MECHANICAL MORNING SAMPLE EXAM...PE Mechanical Sample Exam – Breadth (A.M.) Section Basic...

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MECHANICAL

MORNING SAMPLE EXAM

A psychrometric chart (normal temperature range at sea level) is

provided on page 32 for your possible use. Unless stated otherwise,

assume sea level conditions.

www.SlaythePE.com 1 Copyright © 2016. All rights reserved.


Basic Engineering Practice – 001. Strain hardening occurs when:

(A) The ultimate tensile strength can be estimated from the Brinell hardness number.

(B) A material has been stressed beyond the yield strength to some point in the plastic region, and

then the load is removed.

(C) A part is cyclically loaded so the stress is kept below the endurance limit, thus having a

nominally infinite life.

(D) Maximum shear stress theory predicts the shear strength as one half of the tensile yield strength.

Basic Engineering Practice – 002. The compressibility factor,Z :

(A) Is the ratio of inertial forces to viscous forces in a flow field.

(B) Allows finding the dew point temperature along the 100% relative humidity line in a

psychrometric chart

(C) Is typically neglected when the Mach number is small.

(D) Accounts for the deviation of real gases from ideal-gas behavior.



Basic Engineering Practice – 003. A remotely located facility has no easy access to electricity. They

are considering two options to provide mechanical power to a group of pumps. Option A is to drive the

pumps with a diesel engine and option B is to couple the pumps to a gas turbine. The pumps require a

power input of 450 hp to operate properly.

The table below provides some information regarding the options.

Option A: Diesel Engine Option B: Gas Turbine

Purchase and Installation Cost $100,000 $235,000

Yearly Maintenance Cost $5,000 $9,000

Fuel Diesel Natural Gas

Fuel Costs $2.60 per gallon $2.25 per million Btu

Fuel Heating Value 16,000 Btu per gallon 20,000 Btu per pound

Expected Life 15 years 15 years

For both systems, it is expected that the salvage value will be equal to the book value after 15 years of

depreciation. According to company policy, depreciation is to be calculated with the double-declining

balance method. The thermal efficiency (percentage of energy in the fuel that is converted to useful

mechanical energy) for the Diesel engine plant is 45% while it is 65% for the gas turbine.

Using an interest rate of 6%, the present worth of the salvage value for the gas turbine is nearest:

(A) $4,877

(B) $11,500

(C) $27,500

(D) $235,000



Basic Engineering Practice – 004. Part of the fabrication drawing for a machine part is shown below.

The drawing includes an isometric view, and three orthogonal views. One of the orthogonal views has

been covered with a shaded region.

Four alternatives for the missing view are shown in the next page.


THIRD-ANGLE PROJECTION

Missing View


The view that should be placed on the shaded area is most nearly:

(A)

(B)

(C)

(D)



Basic Engineering Practice – 005. The part shown in the following drawing will be made from a

metal having a density of 7800 kg/m3.

The maximum total weight (pounds) that can be expected of the finished part is most nearly:

(A) 3.0

(B) 4.8

(C) 6.7

(D) 10.3


THIRD-ANGLE PROJECTION

METRIC (mm) DIMENSIONS8XØ42--48

200±520±2

135±5


Basic Engineering Practice - 006. The sketch shows part of a DC circuit. With this arrangement of

resistors, the value ofR1 so that the currentI is divided equally between Branch A and Branch B is

nearest:

(A) 3R /2

(B) 2 R /3

(C) 3R

(D) R /3

Basic Engineering Practice - 007. An induction motor on a 10 kV circuit draws 224 kVA with a power

factor of 0.85 lagging. The amount of capacitive power (kVAR) needed to correct the power factor to

0.95 is most nearly:

(A) 55

(B) 62

(C) 118

(D) 190


R1

R

R R

I

Branch A

Branch B


Basic Engineering Practice – 008. A supplier to the automotive industry uses the same 3D metal

cutting machine to make two different parts: A, and B. The table below summarizes how much each

part costs to fabricate. Also shown is the profit the supplier makes when selling the part to its

customers.

