. Neglecting centrifugal effects,
the minimum coefficient of friction that will prevent slipping between the belt and the
pulley is most nearly:
300-mm-DIAMETER
PULLEY
450 N
3,000 N
MECHANICAL
5.
6.
58
A.
0.60
B.
0.56
C.
0.31
D.
0.20
A 2-kg block slides along a rough horizontal surface and slows to 10 m/s after traveling
20 m. If the kinetic coefficient of friction between the block and surface is 0.2, the initial
speed (m/s) of the block was most nearly:
A.
10.0
B.
10.4
C.
13.4
D.
20.0
Glass is said to be an amorphous material. This means that it:
A.
has a high melting point
B.
is a supercooled vapor
C.
has large cubic crystals
D.
has no apparent crystal structure
7.
The pitot tube shown below is placed at a point where the velocity is 2.0 m/s.
The specific gravity of the fluid is 2.0, and the upper portion of the manometer
contains air. The reading h (m) on the manometer is most nearly:
A.
20.0
B.
10.0
C.
0.40
D.
0.20
AIR
h
2.0 m/s
8.
Conditioned air enters a room at 13°C and 70% relative humidity. The dew-point
temperature of the air is most nearly:
9.
5°C
B.
8°C
C.
10°C
D.
13°C
A heat exchanger is designed to heat liquid water from 150°C to 190°C inside tubes
using steam condensing at 230°C on the outer surface of the tubes. For a constant
flow rate, the effect of fouling of the heat transfer surfaces is to:
A.
increase the temperature rise of the water
B.
decrease the temperature rise of the water
C.
increase heat exchanger effectiveness
D.
make no change in heat exchanger effectiveness
MECHANICAL
10.
A.
A helical compression spring has a spring constant of 38.525 N/mm and a free length of
190 mm. The force (N) required to compress the spring to a length of 125 mm is most nearly:
A.
1,500
B.
2,500
C.
4,800
D.
6,500
59
Solutions
1.
f(x) = x3 + x2 – 3
Inflection point occurs when f "(x) = 0
f '(x) = 3x2 + 2x
f "(x) = 6x + 2
Set equal to zero
6x + 2 = 0
x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
THE CORRECT ANSWER IS: B
2.
Refer to the NCEES Rules of Professional Conduct.
THE CORRECT ANSWER IS: A
3.
F
0
1
2
3
30
500
i = 8%
F = 500(F/P, 8%, 30)
MECHANICAL
= 500 (10.0627)
= $5,031
THE CORRECT ANSWER IS: C
60
Solutions
Solutions
Solutions
Solutions
µθ
4.
F
µθ
=F
F22eeeµθ
4.
F11 ==
F
4.
F
4.
F11 = F22 eµθ µπ
3,000
µπ
3,000 =
= 450e
450eµπ
3,000
3,000 =
= 450e
450eµπ
Set
the static
static coefficient;
coefficient; and
and θθ == π,
π, the
the angle
angle of
of the
the wrap.
wrap.
Set µ
µ equal
equal to
to µ
µss,, the
Set
the static
static coefficient;
coefficient; and
and θθ == π,
π, the
the angle
angle of
of the
the wrap.
wrap.
Set µ
µ equal
equal to
to µ
µss,, the
3, 000
000
3, 000
000
1
= ln
= 11r ln
ln 3,
`n
nssrr =
n=
ln 3,
3,450
000 ,, n
3,450
000
`
` nsr = ln 450
r ln 450
450 , n = r
450
=
n
0
60
.
s
n
= 00..60
nss =
60
THE CORRECT ANSWER IS: A
THE
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: A
A
5.
5.
5.
THE CORRECT
CORRECT ANSWER IS:
IS: C
THE
THE CORRECT ANSWER
ANSWER IS: C
C
6.
6.
