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Fundamentals of Engineering Exam prep
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7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 15
Michael R Lindeburg PE
rac ce ro emsor the Mechanical Engineering PE Exam
A Companion to the Mechanical Engineering Reference Manual
hirteenth Edition
Professional Publications Inc bull Belmont California
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 25
64 Instrumentationand Measurements
PRACTICE PROBLEMS
Indicator Diagrams
1 Diesel engines in a waste-to-energy plant are pow-ered by a gaseous mixture of methane and other diges-tion gases The combustion conditions in each cylinderare continuously monitored by pressure and tempera-ture transducers A particular cylinderrsquos indicator dia-gram is shown The scale selected in the monitoringsoftware is set to 111 kPamm Most nearly what isthe mean effective pressure in the cylinder
p
( k P a )
TDC BDC
A 983101 490 mm2
64 mm
(A) 77 kPa
(B) 15 kPa
(C) 360 kPa
(D) 850 kPa
Variable Inductance Transformers
2 Which of the statements regarding the linear vari-able differential transformer (LVDT) shown is true
output
movable coreinput
(A) The LVDT is a variable reluctance transducerand its output voltage is directly proportional toits core movement
(B) The LVDT is a variable reluctance transducerand its output current is directly proportional toits core movement
(C) The LVDT is a variable capacitance transducerand its output current is directly proportional tocore movement
(D) The LVDT is a variable inductance transducer
and its output voltage is directly proportional tocore movement
Resistance Temperature Detectors
3 A resistance temperature detector (RTD) measurestemperature in a bridge circuit The resistances of resis-tors 1 2 and 3 are 100 200 and 50 respectivelyThe power supply voltage is 10 V The reference resis-tance of the RTD is 100 at 0 C The alpha value forthe RTD is 000392 1C The variation of RTD resis-tance with temperature is linear What is most nearlythe temperature of the RTD when the voltmeter reads4167 V
V+
R 2
RTD R 1
R 3
V b
(A) 130F
(B) 210F
(C) 260F
(D) 330F
P P I
w w w p p i 2 p a s s c o m
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 35
4 The temperature of a steel girder during a fire test ismeasured with a type 404 platinum RTD and a simpletwo-wire bridge as shown The characteristics of theRTD are resistance R 100 at 0C temperaturecoefficient 000385 1C The values of the bridgeresistances are R 1 frac14 1000 and R 3 frac14 1000 Whenthe meter is nulled out during a test R 2 frac14 376 Thelead resistances are each 100 Most nearly what is the
temperature of the beam during the test
R 2
R 3R 1
voltage source
RTD
leadresistance
leadresistance
meter
(A) 130C
(B) 175C
(C) 200C
(D) 450C
Piezoelectric Transducers
5 A compression-style crystal piezoelectric acceler-ometer has a sensitivity of 20 mVg It falls to the floorfrom a height of 3 ft and comes to rest 002 sec aftercontact with the floor What is most nearly the averagevoltage output of the accelerometer during impact
mass
base
crystal
(A) 21 mV
(B) 32 mV
(C) 43 mV
(D) 57 mV
6 A piezoelectric transducer is connected to a chargeamplifier as shown What is the purpose of capacitor C t
C t
V out
V in
C a
piezoelectrictransducer
(A) C t biases the transducer output
(B) C t isolates the transducer from inadvertentamplifier transients
(C) C t rectifies the transducer output
(D) C t prevents DC voltages from being passed to theamplifier
Photosensitive Conductors
7 A velocity indicating system attached to a machineconsists of a light source a light sensor a disk thatrotates with the machinersquos rotation and a countingcircuit There are 12 reflective strips around the periph-ery of the disk As a machine starts up the disk spinsand the sensor detects the pulses reflected back by thereflective strips Given the numbers of counts per min-ute recorded by the sensor what is most nearly theaverage angular acceleration of the disk between 2 secand 4 sec