Part A Part B

Cost to Fabricate ($) 20 10

Profit ($) 50 30

The machine has the capacity to produce up to 100 parts per day. For profitability, the total number of

parts made per day must be at least 70. You may assume that every part made is sold. The company can

spend at most $1200 per day in making these parts. The number of parts A and B that must be made

daily to maximize profits is most nearly:

(A) 30 of part A, and 70 of part B.

(B) 70 of part A, and 30 of part B.

(C) 50 of part A, and 20 of part B.

(D) 20 of part A, and 80 of part B.



Basic Engineering Practice – 009. The following table lists the five activities that comprise the critical

path for a project. Past experience has provided reliable values for the shortest, longest, and most likely

times (statistical modes) to complete each task, which are shown in the table below. The randomness of

activity completion times is well approximated by the “beta” distribution, which has been used to

calculate the mean and variance times for completion for each task. The mean and variance are also

shown in the table.

Activity Shortest Time(days)

Most LikelyTime (days)

Longest Time(days)

Mean (days)

Variance(days)2

A 8 14 20 14.0 4.0

B 14 26 32 25.0 9.0

C 1 2 7 2.7 1.0

D 20 39 44 36.7 16.0

E 22 30 34 29.3 4.0

F 8 14 20 14.0 4.0

Using the PERT technique, the probability of completing the project inN days or less is 30%.

Therefore, the value ofN (days) is most nearly:

(A) 125

(B) 122

(C) 119

(D) 115

The area under the “bell” curve (standard normal distribution)A(z ) to the left ofz , and the

corresponding value ofz is shown here for your possible use in this problem.

A(z ) z

0.5 0.0000

0.6 0.2533

0.7 0.5244

0.8 0.8416

0.9 1.2816


A(z)

z


Basic Engineering Practice – 010. In a manufacturing facility, two identical compressors will be

installed in parallel to form a “1-out-of-2” redundant system; that is, only one compressor need be

operational at a time. The overall system reliability over 3 years is required to be 0.85. There are four

choices of compressor models. Each model has a different, constant failure rate (and total initial cost)

as shown in the table:

Model A Model B Model C Model D

Individual Compressor Constant Failure Rate (1/yr) 0.2 0.13 0.09 0.05

Purchase and Installation Cost per Compressor Pair ($) 20,000 35,000 45,000 75,000

The compressor model selected for this duplex system will be the least expensive that satisfies the

reliability requirement. Under these circumstances, the model that most nearly meets the requirements

is:

(A) Model A

(B) Model B

(C) Model C

(D) Model D



Basic Engineering Practice – 011. Alternative energy researchers have found that the power carried

by a deep-sea wave can be expressed as:

P=0.0329H 2√ L [1�4.935( HL )

2

]whereH is the height of the wave in feet,L is the length in feet between successive crests, and P is the

power per foot of wave width, in hp/ft. The appropriate form of this correlation ifL andH are in m and

P is in kW/m is:

(A) P=0.0805H 2√ L [1�4.935(HL )

2

](B) P=0.0329H 2√ L [1�1.505( H

L )2

](C) P=1.569H 2√L [1�4.935(H

L )2

](D) Cannot be determined with the information provided.

Basic Engineering Practice – 012. A cooling chamber in a pharmaceutical manufacturing process is

normally 30ºF lower than the ambient plant temperature. A process upset resulted in a momentary rise

of the chamber temperature such that the temperature difference with the ambient was reduced by 75%

before returning to normal. The lowest temperature difference with ambient plant temperature

(ºC) experienced in the chamber during the process upset is nearest:

(A) -13.6

(B) 4.2

(C) 7.5

(D) 22.5



Mechanical Systems and Materials – 001. A solid circular rod that is 24 inches long and 0.7874

inches in diameter is subjected to an axial load of 11,240 pounds-force. The elongation of the rod is

0.0551 inches and its diameter becomes 0.7868 inches. Assuming there is no yielding, the shear

modulus of elasticity (ksi) for the material, is most nearly:

(A) 3,800

(B) 6,400

(C) 10,000

(D) 14,500

Mechanical Systems and Materials – 002. A 30 mm diameter shaft used to transmit 65 kW of power

at 2,000 rpm is made from a steel with a yield strength of 650 MPa in compression and tension. Using

the Tresca failure theory, the factor of safety is most nearly:

(A) 3.8

(B) 4.7

(C) 4.0

(D) 5.0

Mechanical Systems and Materials – 003. A block weighing 60 pounds is resting on a horizontal

surface. The coefficient of static friction between the block and the surface is 0.7 and a forceF will be

applied at an angleθ=30º as shown in the figure. The magnitude of the force will be slowly increased

from zero up to 65 pounds and maintained indefinitely at that value. Of the following statements

regarding the block, the one that is most nearly true is:

(A) It will not slip and will not tip over.

(B) It will slide and not tip over the right lower edge.

(C) It will tip over the right lower edge and not slide.

(D) It will slip to the right and eventually will tip over.


20 in10 in

F

θ


Mechanical Systems and Materials – 004. After application of the load P, the longitudinal strain of

wire BC is 6.66×10�4 in/in. Wire BC is made of A-36 steel (Young's Modulus =29×103ksi , Yield

Strength =36 ksi ) and has a diameter of 1/8 in. The magnitude of P (pound-force) is nearest:

(A) 158

(B) 237

(C) 703

(D) 956

Mechanical Systems and Materials – 005. Using a special test rig, a series of ferrous metal specimens

were subjected to a specified cyclical stress until failure. The loading was fully reversed. When the

applied stress amplitude was 64.5 ksi, the specimens consistently failed at roughly ten thousand

(10,000) cycles. Similarly, when the applied stress amplitude was 45 ksi, the specimens failed at

roughly one million (1,000,000) cycles. The data indicated that the endurance limit is lower than 45 ksi.

The expected life (cycles) of a specimen under a completely reversed stress of 55 ksi is nearest:

(A) 78,000

(B) 285,000

(C) 492,000

(D) Infinity, because the specimens will not experience fatigue failure at 55 ksi.


P

B

16 in.

A

C

12 in. 8 in.


Mechanical Systems and Materials – 006. A spring made from 0.072-in music wire (Young's

modulus of 28.5⋅103 ksi ) has 8½ body turns with straight torsion ends. The spring will be statically

loaded with a forceF as shown. The coil outside diameter is 27/32 in.

The spring rate constant for the complete spring (lbf⋅in / turn ) is most nearly:

(A) 9.1

(B) 10.8

(C) 12.4

(D) 17.0


F

F

1 in

1 in


Mechanical Systems and Materials – 007. A lead-tin alloy sample is initially completely liquid. The

sample will be slowly cooled until it has completely solidified. If the eutectic reaction is desired, the

lead (Pb) concentration (wt%) should be most nearly:

(A) 18.3

(B) 38.1

(C) 61.9

(D) 97.8

A phase diagram for Lead-Tin (Pb-Sn) is provided below for your possible use:


232°C(450°F)

327°C(621°F)

61.918.3 97.8

Liquid

α + β

α

α + L

β + L

β

Tem

pera

ture

(°C

)

300

200

100

150

250

Tem

pera

ture

(°F

)

183°C

(361°F)

500

600

400

300

200

Composition (wt% Sn)

20 40 60 80

(Pb) (Sn)

0 100

20 40 60 800 100


Mechanical Systems and Materials – 008. For a single degree of freedom, linear spring-mass-dashpot

system, the spring constant is 3.5 kN/m and the mass is 4.5 kg. The mass is displaced from its initial

resting position by an amountx0 and released. The ensuing oscillations occur in one spatial dimension

only. A graphical representation of the oscillatory movement is shown here:

Of the following statements, the one that is most likely to be correct is:

(A) The coefficient of viscous damping is greater than250 N⋅s/m .

(B) The undamped angular natural frequency of vibration,ω is 0.36 rad/s.

(C) The undamped angular natural frequency of vibration,ω is 1.13 rad/s.

(D) The coefficient of viscous damping is less than250 N⋅s/m .