6.
x,
x, vv
x,
x, vv
+ U2 =
= T1 + U
= - Fx
T2 +
U1 + W
W1 " 2, W1 " 2 =
Fx
TT
22 + U
+ U11 +
+ W11 "" 22,, W
- Fx
U22 = TT11 +
W11 "" 22 = 111 mv222 =
= 1112 mv
- n k mgx
mv1222 mgx
mv
2
2
nkk mgx
22 mv 2 = 22 mv11 - n
1
= 111 v122 - 0.2(
Cancel m to
to obtain "
" 11 (10))222 =
0.2(9.81)(
)(20))
Cancel
- 0.2(99..81
Cancel m
m to obtain
obtain " 222 ((10
10) = 222 vv112 81)(20
20)
= 13.4
13.4 m/s
m/s
vvv11 =
1 = 13.4 m/s
m
m
m
m
F
F
F
F
N
N
N
N
F=
F= μ
μkmg
mg
F=
F= μμkkkmg
mg
By definition, amorphous
amorphous materials do
do not have
have a crystal structure.
structure.
By
By definition,
definition, amorphous materials
materials do not
not have aa crystal
crystal structure.
7.
7.
7.
tvv222
tt
= gghh ((tt - ttair))
v =
air)
222 = gh (t - tair
tvv222
t
=
`h
.
tv
`
- ttair)) .
= 22gg ((tt ` hh =
.
air
2g (t - tair)
MECHANICAL
THE CORRECT ANSWER
ANSWER IS: D
D
THE
THE CORRECT
CORRECT ANSWER IS:
IS: D
2
2
vvv22 . (((222)))22 . 0.204 m
.
. 0.204 m
222ggg . (((222))) (((999...888))) . 0.204 m
THE CORRECT ANSWER
ANSWER IS: D
D
THE
THE CORRECT
CORRECT ANSWER IS:
IS: D
555
61
Solutions
Refer to the appropriate psychrometric chart.
E
RV
U
C
SPECIFIC HUMIDITY ω
8.
N
IO
T
A
UR
φ = 70%
T
DEW
SA ω
POINT
tdb
φ = RELATIVE HUMIDITY
tdb = DRY-BULB TEMPERATURE
13°C
DRY-BULB TEMPERATURE
At the given state, tdb = 13°C, ϕ = 70%, ω = 6.5 g/kg da, da = dry air.
Follow the ω = 6.5 line to the left until the saturation curve is reached.
This point is the dew point. Read down to find the dew-point temperature of 7.6°C.
THE CORRECT ANSWER IS: B
9.
The effect of fouling on the heat-transfer surfaces is to reduce the heat-transfer rate by
increasing the surface resistance. The results on the water being heated would be to
reduce the outlet temperature of the water.
THE CORRECT ANSWER IS: B
MECHANICAL
10.
The force required to displace a spring an amount δ from its free length is F = kδ,
where k is the spring constant or rate. In this case:
δ = free length – compressed length
= 190 mm – 125 mm
= 65 mm
The force required to deflect the spring this amount is:
F = kδ = (38.525 N/mm)(65 mm) = 2,504 N
THE CORRECT ANSWER IS: B
62
Fundamentals of Engineering (FE)
OTHER DISCIPLINES CBT Exam Specifications
Effective Beginning with the January 2014 Examinations
•
•
•
The FE exam is a computer-based test (CBT). It is closed book with an electronic reference.
Examinees have 6 hours to complete the exam, which contains 110 multiple-choice questions.
The 6-hour time also includes a tutorial, a break, and a brief survey at the conclusion.
The FE exam uses both the International System of Units (SI) and the US Customary System (USCS).
Knowledge Number of Questions
Mathematics and Advanced Engineering Mathematics
A. Analytic geometry and trigonometry
B. Calculus
C. Differential equations (e.g., homogeneous, nonhomogeneous,
Laplace transforms)
D. Numerical methods (e.g., algebraic equations, roots of equations,
approximations, precision limits)
E. Linear algebra (e.g., matrix operations)
12–18
2.
Probability and Statistics A. Measures of central tendencies and dispersions (e.g., mean, mode,
variance, standard deviation)
B. Probability distributions (e.g., discrete, continuous, normal, binomial)
C. Estimation (e.g., point, confidence intervals)
D. Expected value (weighted average) in decision making
E. Sample distributions and sizes
F. Goodness of fit (e.g., correlation coefficient, least squares)
6–9
3.
Chemistry
A. Periodic table (e.g., nomenclature, metals and nonmetals, atomic
structure of matter)
B. Oxidation and reduction
C. Acids and bases
D. Equations (e.g., stoichiometry, equilibrium)
E. Gas laws (e.g., Boyle’s and Charles’ Laws, molar volume)
7–11
4.