light source
sensor
reflective
strip
startup counts
disk detail
time (sec)
0
1
2
4
counts (min)
0
150
1200
10800
(A) 35 radsec2
(B) 21 radsec2
(C) 42 radsec2
(D) 84 radsec2
P P I
w w w p p i 2 p a s s c o m
64-2 P R A C T I C E P R O B L E M S F O R T H E M E C H A N I C A L E N G I N E E R I N G P E E X A M
P l ant
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 45
21 Two iron-constantan thermocouples are wired inseries to monitor the cylinder head temperature in anaircraft engine The voltage across the thermocouples isread in the cockpit as 1652 mV The cockpit tempera-ture is 70F What is most nearly the average tempera-ture of the cylinder head
cylinder head
cockpit
V out
(A) 290F
(B) 330F
(C) 350F
(D) 380F
22 A copper-constantan thermocouple is used with anice bath to measure the temperature of waste sludgeduring digestion The voltage is proportional to thedifference in temperature between the junctions Whenthe thermocouple is calibrated it generates a voltage of 507 103 V when the temperature of the hot junctionis 1089C and the reference temperature is at 0C Mostnearly what is the temperature of waste sludge whenthe voltage is 183 103 V
(A) 40C
(B) 45C
(C) 50C
(D) 55C
SOLUTIONS
1 The average height of the pressure plot is
h frac14 A
w frac14 490 mm2
64 mm frac14 7656 mm
The average pressure is
pfrac14 kh frac14 111 kPamm
eth7656 mmTHORN
frac14 8498 kPa eth850 kPaTHORN
The answer is (D)
2 A coil of wire particularly a coil with an iron corebehaves as an inductor in an AC circuit In an LVDTthe movable transformer core changes the inductance
between the primary and secondary windings Thetransformer is constructed so that the output voltageof the LVDT is directly proportional to the movablecore position A linear variable differential transformer(LVDT) is a variable inductance transducer
The answer is (D)
3 Since the voltage is not zero the bridge is notbalanced Rearrange Eq 6416 to find the RTDresistance
R RTD frac14V bR 1R 3
thornV ethR 1R 3
thornR 2R 3
THORNV bR 2 V ethR 1 thorn R 2THORN
frac14
eth10 VTHORNeth100 THORNeth50 THORN
thorn eth4167 VTHORNeth100 THORNeth50 THORNthorn eth200 THORNeth50 THORN
eth10 VTHORNeth200 THORN eth4167 VTHORN eth100 thorn 200 THORN
frac14 1500
Rearrange Eq 643 to find the temperature Since tem-perature varies linearly with resistance only the alpha-value is required
T frac14 R ref ethT ref 1THORN thorn R RTD
R ref
frac14eth100 THORN 000392
1C
eth0CTHORN 1
thorn 1500
eth100 THORN 000392 1C
frac14 1276C
P P I
w w w p p i 2 p a s s c o m
64-6 P R A C T I C E P R O B L E M S F O R T H E M E C H A N I C A L E N G I N E E R I N G P E E X A M
P l ant
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 55
Convert to the Fahrenheit scale
T F frac14 32 thorn 95T C frac14 32F thorn 9
5
eth1276CTHORNfrac14 2617F eth260FTHORN
The answer is (C)
4 When the meter is nulled out the resistance of theleg containing the RTD is
R 4 frac14 R RTD thorn 2R lead frac14 R 2R 3R 1
frac14 eth376 THORNeth1000 THORN1000
frac14 376
The resistance of the RTD is
R RTD frac14 R 4 2R lead frac14 376 eth2THORNeth100 THORN frac14 176
The relationship between temperature and resistance for
an RTD is
R T frac14 R 0eth1 thornAT thornBT 2THORN
For a platinum RTD with = 000385 1C the resis-tance is
R T frac14 R 01 thorn eth39083 103THORNT
thorn eth5775 107THORNT 2
R 0
1 thorn eth39083 103THORNT
176 eth100 THORN1 thorn eth39083 103THORNT
T 1945C eth200CTHORN
(If the squared term is kept the temperature is 2003C)
The answer is (C)
5 The displacement of the falling accelerometer is
x frac14 x 0 thorn v0t 12gt
2
The initial displacement and the initial velocity are bothzero The time required to fall a distance of x is
x frac14 ffiffiffiffiffi2x g
r The impact velocity is
vfrac14 gt frac14 g
ffiffiffiffiffi2x g
r frac14 ffiffiffiffiffiffiffiffi
2xg p
frac14 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffieth2THORNeth3 ftTHORN 322
ftsec2
r frac14 139 ft=sec
The average acceleration is
a frac14 vDt frac14