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1.0

-0.5

0.0

0.5

1.0

time (s)

x(t)

/x0


Hydraulics & Fluids – 001. A cylindrical, atmospheric-pressure tank with a diameter of 10m has one

inlet pipe and one outlet pipe. The tank is used for the storage of liquid jet fuel. During simultaneous

loading and unloading, liquid jet fuel is delivered to the tank at a rate of 1 m3/s through the inlet pipe.

If the level inside the tank is to rise at a rate no greater than 0.5m/minute, the lowest flow rate (gpm) at

which the jet fuel must be drawn from the tank through the outlet pipe is most nearly:

(A) Cannot be determined

(B) 0.35

(C) 20.7

(D) 5,476

Hydraulics & Fluids - 002. A vacuum cleaner is capable of creating a vacuum of 0.3 psi just inside the

hose. The maximum velocity (m/s) that could be expected in the hose is most nearly:

(A) 58

(B) 34

(C) 191

(D) 11

Hydraulics & Fluids – 003. A Pitot static tube in an air flow stream indicates a static pressure of 17

psig and a stagnation pressure of 25 psig. The Mach number for the flow at the location of the Pitot

static tube is nearest:

(A) 0.80

(B) 0.75

(C) 0.70

(D) 0.60



Hydraulics & Fluids – 004. A valve manufacturer uses the test rig shown below to determine the loss

coefficient K for their valves. The working fluid is water ( kinematic viscosity, ν = 1.12 cSt, density, ρ =

62.4 lb/ft3 ). The flow rate is 400 gallons per minute, and all piping is 4-in, schedule 40, steel pipe (ID =

4.026 in). A differential U-tube manometer measures the pressure drop across the valve as 8.5 inches of

mercury. The loss coefficient K for the valve, is most nearly:

(A) 8.5

(B) 12

(C) 6

(D) 24


Pump A

Water from remote reservoir

PressurizedSurge Tank

To plant water pipe networkManometer

Valve being tested


Hydraulics & Fluids – 005. A pressurized, insulated hot water tank stores heated liquid water at 25

psi (absolute) and 180ºF. A pump is used to take water from the tank at a rate of 1100 gpm. The pump

performance curves are provided below. Neglecting friction and minor losses, the maximum height

(feet) above the water surface of the suction reservoir this pump can be located without experiencing

cavitation is nearest:

(A) 8

(B) 34

(C) 60

(D) 224


0 500 1000 1500 2000

0 500 1000 1500 2000

150

160

170

180

190

200

210

220

230

240

250

0

5

10

15

20

25

30

Flow Rate, GPM

NP

SH

R (

FT

)

Hea

d (F

T)

NPSHR

Head

Flow Rate, GPM


Hydraulics & Fluids – 006. A valve manufacturer uses the rig shown below to test their valves. The

working fluid is water ( kinematic viscosity = 1.12 cSt, density = 62.4 lb/ft3 ). The flow rate is 400

gallons per minute, and all piping is 4-in, schedule 40, steel pipe (ID = 4.026 in). The test section

(between pressure gauges PG001 and PG002) is 1,000 feet long of horizontal, straight pipe. For the test

conditions, the Moody friction factor is known to be 0.018. Upon achieving steady state flow, the

pressure readings are 70 psig for PG001 and 25 psig for PG002. For the valve being tested, the

equivalent length in feet is most nearly:

(A) 0

(B) 110

(C) 220

(D) 1,000


Pump A

Water from remote reservoir

To plant water pipe network

Valve being tested

PG001 PG002


Hydraulics & Fluids – 007. An axial flow hydraulic turbine develops 5,000 hp at the shaft when

operating with a head of 40 ft. A plot showing the variation of axial flow turbine efficiency with

specific speed is provided for your potential use. If the turbine is to operate at peak efficiency, the

rotational speed (rpm) is most nearly:

(A) 300

(B) 140

(C) 100

(D) 96

Energy/Power Systems – 001 An ideal Diesel cycle uses air (R=0.3704 psia⋅ft3/(lb⋅°R) ,

c p=0.240 Btu/(lb⋅°R) , k=1.4) and at the start of the compression process the working fluid is at

80°F and 14.7 psia. If the maximum absolute pressure achieved in the cycle is 58 bar, the compression

ratio is nearest:

(A) 58

(B) 18

(C) 8

(D) 2.7


50 60 70 80 90 100 110 120 13080

85

90

95

100

Specific speed, Nsd

,US customary units

η(%)

Representative Efficiency of Axial Hydraulic Turbines as a Function of Specific Speed


Energy/Power Systems – 002. A carbonated beverage facility has a tank for liquid carbon dioxide

(CO2) storage. The tank is always maintained at -12°C and at the corresponding saturation pressure.

