PART 1
1. A dynamometer shows that the average pull required for a certain machine is 20KN. If the tractor
travels at 5kph, what is the power developed?
Given: F = 20KN, S = 5kph
Required: power developed
Solution:
m
(20,000 N x 5000 s )
P= = 27.78 kW
3600sec
2. A dynamometer test shows that an engine delivers an average output of 50hp at a speed of
1500rpm. What torque is exerted?
Given: P = 50hp, N = 1500rpm
Required: torque
Solution:
P (50hp) (76.2kg.m/s) (9.8N)
P = 2πTN; T = 2πN = = 237.7 N-m
2π(1500/60min)
3. What is the piston displacement in cubic inches of a 4.5 in by 6 in cylinder engine?
Given: D = 4.5 in, H = 6 in
Solution:
πD2 L π(4.5in)2 (6in)
PD = = = 95.42 in3
4 4
4. An engine with 60mm x 60mm engine runs 1500rpm. What is the maximum piston speed inside
the cylinder?
Given: Engine dimension: 60mm x 60mm
Solution:
π(0.06m) (1500)
V = πDN = = 4.71 m/s
60 sec
5. A tractor pulls a 2500kg of loads at a speed of 5kph on a flat ground. If the coefficient of rolling
resistance is 0.25, what is the drawbar power that the tractor generates?
Given: F = 2500kg, RS = 0.25, V = 5kph
Solution:
m
(2500kg) (5000m) 3472.20kg. s
DHP = FV = = m = 45.57hp x 0.25 = 11.40hp
3600 sec 76.2kg. s
6. A gasoline engine was tested for continuous 5hrs of operation. It consumed a total of 9 liters of
fuels and developed a constant power of 3 kW. If the fuel contains 34,636MJ/m3, what is the
approximate thermal efficiency?
Solution:
W 3kW
ηth = = = 17.32%
Q 17.318kW
(9 liters/5hrs) (34636MJ/m3 )
Q= = 17.318 KW
(1000 lit) (3600 sec)
7. A pony brake test of an engine shows that the crankshaft rotates at 1530 rpm. The brake arm
length is 0.75m and the net load on the scales is 20kgf. What if the power developed?
Given: N = 1530 rpm, a = 0.75 m, F = 20kgf
, Solution:
2π(20kgf)(1530rpm)(0.75m) m 9.8N
P = 2πFNa = = (2403.3kgf. ) ( )
60sec s kgf
m J
= 23552.52 N − or 23552.52 or 23.55 kW
s s
= 23.55 kW x 1.34hp
= 31. 56hp
8. Determine that brake thermal efficiency of an engine if its mechanical efficiency if 87% and the
indicated thermal efficiency is 45%
Given: ME = 87%, ITE = 45%
Solution:
BTE = 0.87 x 0.45 x 100 = 39%
9. What is the rim speed of a 9 in diameter flywheel turning at 1800 rpm?
Given: D = 9 in, N – 1800rpm
Solution:
9in
V = πDN = π ( ) (1800rpm) = 4241.1ft/min
12in
10. What is the speed ratio of the transmission unit to give the tractor a speed of 3.5kph? The engine
speed is 2200 rpm and a rear wheel diameter of 55 cm.
Given: S = 3.5kph, N = 2200 rpm, D = 55cm
Solution:
60sec
V = πDN = π(0.55m)(2200rpm) ( ) = 228.08kph
1000
228.08kph
SR = = 65.2: 1
3.5kph
11. What is the efficiency of the transmission if the input speed is 2000 rpm, input torque of 220lb.ft
and an output of torque at the final drive is 19lb-ft at 17,000rpm?
Solution:
(17,000rpm)(19lb − ft)
Efficiency = = 73.4%
(2000rpm)(220lb − ft)
12. How much power is actually received by a pump run by a 7.5hp engine running at 2800 rpm? If a
3% slip is allowed between bolt and pulley.
Solution:
P = 7.5hp – (7.5hp x 0.03) = 7.3hp
13. Determine the brake thermal efficiency of a 5hp gasoline engine consuming 2 liters of fuel in an
hour?
Solution:
5 hp 5hp
BTE = = = 19%
2lit 34330MJ 1m 1hr 26hp
( )( )( )( )
hr m3 31000lit 3600sec
14. A gasoline engine has a thermal efficiency of 23%. Test shows it uses 1.2 liter of premium gasoline
fuel per hour. What is the approximate power it generates?
Solution:
liter 34330MJ
(1.2 .) ( ) J
P = hr m3 = 11443.30 x 0.23 = 2.632 kW
(1000lit) (3600sec) s
,15. If clearance volume of 3.5 x 4 in gasoline engine is 7 cubic inches, what is the compression ratio?
Solution:
TV πD2 L π(3.5)2 (4in)
CR = ; TV = PD + CV = + 7in3 = + 7in3 = 45.48in3
CV 4 4
TV 45.48in3
CR = = = 6.5: 1
CV 7in3
16. A diesel engine produces 100kW of brake power while it is running at 2000rpm rated speed and
consuming 37kg/hr. of fuel. Calculate the specific fuel consumption.
Solution:
37kg
( .)
SFC = hr = 0.37kg/kW − hr
(100kW)
17. An engine is tested on a dynamometer and produced 450 N-m of torque at a speed of 2400 rpm.
Calculate the power output.