139 ftsec
eth002 secTHORN 322 ftsec2-g
frac14 2158 g
The average voltage output is
V frac14 ka frac14 20 mV
g
eth2158 gTHORN
frac14 4316 mV eth43 mVTHORN
The answer is (C)
6 The transducer capacitance C t prevents DC volt-ages from being passed to the amplifier The value of C t does not influence the amplifier gain
The answer is (D)
7 Each revolution produces 12 counts UsingEq 5718 the average angular acceleration is
ave frac14 2 1
t 2 t 1
frac142p
radrev
10800
countsmin
1200 counts
min
eth4 sec 2 secTHORN 12
countsrev
60
secmin
frac14 4189 rad=sec2 eth42 rad=sec2THORN
The answer is (C)
8 The weight of the object is equal to the force on thescale
F frac14 pA frac14 p p
4
ethD 2t THORN2
frac14 50 lbf in2
p
4
eth2 ftTHORN 12
inft
eth2THORNeth2 inTHORN
2
frac14 15708 lbf eth16000 lbf THORN
The answer is (B)
9 From Eq 6411 the strain is
frac14 DR g
ethGFTHORNR g frac141001 100 eth60THORNeth100 THORN frac14 167 104
From Eq 6424 the stress is
frac14 E frac14 30 106 lbf in2
eth167 104THORN
frac14 50 103 lbf =in2
P P I
w w w p p i 2 p a s s c o m
I N S T R U M E N T A T I O N A N D M E A S U R E M E N T S 64-7
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 25
64 Instrumentationand Measurements
PRACTICE PROBLEMS
Indicator Diagrams
1 Diesel engines in a waste-to-energy plant are pow-ered by a gaseous mixture of methane and other diges-tion gases The combustion conditions in each cylinderare continuously monitored by pressure and tempera-ture transducers A particular cylinderrsquos indicator dia-gram is shown The scale selected in the monitoringsoftware is set to 111 kPamm Most nearly what isthe mean effective pressure in the cylinder
p
( k P a )
TDC BDC
A 983101 490 mm2
64 mm
(A) 77 kPa
(B) 15 kPa
(C) 360 kPa
(D) 850 kPa
Variable Inductance Transformers
2 Which of the statements regarding the linear vari-able differential transformer (LVDT) shown is true
output
movable coreinput
(A) The LVDT is a variable reluctance transducerand its output voltage is directly proportional toits core movement
(B) The LVDT is a variable reluctance transducerand its output current is directly proportional toits core movement
(C) The LVDT is a variable capacitance transducerand its output current is directly proportional tocore movement
(D) The LVDT is a variable inductance transducer
and its output voltage is directly proportional tocore movement
Resistance Temperature Detectors
3 A resistance temperature detector (RTD) measurestemperature in a bridge circuit The resistances of resis-tors 1 2 and 3 are 100 200 and 50 respectivelyThe power supply voltage is 10 V The reference resis-tance of the RTD is 100 at 0 C The alpha value forthe RTD is 000392 1C The variation of RTD resis-tance with temperature is linear What is most nearlythe temperature of the RTD when the voltmeter reads4167 V
V+
R 2
RTD R 1
R 3
V b
(A) 130F
(B) 210F
(C) 260F
(D) 330F
P P I
w w w p p i 2 p a s s c o m
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 35
4 The temperature of a steel girder during a fire test ismeasured with a type 404 platinum RTD and a simpletwo-wire bridge as shown The characteristics of theRTD are resistance R 100 at 0C temperaturecoefficient 000385 1C The values of the bridgeresistances are R 1 frac14 1000 and R 3 frac14 1000 Whenthe meter is nulled out during a test R 2 frac14 376 Thelead resistances are each 100 Most nearly what is the
temperature of the beam during the test
R 2
R 3R 1
voltage source
RTD
leadresistance
leadresistance
meter
(A) 130C
(B) 175C
(C) 200C
(D) 450C
Piezoelectric Transducers
5 A compression-style crystal piezoelectric acceler-ometer has a sensitivity of 20 mVg It falls to the floorfrom a height of 3 ft and comes to rest 002 sec aftercontact with the floor What is most nearly the averagevoltage output of the accelerometer during impact
mass
base
crystal
(A) 21 mV
(B) 32 mV
(C) 43 mV
(D) 57 mV
6 A piezoelectric transducer is connected to a chargeamplifier as shown What is the purpose of capacitor C t
C t
V out
V in
C a
piezoelectrictransducer