The tank initially contains 500 kg of a liquid-vapor mixture of CO2 with a 5% quality. In steady state

operation, the liquid is drawn from the bottom of the tank and sent to a series of heaters and pressure

regulators that deliver the CO2 in gaseous form at ambient temperature (22°C) and a pressure of 170

kPa absolute for use in the carbonation process. A flow meter at the carbonation machines shows a

continuous consumption of 0.1 actual m3 of gaseous CO2

per hour. Under these conditions, the time

(hours) until the mass inside the tank is reduced to 50 kg is nearest:

(A) 4.5

(B) 68

(C) 148

(D) 1475

The following table has selected data for CO2 for your potential use:

Saturation Properties for CO2

Temp.(°C)

AbsolutePressure

(MPa)

Volume(m3/kg)

Enthalpy(kJ/kg)

Entropy(kJ/kg·°C)

Liquid Vapor Liquid Vapor Liquid Vapor

-14 2.359 0.000997 0.01595 167.55 436.09 0.8825 1.9187

-13 2.429 0.001002 0.01545 169.78 435.89 0.8908 1.9137

-12 2.501 0.001007 0.01497 172.01 435.66 0.8991 1.9086

-11 2.574 0.001012 0.01450 174.26 435.41 0.9074 1.9036

-10 2.649 0.001017 0.01405 176.52 435.14 0.9157 1.8985



Energy/Power Systems – 003. Octane is burned in a constant pressure burner and the combustion

equation for the actual process is:

C8H

18 + 16.32(O

2+3.76N

2) → 7.37CO

2 + 0.65CO + 4.13O

2 + 61.38N

2 + 9H

2O

The percent excess air being used is nearest:

(A) 1475

(B) 131

(C) 16

(D) 31

Energy/Power Systems – 004. A geothermal power plant uses geothermal water extracted as high-

pressure saturated liquid at 450°F. This water is throttled down to a pressure of 70 psia before entering

a separator tank. This sudden pressure drop results in the “flashing” of the liquid into a liquid-vapor

mixture. In the separator tank the resulting vapor is separated from the liquid and directed to a turbine.

On a mass basis, the percent of geothermal water that is sent in vapor form to the turbine is nearest:

(A) Cannot be determined

(B) 17%

(C) 32%

(D) 94%


Separatorp = 70 psia

Vapor to turbine

From Production Well: Saturated liquid water 450ºF

Liquid to re-injection well

Throttle


Energy/Power Systems – 005. A solid copper sphere with a diameter of ½ inch is initially at a

spatially uniform temperature of 150°F before being inserted into a stream of air at 80°F. A

thermocouple at the surface of the sphere indicates a temperature of 130°F after 1 minute and 10

seconds. The heat transfer coefficient (Btu /(ft 2h °F) ) is nearest:

(A) 148

(B) 220

(C) 558

(D) 955



Energy/Power Systems – 006 Points A and B in the Mollier diagram below represent respectively the

inlet and outlet of a steam turbine operating at steady state. There is only one inlet and one outlet. The

isentropic efficiency of this turbine is nearest:

(A) 21%

(B) 63%

(C) 71%

(D) 84%


A

B

Entropy, Btu/(lb·°R)

Ent

halp

y, B

tu/lb

cons

tant

pre

ssur

e, p

sia

1

0.15

0.20.