Instrumentation and Data Acquisition A. Sensors (e.g., temperature, pressure, motion, pH, chemical constituents)
B. Data acquisition (e.g., logging, sampling rate, sampling range,
filtering, amplification, signal interface)
C. Data processing (e.g., flow charts, loops, branches)
4–6
5.
Ethics and Professional Practice
A. Codes of ethics
B. NCEES Model Law
C. Public protection issues (e.g., licensing boards)
3–5
OTHER
DISCIPLINES
1.
63
OTHER
DISCIPLINES
64
6.
Safety, Health, and Environment A. Industrial hygiene (e.g., carcinogens, toxicology, MSDS, lower
exposure limits)
B. Basic safety equipment (e.g., pressure relief valves, emergency
shut-offs, fire prevention and control, personal protective equipment)
C. Gas detection and monitoring (e.g., O2, CO, CO2, CH4, H2S, Radon)
D. Electrical safety
4–6
7.
Engineering Economics
A. Time value of money (e.g., present worth, annual worth, future worth,
rate of return)
B. Cost (e.g., incremental, average, sunk, estimating)
C. Economic analyses (e.g., breakeven, benefit-cost, optimal economic life)
D. Uncertainty (e.g., expected value and risk)
E. Project selection (e.g., comparison of unequal life projects,
lease/buy/make, depreciation, discounted cash flow)
7–11
8.
Statics
A. Resultants of force systems and vector analysis
B. Concurrent force systems
C. Force couple systems
D. Equilibrium of rigid bodies
E. Frames and trusses
F. Area properties (e.g., centroids, moments of inertia, radius of gyration)
G. Static friction
8–12
9.
Dynamics
A. Kinematics
B. Linear motion (e.g., force, mass, acceleration)
C. Angular motion (e.g., torque, inertia, acceleration)
D. Mass moment of inertia
E. Impulse and momentum (linear and angular)
F. Work, energy, and power
G. Dynamic friction
H. Vibrations
7–11
10. Strength of Materials
A. Stress types (e.g., normal, shear, bending, torsion)
B. Combined stresses
C. Stress and strain caused by axial loads, bending loads, torsion, or shear
D. Shear and moment diagrams
E. Analysis of beams, trusses, frames, and columns
F. Deflection and deformations (e.g., axial, bending, torsion)
G. Elastic and plastic deformation
H. Failure theory and analysis (e.g., static/dynamic, creep, fatigue,
fracture, buckling)
8–12
11.
6–9
Materials Science
A. Physical, mechanical, chemical, and electrical properties of ferrous metals
B. Physical, mechanical, chemical, and electrical properties of nonferrous metals
C. Physical, mechanical, chemical, and electrical properties of engineered
materials (e.g., polymers, concrete, composites)
D. Corrosion mechanisms and control
Fluid Mechanics and Dynamics of Liquids
A. Fluid properties (e.g., Newtonian, non-Newtonian)
B. Dimensionless numbers (e.g., Reynolds number, Froude number)
C. Laminar and turbulent flow
D. Fluid statics
E. Energy, impulse, and momentum equations (e.g., Bernoulli equation)
F. Pipe flow and friction losses (e.g., pipes, valves, fittings, Darcy-Weisbach
equation, Hazen-Williams equation)
G. Open-channel flow (e.g., Manning equation, drag)
H. Fluid transport systems (e.g., series and parallel operations)
I. Flow measurement
J. Turbomachinery (e.g., pumps, turbines)
8–12
13.
Fluid Mechanics and Dynamics of Gases A. Fluid properties (e.g., ideal and non-ideal gases)
B. Dimensionless numbers (e.g., Reynolds number, Mach number)
C. Laminar and turbulent flow
D. Fluid statics
E. Energy, impulse, and momentum equations
F. Duct and pipe flow and friction losses
G. Fluid transport systems (e.g., series and parallel operations)
H. Flow measurement
I. Turbomachinery (e.g., fans, compressors, turbines)
4–6
14.
Electricity, Power, and Magnetism
A. Electrical fundamentals (e.g., charge, current, voltage, resistance,
power, energy)
B. Current and voltage laws (Kirchhoff, Ohm)
C. DC circuits
D. Equivalent circuits (series, parallel, Norton’s theorem, Thevenin’s theorem)
E. Capacitance and inductance
F. AC circuits (e.g., real and imaginary components, complex numbers, power
factor, reactance and impedance)
G. Measuring devices (e.g., voltmeter, ammeter, wattmeter)
7–11
15.