(A) C t biases the transducer output
(B) C t isolates the transducer from inadvertentamplifier transients
(C) C t rectifies the transducer output
(D) C t prevents DC voltages from being passed to theamplifier
Photosensitive Conductors
7 A velocity indicating system attached to a machineconsists of a light source a light sensor a disk thatrotates with the machinersquos rotation and a countingcircuit There are 12 reflective strips around the periph-ery of the disk As a machine starts up the disk spinsand the sensor detects the pulses reflected back by thereflective strips Given the numbers of counts per min-ute recorded by the sensor what is most nearly theaverage angular acceleration of the disk between 2 secand 4 sec
light source
sensor
reflective
strip
startup counts
disk detail
time (sec)
0
1
2
4
counts (min)
0
150
1200
10800
(A) 35 radsec2
(B) 21 radsec2
(C) 42 radsec2
(D) 84 radsec2
P P I
w w w p p i 2 p a s s c o m
64-2 P R A C T I C E P R O B L E M S F O R T H E M E C H A N I C A L E N G I N E E R I N G P E E X A M
P l ant
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 45
21 Two iron-constantan thermocouples are wired inseries to monitor the cylinder head temperature in anaircraft engine The voltage across the thermocouples isread in the cockpit as 1652 mV The cockpit tempera-ture is 70F What is most nearly the average tempera-ture of the cylinder head
cylinder head
cockpit
V out
(A) 290F
(B) 330F
(C) 350F
(D) 380F
22 A copper-constantan thermocouple is used with anice bath to measure the temperature of waste sludgeduring digestion The voltage is proportional to thedifference in temperature between the junctions Whenthe thermocouple is calibrated it generates a voltage of 507 103 V when the temperature of the hot junctionis 1089C and the reference temperature is at 0C Mostnearly what is the temperature of waste sludge whenthe voltage is 183 103 V
(A) 40C
(B) 45C
(C) 50C
(D) 55C
SOLUTIONS
1 The average height of the pressure plot is
h frac14 A
w frac14 490 mm2
64 mm frac14 7656 mm
The average pressure is
pfrac14 kh frac14 111 kPamm
eth7656 mmTHORN
frac14 8498 kPa eth850 kPaTHORN
The answer is (D)
2 A coil of wire particularly a coil with an iron corebehaves as an inductor in an AC circuit In an LVDTthe movable transformer core changes the inductance
between the primary and secondary windings Thetransformer is constructed so that the output voltageof the LVDT is directly proportional to the movablecore position A linear variable differential transformer(LVDT) is a variable inductance transducer
The answer is (D)
3 Since the voltage is not zero the bridge is notbalanced Rearrange Eq 6416 to find the RTDresistance
R RTD frac14V bR 1R 3
thornV ethR 1R 3
thornR 2R 3
THORNV bR 2 V ethR 1 thorn R 2THORN
frac14
eth10 VTHORNeth100 THORNeth50 THORN
thorn eth4167 VTHORNeth100 THORNeth50 THORNthorn eth200 THORNeth50 THORN
eth10 VTHORNeth200 THORN eth4167 VTHORN eth100 thorn 200 THORN
frac14 1500
Rearrange Eq 643 to find the temperature Since tem-perature varies linearly with resistance only the alpha-value is required
T frac14 R ref ethT ref 1THORN thorn R RTD
R ref
frac14eth100 THORN 000392
1C
eth0CTHORN 1
thorn 1500
eth100 THORN 000392 1C
frac14 1276C
P P I
w w w p p i 2 p a s s c o m
64-6 P R A C T I C E P R O B L E M S F O R T H E M E C H A N I C A L E N G I N E E R I N G P E E X A M
P l ant
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 55
Convert to the Fahrenheit scale
T F frac14 32 thorn 95T C frac14 32F thorn 9
5
eth1276CTHORNfrac14 2617F eth260FTHORN
The answer is (C)
4 When the meter is nulled out the resistance of theleg containing the RTD is
R 4 frac14 R RTD thorn 2R lead frac14 R 2R 3R 1
frac14 eth376 THORNeth1000 THORN1000
frac14 376
The resistance of the RTD is
R RTD frac14 R 4 2R lead frac14 376 eth2THORNeth100 THORN frac14 176
The relationship between temperature and resistance for
an RTD is
R T frac14 R 0eth1 thornAT thornBT 2THORN
For a platinum RTD with = 000385 1C the resis-tance is