5

35

1014.730

constant temperature, 600 °F

50

10020

030

050

0

1000

1500

100

200

300

400

500

700

800

900

1000

1100

1150


Energy/Power Systems – 007 Water enters the tubes of a small parallel flow heat exchanger at 74 ºF at

a rate of 30 gpm. On the shell side 10,700 lb/hour of a heat transfer oil enters at 175 ºF. The heat

transfer surface area is 94 ft2,, and the overall heat transfer coefficient is 200 Btu/(hr·ft2·ºF). For this

heat exchanger, the number of transfer units (NTU) is most nearly:

(A) Cannot be determined(B) 2.5(C) 3.0(D) 3.5

If needed, you may use the following property values:

coil

= 0.7 Btu/(lb·ºF) ρoil

= 81.1 lb/ft3

cwater

= 1.0 Btu/(lb·ºF) ρwater

= 62.4 lb/ft3

Also, this is a plot of heat exchanger effectiveness for your potential use:


0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

NTU = UA/Cmin

Hea

t exc

hang

er e

ffect

iven

ess,

ε

Parallel-Flow

Cmin/Cmax = 1

0.75

0.50

0.25

Cmin/Cmax = 0


HVAC/Refrigeration – 001. An atmospheric pressure air stream of 300 CFM at 65°F, with a humidity

ratio of 55 grains of moisture per pound of dry air is to be cooled by flowing over a coil. Condensation

is to be avoided, so the cooling process shall end with the air at a temperature 5°F above the dew point.

Under these conditions, the maximum allowable dry-bulb temperature drop for the air (°F) is most

nearly:

(A) 3

(B) 9

(C) 19

(D) 51

HVAC/Refrigeration – 002. A simple ammonia vapor compression refrigeration system has a load of

5 tons. The evaporator temperature is 5°F. The ammonia leaves the expansion device with a quality of

30% and enters the compressor as saturated vapor. The required flow rate of ammonia (lbs/hr) is

nearest:

(A) 50

(B) 75

(C) 150

(D) 200

Note: A P-h diagram for ammonia is provided in the next page for your potential use.





HVAC/Refrigeration – 003. A simple vapor compression refrigeration system has a load of 5 tons. The

power consumed by the compressor is 75 hp. The rate of heat rejection (Btu/hr) at the condenser is

nearest:

(A) Cannot be determined with the information provided

(B) 60,075

(C) 190,800

(D) 250,800

HVAC/Refrigeration – 004. The temperature inside an industrial freezer in a food processing facility

is always kept 30ºF below that of the space outside. When newly installed, the walls of the freezer had

a total R-value insulation of 25 hr·ft2·ºF/Btu. Over the course of several years, the insulation has

degraded down to an aged R-value of 11 hr·ft2·ºF/Btu. Among the following statements, the one that is

most nearly correct is:

(A) The heat transfer rate through the freezer walls is now roughly 44% of what it was when the freezer

was new.

(B) The overall heat transfer coefficient U for the walls has likely remained unchanged.

(C) The overall heat transfer coefficient U for the walls has likely decreased by a factor of 2.3

(D) The heat transfer rate through the freezer walls has likely increased by a factor of 2.3



HVAC/Refrigeration – 005. On summer days, only the cooling coil of the Air Handler Unit (AHU)

shown in the sketch is operating:

At summer design conditions, the following information is known:

Location Dry Bulb T (°F) Wet Bulb T (°F) Rel. Humidity (%)

r 75 - -

OA 95 78 -

s 56 - 100

For ventilation purposes, 10% outside air (OA) is required. The sensible heat gain for the space,Q s , is

129,000 Btu/hr. The moisture gain for the space,m s is 55.7 lb/hr. The summer design air flow rate to

the space, in CFM is most nearly:

(A) 800

(B) 1550

(C) 3100

(D) 6200


Supply air Conditioned Space

Return air r s

Outside Air

Fan

Air Handler Unit(AHU)

OA

Exhaust

Q s=129,000 Btu/hr Sensible Heat Gain:

Moisture Gain:m s=55.7 lb/hr


HVAC/Refrigeration – 006. A gas furnace produces 90,000 Btu/h with an airflow of 4,000 cfm heated

air with an inlet condition of 65°F and relative humidity of 45%. The relative humidity (%) of the air at

the furnace discharge is nearest:

(A) 12

(B) 23

(C) 45

(D) 51

This completes the practice test.

To purchase detailed, step-by-step solutions to all the problems in this

practice test, visit www.SlaythePE.com




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