Heat, Mass, and Energy Transfer 9–14
A. Energy, heat, and work
B. Thermodynamic laws (e.g., 1st law, 2nd law)
C. Thermodynamic equilibrium
D. Thermodynamic properties (e.g., entropy, enthalpy, heat capacity)
E. Thermodynamic processes (e.g., isothermal, adiabatic, reversible, irreversible)
F. Mixtures of nonreactive gases
G. Heat transfer (e.g., conduction, convection, and radiation)
H. Mass and energy balances
I. Property and phase diagrams (e.g., T-s, P-h)
J. Phase equilibrium and phase change
K. Combustion and combustion products (e.g., CO, CO2, NOX, ash, particulates)
L. Psychrometrics (e.g., relative humidity, wet-bulb)
OTHER
DISCIPLINES
12.
65
1.
2.
3.
The only point of inflection on the curve representing the equation y = x3 + x2 – 3 is at:
A.
2
x=- 3
B.
1
x=- 3
C.
x=0
D.
1
x= 3
You wish to estimate the mean M of a population from a sample of size n drawn from
the population. For the sample, the mean is x and the standard deviation is s.
The probable accuracy of the estimate improves with an increase in:
A.
M
B.
n
C.
s
D.
M+s
The following segment of pseudocode describes a segment of a computer program:
Set A = 17
Set K = 2
While K ≤ 4
A = A/K
K=K+1
End While
Print A
OTHER
DISCIPLINES
The value of A that is printed is most nearly:
66
A.
0.71
B.
2.83
C.
4.25
D.
408
4.
As a professional engineer originally licensed 30 years ago, you are asked to evaluate
a newly developed computerized control system for a public transportation system.
You may accept this project if:
A.
B.
5.
you are competent in the area of modern control systems
you do not live in the jurisdiction where the transportation system is being
installed
C.
your original area of specialization was in transportation systems
D.
you have regularly attended meetings of a professional engineering society
Portable electric tools are frequently used where operators may encounter water or other
conductive materials. The safety device required by The National Electrical Code to protect against accidental electrocution in wet/damp environments is known as a:
A.
ground rod
B.
properly sized circuit breaker
C.
ground fault interrupter (GFI)
D.
two-conductor power cord
6.
If $500 is invested at an annual interest rate of 8% per year, its future worth at the end
of 30 years will be most nearly:
$1,200
B.
$1,700
C.
$5,031
D.
$15,000
The pressure gage in an air cylinder reads 1,680 kPa. The cylinder is constructed of a
12-mm rolled-steel plate with an internal diameter of 700 mm. The tangential stress
(MPa) inside the tank is most nearly:
A.
25
B.
50
C.
77
D.
100
OTHER
DISCIPLINES
7.
A.
67
8.
A silver/copper binary phase diagram is shown below. An alloy that is 70% copper by
weight is fully melted and allowed to cool slowly. The temperature at which solidification
begins is most nearly:
1,100
1,084°
TEMPERATURE, °C
1,000
LIQUID
962°
900
800
α+L
β+L
α
700
8.8
28.1
780°
600
0
Ag
20
80
40
60
60
40
80
20
OTHER
DISCIPLINES
COMPOSITION, % BY WEIGHT
68
A.
962°C
B.
920°C
C.
800°C
D.
780°C
92
α+β
500
400
β
Cu
0
9.
10.
An insulated tank contains half liquid and half vapor by volume in equilibrium. The release
of a small quantity of the vapor without the addition of heat will cause:
A.
evaporation of some liquid in the tank
B.
superheating of the vapor in the tank
C.
a rise in temperature
D.
an increase in enthalpy
A Rankine cycle with water as the working medium operates with the conditions shown
in the figure.
P5 = 121 kPa
t5 = 105°C
X5 = 95%
(5)
SUPERHEATER
Q5
STEAM
BOILER
QSS
(1) P1 = 1,000 kPa
t1 = 400°C
WORK OUT
TURBINE
WATER IN 21°C
PUMP
(4)
t4 = 60°C
LEGEND:
P = PRESSURE
t = TEMPERATURE
X = QUALITY
Q = HEAT
P2 = 199 kPa
(2) t2 = 120°C
X2 = 84%
CONDENSER
WATER OUT 32°C
(3) t3 = 60°C
WORK IN
A.