R T frac14 R 01 thorn eth39083 103THORNT
thorn eth5775 107THORNT 2
R 0
1 thorn eth39083 103THORNT
176 eth100 THORN1 thorn eth39083 103THORNT
T 1945C eth200CTHORN
(If the squared term is kept the temperature is 2003C)
The answer is (C)
5 The displacement of the falling accelerometer is
x frac14 x 0 thorn v0t 12gt
2
The initial displacement and the initial velocity are bothzero The time required to fall a distance of x is
x frac14 ffiffiffiffiffi2x g
r The impact velocity is
vfrac14 gt frac14 g
ffiffiffiffiffi2x g
r frac14 ffiffiffiffiffiffiffiffi
2xg p
frac14 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffieth2THORNeth3 ftTHORN 322
ftsec2
r frac14 139 ft=sec
The average acceleration is
a frac14 vDt frac14
139 ftsec
eth002 secTHORN 322 ftsec2-g
frac14 2158 g
The average voltage output is
V frac14 ka frac14 20 mV
g
eth2158 gTHORN
frac14 4316 mV eth43 mVTHORN
The answer is (C)
6 The transducer capacitance C t prevents DC volt-ages from being passed to the amplifier The value of C t does not influence the amplifier gain
The answer is (D)
7 Each revolution produces 12 counts UsingEq 5718 the average angular acceleration is
ave frac14 2 1
t 2 t 1
frac142p
radrev
10800
countsmin
1200 counts
min
eth4 sec 2 secTHORN 12
countsrev
60
secmin
frac14 4189 rad=sec2 eth42 rad=sec2THORN
The answer is (C)
8 The weight of the object is equal to the force on thescale
F frac14 pA frac14 p p
4
ethD 2t THORN2
frac14 50 lbf in2
p
4
eth2 ftTHORN 12
inft
eth2THORNeth2 inTHORN
2
frac14 15708 lbf eth16000 lbf THORN
The answer is (B)
9 From Eq 6411 the strain is
frac14 DR g
ethGFTHORNR g frac141001 100 eth60THORNeth100 THORN frac14 167 104
From Eq 6424 the stress is
frac14 E frac14 30 106 lbf in2
eth167 104THORN
frac14 50 103 lbf =in2
P P I
w w w p p i 2 p a s s c o m
I N S T R U M E N T A T I O N A N D M E A S U R E M E N T S 64-7
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 35
4 The temperature of a steel girder during a fire test ismeasured with a type 404 platinum RTD and a simpletwo-wire bridge as shown The characteristics of theRTD are resistance R 100 at 0C temperaturecoefficient 000385 1C The values of the bridgeresistances are R 1 frac14 1000 and R 3 frac14 1000 Whenthe meter is nulled out during a test R 2 frac14 376 Thelead resistances are each 100 Most nearly what is the
temperature of the beam during the test
R 2
R 3R 1
voltage source
RTD
leadresistance
leadresistance
meter
(A) 130C
(B) 175C
(C) 200C
(D) 450C
Piezoelectric Transducers
5 A compression-style crystal piezoelectric acceler-ometer has a sensitivity of 20 mVg It falls to the floorfrom a height of 3 ft and comes to rest 002 sec aftercontact with the floor What is most nearly the averagevoltage output of the accelerometer during impact
mass
base
crystal
(A) 21 mV
(B) 32 mV
(C) 43 mV
(D) 57 mV
6 A piezoelectric transducer is connected to a chargeamplifier as shown What is the purpose of capacitor C t
C t
V out
V in
C a
piezoelectrictransducer
(A) C t biases the transducer output
(B) C t isolates the transducer from inadvertentamplifier transients
(C) C t rectifies the transducer output
(D) C t prevents DC voltages from being passed to theamplifier
Photosensitive Conductors
7 A velocity indicating system attached to a machineconsists of a light source a light sensor a disk thatrotates with the machinersquos rotation and a countingcircuit There are 12 reflective strips around the periph-ery of the disk As a machine starts up the disk spinsand the sensor detects the pulses reflected back by thereflective strips Given the numbers of counts per min-ute recorded by the sensor what is most nearly theaverage angular acceleration of the disk between 2 secand 4 sec
light source
sensor
reflective
strip
startup counts
disk detail
time (sec)
0
1
2
4
counts (min)
0
150
1200
10800
(A) 35 radsec2
(B) 21 radsec2
(C) 42 radsec2
(D) 84 radsec2
P P I
w w w p p i 2 p a s s c o m
64-2 P R A C T I C E P R O B L E M S F O R T H E M E C H A N I C A L E N G I N E E R I N G P E E X A M
P l ant
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 45
21 Two iron-constantan thermocouples are wired inseries to monitor the cylinder head temperature in anaircraft engine The voltage across the thermocouples isread in the cockpit as 1652 mV The cockpit tempera-ture is 70F What is most nearly the average tempera-ture of the cylinder head
cylinder head
cockpit
V out
(A) 290F
(B) 330F
(C) 350F
(D) 380F
22 A copper-constantan thermocouple is used with anice bath to measure the temperature of waste sludgeduring digestion The voltage is proportional to thedifference in temperature between the junctions Whenthe thermocouple is calibrated it generates a voltage of 507 103 V when the temperature of the hot junctionis 1089C and the reference temperature is at 0C Mostnearly what is the temperature of waste sludge whenthe voltage is 183 103 V
(A) 40C
(B) 45C
(C) 50C
(D) 55C
SOLUTIONS
1 The average height of the pressure plot is
h frac14 A
w frac14 490 mm2
64 mm frac14 7656 mm
The average pressure is
pfrac14 kh frac14 111 kPamm
eth7656 mmTHORN
frac14 8498 kPa eth850 kPaTHORN
The answer is (D)
2 A coil of wire particularly a coil with an iron corebehaves as an inductor in an AC circuit In an LVDTthe movable transformer core changes the inductance
between the primary and secondary windings Thetransformer is constructed so that the output voltageof the LVDT is directly proportional to the movablecore position A linear variable differential transformer(LVDT) is a variable inductance transducer
The answer is (D)
3 Since the voltage is not zero the bridge is notbalanced Rearrange Eq 6416 to find the RTDresistance
R RTD frac14V bR 1R 3
thornV ethR 1R 3
thornR 2R 3
THORNV bR 2 V ethR 1 thorn R 2THORN
frac14
eth10 VTHORNeth100 THORNeth50 THORN
thorn eth4167 VTHORNeth100 THORNeth50 THORNthorn eth200 THORNeth50 THORN
eth10 VTHORNeth200 THORN eth4167 VTHORN eth100 thorn 200 THORN
frac14 1500
Rearrange Eq 643 to find the temperature Since tem-perature varies linearly with resistance only the alpha-value is required
T frac14 R ref ethT ref 1THORN thorn R RTD
R ref
frac14eth100 THORN 000392
1C
eth0CTHORN 1
thorn 1500
eth100 THORN 000392 1C
frac14 1276C
P P I
w w w p p i 2 p a s s c o m
64-6 P R A C T I C E P R O B L E M S F O R T H E M E C H A N I C A L E N G I N E E R I N G P E E X A M
P l ant
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 55
Convert to the Fahrenheit scale
T F frac14 32 thorn 95T C frac14 32F thorn 9
5
eth1276CTHORNfrac14 2617F eth260FTHORN
The answer is (C)
4 When the meter is nulled out the resistance of theleg containing the RTD is
R 4 frac14 R RTD thorn 2R lead frac14 R 2R 3R 1
frac14 eth376 THORNeth1000 THORN1000
frac14 376
The resistance of the RTD is
R RTD frac14 R 4 2R lead frac14 376 eth2THORNeth100 THORN frac14 176
The relationship between temperature and resistance for
an RTD is
R T frac14 R 0eth1 thornAT thornBT 2THORN
For a platinum RTD with = 000385 1C the resis-tance is
R T frac14 R 01 thorn eth39083 103THORNT
thorn eth5775 107THORNT 2
R 0
1 thorn eth39083 103THORNT
176 eth100 THORN1 thorn eth39083 103THORNT
T 1945C eth200CTHORN
(If the squared term is kept the temperature is 2003C)
The answer is (C)
5 The displacement of the falling accelerometer is
x frac14 x 0 thorn v0t 12gt
2
The initial displacement and the initial velocity are bothzero The time required to fall a distance of x is
x frac14 ffiffiffiffiffi2x g
r The impact velocity is
vfrac14 gt frac14 g
ffiffiffiffiffi2x g
r frac14 ffiffiffiffiffiffiffiffi
2xg p
frac14 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffieth2THORNeth3 ftTHORN 322
ftsec2
r frac14 139 ft=sec
The average acceleration is
a frac14 vDt frac14
139 ftsec
eth002 secTHORN 322 ftsec2-g
frac14 2158 g
The average voltage output is
V frac14 ka frac14 20 mV
g
eth2158 gTHORN
frac14 4316 mV eth43 mVTHORN
The answer is (C)
6 The transducer capacitance C t prevents DC volt-ages from being passed to the amplifier The value of C t does not influence the amplifier gain
The answer is (D)