560
B.
910
C.
1,410
D.
2,760
OTHER
DISCIPLINES
Disregarding pressure losses throughout the cycle and assuming a steady flow with adiabatic
expansion in the turbine, the specific shaft work deliverable by the turbine (kJ/kg) is most
nearly:
69
Solutions
1.
f(x) = x3 + x2 – 3
Inflection point occurs when f "(x) = 0
f '(x) = 3x2 + 2x
f "(x) = 6x + 2
Set equal to zero
6x + 2 = 0
x = –1/3
f "(x) is negative below x = –1/3 and positive above x = –1/3
Since f "(x) = 0 and f "(x) changes signs at x = –1/3, the inflection point is at x = –1/3.
THE CORRECT ANSWER IS: B
2.
Accuracy increases with increasing sample size.
THE CORRECT ANSWER IS: B
3.
K = 2 gives A = 17/2 = 8.5
K = 3 gives A = 8.5/3 = 2.83
K = 4 gives A = 2.83/4 = 0.71
THE CORRECT ANSWER IS: A
4.
Refer to the NCEES Rules of Professional Conduct.
THE CORRECT ANSWER IS: A
5.
Ground fault interrupters are required for exterior residential power outlets.
OTHER
DISCIPLINES
THE CORRECT ANSWER IS: C
70
Solutions
Solutions
Solutions
6.
6.
0
0
1
1
2
2
3
3
F
F
30
30
500
500
i = 8%
i = 8%
F=
=
500(F/P, 8%,
8%, 30)
30)
=500(F/P,
F
==
500 (10.0627)
(10.0627)
= 500
==
$5,031
= $5,031
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: C
C
THE
7.
7.
1
# 1 rri..
The cylinder
cylinder can
can be
be considered
considered thin-walled
thin-walled if
if tt #
The
10
10 i
In
this
case
In this case
= 700
700 mm
mm
ddii =
=12
12 mm
mm
tt =
= ddi +
+ 2t = 700 + 2 (12) = 724 mm
ddoo =
i 2t = 700 + 2 (12) = 724 mm
d
= dii =
= 350
350 mm
mm
rrii =
22
ddii
ddoo
tt
ddoo = 362 mm
=
r
o
ro = 2 = 362 mm
2
r +r
350 + 362
= rii + roo =
= 350 + 362 =
= 356
356 mm
where rr =
mm
where
2
2
22
680 MPa
MPa))((356
356 mm
mm))
P r ((11..680
= Piir =
=
= 49
49..88 MPa
MPa
=
vvtt =
12 mm
mm
tt
12
THE CORRECT
CORRECT ANSWER
ANSWER IS:
IS: B
B
THE
OTHER
DISCIPLINES
66
71
Solutions
8.
The solidification path of an Ag-70 w/o Cu alloy is shown as the vertical line.
The temperature at which solidification begins is shown as the horizontal dashed
line and is 920°C.
1,100
1,084°
TEMPERATURE, °C
1,000
LIQUID
962°
900
α+ L
β +L
α
800
28.1
8.8
780°
700
β
92
600
α+β
500
400
0
Ag
20
80
40
60
80
60
40
20
COMPOSITION, % BY WEIGHT
Cu
0
THE CORRECT ANSWER IS: B
9.
As vapor escapes, the mass within the tank is reduced. With constant volume, the specific
volume within the tank must increase. This can happen only if liquid evaporates.
OTHER
DISCIPLINES
VAPOR
VAPOR
LIQUID
THE CORRECT ANSWER IS: A
72
Solutions
10.
The equation for work done by the turbine is
Wturbine = h1 − h2
where h1 is enthalpy of superheated steam at 1 MPa and 400°C, and h2 is enthalpy of
84% quality saturated steam at 199 kPa and 120°C. Enthalpy values in steam tables.
h1
= 3,263.9 kJ/kg
h2
= (1 − X2)(hc) + (X2)(hr) = (0.16)(503.71 kJ/kg) + (0.84)(2,706.3 kJ/kg)
= 2,353.9 kJ/kg
Wturbine = (3,263.9 − 2,353.9) kJ/kg = 910 kJ/kg
THE CORRECT ANSWER IS: B
OTHER
DISCIPLINES
73
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