7 Each revolution produces 12 counts UsingEq 5718 the average angular acceleration is
ave frac14 2 1
t 2 t 1
frac142p
radrev
10800
countsmin
1200 counts
min
eth4 sec 2 secTHORN 12
countsrev
60
secmin
frac14 4189 rad=sec2 eth42 rad=sec2THORN
The answer is (C)
8 The weight of the object is equal to the force on thescale
F frac14 pA frac14 p p
4
ethD 2t THORN2
frac14 50 lbf in2
p
4
eth2 ftTHORN 12
inft
eth2THORNeth2 inTHORN
2
frac14 15708 lbf eth16000 lbf THORN
The answer is (B)
9 From Eq 6411 the strain is
frac14 DR g
ethGFTHORNR g frac141001 100 eth60THORNeth100 THORN frac14 167 104
From Eq 6424 the stress is
frac14 E frac14 30 106 lbf in2
eth167 104THORN
frac14 50 103 lbf =in2
P P I
w w w p p i 2 p a s s c o m
I N S T R U M E N T A T I O N A N D M E A S U R E M E N T S 64-7
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 45
21 Two iron-constantan thermocouples are wired inseries to monitor the cylinder head temperature in anaircraft engine The voltage across the thermocouples isread in the cockpit as 1652 mV The cockpit tempera-ture is 70F What is most nearly the average tempera-ture of the cylinder head
cylinder head
cockpit
V out
(A) 290F
(B) 330F
(C) 350F
(D) 380F
22 A copper-constantan thermocouple is used with anice bath to measure the temperature of waste sludgeduring digestion The voltage is proportional to thedifference in temperature between the junctions Whenthe thermocouple is calibrated it generates a voltage of 507 103 V when the temperature of the hot junctionis 1089C and the reference temperature is at 0C Mostnearly what is the temperature of waste sludge whenthe voltage is 183 103 V
(A) 40C
(B) 45C
(C) 50C
(D) 55C
SOLUTIONS
1 The average height of the pressure plot is
h frac14 A
w frac14 490 mm2
64 mm frac14 7656 mm
The average pressure is
pfrac14 kh frac14 111 kPamm
eth7656 mmTHORN
frac14 8498 kPa eth850 kPaTHORN
The answer is (D)
2 A coil of wire particularly a coil with an iron corebehaves as an inductor in an AC circuit In an LVDTthe movable transformer core changes the inductance
between the primary and secondary windings Thetransformer is constructed so that the output voltageof the LVDT is directly proportional to the movablecore position A linear variable differential transformer(LVDT) is a variable inductance transducer
The answer is (D)
3 Since the voltage is not zero the bridge is notbalanced Rearrange Eq 6416 to find the RTDresistance
R RTD frac14V bR 1R 3
thornV ethR 1R 3
thornR 2R 3
THORNV bR 2 V ethR 1 thorn R 2THORN
frac14
eth10 VTHORNeth100 THORNeth50 THORN
thorn eth4167 VTHORNeth100 THORNeth50 THORNthorn eth200 THORNeth50 THORN
eth10 VTHORNeth200 THORN eth4167 VTHORN eth100 thorn 200 THORN
frac14 1500
Rearrange Eq 643 to find the temperature Since tem-perature varies linearly with resistance only the alpha-value is required
T frac14 R ref ethT ref 1THORN thorn R RTD
R ref
frac14eth100 THORN 000392
1C
eth0CTHORN 1
thorn 1500
eth100 THORN 000392 1C
frac14 1276C
P P I
w w w p p i 2 p a s s c o m
64-6 P R A C T I C E P R O B L E M S F O R T H E M E C H A N I C A L E N G I N E E R I N G P E E X A M
P l ant
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 55
Convert to the Fahrenheit scale
T F frac14 32 thorn 95T C frac14 32F thorn 9
5
eth1276CTHORNfrac14 2617F eth260FTHORN
The answer is (C)
4 When the meter is nulled out the resistance of theleg containing the RTD is
R 4 frac14 R RTD thorn 2R lead frac14 R 2R 3R 1
frac14 eth376 THORNeth1000 THORN1000
frac14 376
The resistance of the RTD is
R RTD frac14 R 4 2R lead frac14 376 eth2THORNeth100 THORN frac14 176
The relationship between temperature and resistance for
an RTD is
R T frac14 R 0eth1 thornAT thornBT 2THORN
For a platinum RTD with = 000385 1C the resis-tance is
R T frac14 R 01 thorn eth39083 103THORNT
thorn eth5775 107THORNT 2
R 0
1 thorn eth39083 103THORNT
176 eth100 THORN1 thorn eth39083 103THORNT
T 1945C eth200CTHORN
(If the squared term is kept the temperature is 2003C)
The answer is (C)
5 The displacement of the falling accelerometer is
x frac14 x 0 thorn v0t 12gt
2
The initial displacement and the initial velocity are bothzero The time required to fall a distance of x is
x frac14 ffiffiffiffiffi2x g
r The impact velocity is
vfrac14 gt frac14 g
ffiffiffiffiffi2x g
r frac14 ffiffiffiffiffiffiffiffi
2xg p
frac14 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffieth2THORNeth3 ftTHORN 322
ftsec2
r frac14 139 ft=sec
The average acceleration is
a frac14 vDt frac14
139 ftsec
eth002 secTHORN 322 ftsec2-g
frac14 2158 g
The average voltage output is
V frac14 ka frac14 20 mV
g
eth2158 gTHORN
frac14 4316 mV eth43 mVTHORN
The answer is (C)
6 The transducer capacitance C t prevents DC volt-ages from being passed to the amplifier The value of C t does not influence the amplifier gain
The answer is (D)
7 Each revolution produces 12 counts UsingEq 5718 the average angular acceleration is
ave frac14 2 1
t 2 t 1
frac142p
radrev
10800
countsmin
1200 counts
min
eth4 sec 2 secTHORN 12
countsrev
60
secmin
frac14 4189 rad=sec2 eth42 rad=sec2THORN
The answer is (C)
8 The weight of the object is equal to the force on thescale
F frac14 pA frac14 p p
4
ethD 2t THORN2
frac14 50 lbf in2
p
4
eth2 ftTHORN 12
inft
eth2THORNeth2 inTHORN
2
frac14 15708 lbf eth16000 lbf THORN
The answer is (B)
9 From Eq 6411 the strain is
frac14 DR g
ethGFTHORNR g frac141001 100 eth60THORNeth100 THORN frac14 167 104
From Eq 6424 the stress is
frac14 E frac14 30 106 lbf in2
eth167 104THORN
frac14 50 103 lbf =in2
P P I
w w w p p i 2 p a s s c o m
I N S T R U M E N T A T I O N A N D M E A S U R E M E N T S 64-7
7172019 Me Pp Sample
httpslidepdfcomreaderfullme-pp-sample 55
Convert to the Fahrenheit scale
T F frac14 32 thorn 95T C frac14 32F thorn 9
5
eth1276CTHORNfrac14 2617F eth260FTHORN
The answer is (C)
4 When the meter is nulled out the resistance of theleg containing the RTD is
R 4 frac14 R RTD thorn 2R lead frac14 R 2R 3R 1
frac14 eth376 THORNeth1000 THORN1000
frac14 376
The resistance of the RTD is
R RTD frac14 R 4 2R lead frac14 376 eth2THORNeth100 THORN frac14 176
The relationship between temperature and resistance for
an RTD is
R T frac14 R 0eth1 thornAT thornBT 2THORN
For a platinum RTD with = 000385 1C the resis-tance is
R T frac14 R 01 thorn eth39083 103THORNT
thorn eth5775 107THORNT 2
R 0
1 thorn eth39083 103THORNT
176 eth100 THORN1 thorn eth39083 103THORNT
T 1945C eth200CTHORN
(If the squared term is kept the temperature is 2003C)
The answer is (C)
5 The displacement of the falling accelerometer is
x frac14 x 0 thorn v0t 12gt
2
The initial displacement and the initial velocity are bothzero The time required to fall a distance of x is
x frac14 ffiffiffiffiffi2x g
r The impact velocity is
vfrac14 gt frac14 g
ffiffiffiffiffi2x g
r frac14 ffiffiffiffiffiffiffiffi
2xg p
frac14 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffieth2THORNeth3 ftTHORN 322
ftsec2
r frac14 139 ft=sec
The average acceleration is
a frac14 vDt frac14
139 ftsec
eth002 secTHORN 322 ftsec2-g
frac14 2158 g
The average voltage output is
V frac14 ka frac14 20 mV
g
eth2158 gTHORN
frac14 4316 mV eth43 mVTHORN
The answer is (C)
6 The transducer capacitance C t prevents DC volt-ages from being passed to the amplifier The value of C t does not influence the amplifier gain
The answer is (D)
7 Each revolution produces 12 counts UsingEq 5718 the average angular acceleration is
ave frac14 2 1
t 2 t 1
frac142p
radrev
10800
countsmin
1200 counts
min
eth4 sec 2 secTHORN 12
countsrev
60
secmin
frac14 4189 rad=sec2 eth42 rad=sec2THORN
The answer is (C)
8 The weight of the object is equal to the force on thescale
F frac14 pA frac14 p p
4
ethD 2t THORN2
frac14 50 lbf in2
p
4
eth2 ftTHORN 12
inft
eth2THORNeth2 inTHORN
2
frac14 15708 lbf eth16000 lbf THORN
The answer is (B)
9 From Eq 6411 the strain is
frac14 DR g
ethGFTHORNR g frac141001 100 eth60THORNeth100 THORN frac14 167 104
From Eq 6424 the stress is
frac14 E frac14 30 106 lbf in2
eth167 104THORN
frac14 50 103 lbf =in2
P P I
w w w p p i 2 p a s s c o m
I N S T R U M E N T A T I O N A N D M E A S U R E M E N T S 64-7