Solution:
2π(2400rpm) (450N − m)
P = 2πNT = = 113kW
(1000) (60sec)
18. The firing interval and firing order of a 4 stroke, 3 cylinder in-line engine?
Solution:
(360) (2)
FI = = 240o
3
3 1
19. What is the engine displacement of an 3 x4 in 4 cylinder engine?
4 4
Solution:
πD2 L π(3.75in)2 (4.25in)(4)
PD = = = 187.8 in3
4 4
20. What should be the number of teeth to be meshed with T3 to combine the linear speed of a 2
wheel tractor running at 2.175mph given the following data?
Ground wheel
1st reduction 2nd reduction 3rd reduction
diameter
N1 = 2000rpm T3 = 13t T5 = 30t D = 500mm
D1 = 300mm T4 =? T6 = 90t
D2 = 600mm
Solution:
Forward speed = πDN = 2.175mph, N or N6 = 37.15rpm
N5T5 = N6T6, N5 = 111.44rpm, N5 = N4
N1D1 = N2D2, N2 = 1000rpm
T3N3 = T4N4,
T4 = 108t
21. Determine the time in hours to plow a 3 ha field using 200mm animal drawn plow with an average
depth of cut of 100mm traveling at a speed of 1.554mph and efficiency of 85%. What is the total
distance traveled in kilometer by the farmer upon completion of the plowing operation?
Given:
A = 3 ha; d = 100mm; Efficiency = 85%
W = 200mm; S = 1.554mph
, Solution:
SWEff (1.554mphx1.609km)(0.2m)(0.85) ha
EFC = = = 0.0425 .
10 10 hr
3ha
T = = 70.5 hrs
0.0425ha
.
hr
D = 1.554mph x 1.609x70.5 = 176.3km
22. The application rate of a certain chemical is recommended at 5 kg/ha. The calibration test of a 15
liter knapsack sprayer is as follows: Nozzle discharge = 1.5 lit/min, Swath = 2700mm and walking
speed = 18m/min. Determine the total volume of water applied per hectare?
Given:
𝑄𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑒𝑑= 5kg/ha = 5lit/ha
Capacity = 15 liters
𝑄𝑠𝑝𝑒𝑒𝑑 = 1.5 lit/min
W = 2.7m
S = 18m/min
Solution:
(1min)(10,000m2 )(1.5lit)
Vt = = 308.6 lit/ha
18m x2.7m
23. Determine the efficiency of a 64V starting system if the rate for the battery when the engine crank
is 190 ampere and the maximum power required for the cranking of the engine is 5hp.
Given:
V = 64 I = 190amp P = 5hp
Solution:
P = EI = (64V)(190amp) = 12,160W = 16.29hp
5hp
Eff = = 31%
16.29hp
24. Compute the velocity of a windmill having 9ft diameter wheel and an efficiency of 25%. The actual
power output is said to be 0.7235hp.
Solution:
ρAV 3 0.7235hp m m
P= ;P = = 540N − = 55.1kg −
2 1.34hp s s
2
9ft
1.2kg π (3.28ft)
m ( 3 )( )V 3
m 4
(55.1kg − ) =
s 2
110.2 2.50 9.98m
V =( )= =
(1.2)(5.91) 0.25 s
25. A drawer dynamometer show that the average pull required for a certain machine is 2460lbs. if
the tractor travels 1,670ft in 55 min, what is the rate of travel in mph?
Solution:
(1,670ft)(60min)(1km)(1mile)(1m)
V= = 0.345mph
(55min)(3.28ft)(1000m)(1.609km)(1hr)
26. What would be the operating efficiency of an engine if its size to operate a 120V direct current
electric generator is 18,91hp? Assume that it has maximum output of 65 amperes.
Solution:
1. A dynamometer shows that the average pull required for a certain machine is 20KN. If the tractor
travels at 5kph, what is the power developed?
Given: F = 20KN, S = 5kph
Required: power developed
Solution:
m
(20,000 N x 5000 s )
P= = 27.78 kW
3600sec
2. A dynamometer test shows that an engine delivers an average output of 50hp at a speed of
1500rpm. What torque is exerted?
Given: P = 50hp, N = 1500rpm
Required: torque
Solution:
P (50hp) (76.2kg.m/s) (9.8N)
P = 2πTN; T = 2πN = = 237.7 N-m
2π(1500/60min)
3. What is the piston displacement in cubic inches of a 4.5 in by 6 in cylinder engine?
Given: D = 4.5 in, H = 6 in
Solution:
πD2 L π(4.5in)2 (6in)
PD = = = 95.42 in3
4 4
4. An engine with 60mm x 60mm engine runs 1500rpm. What is the maximum piston speed inside
the cylinder?
Given: Engine dimension: 60mm x 60mm
Solution:
π(0.06m) (1500)
V = πDN = = 4.71 m/s
60 sec
5. A tractor pulls a 2500kg of loads at a speed of 5kph on a flat ground. If the coefficient of rolling
resistance is 0.25, what is the drawbar power that the tractor generates?
Given: F = 2500kg, RS = 0.25, V = 5kph
Solution:
m
(2500kg) (5000m) 3472.20kg. s
DHP = FV = = m = 45.57hp x 0.25 = 11.40hp
3600 sec 76.2kg. s
6. A gasoline engine was tested for continuous 5hrs of operation. It consumed a total of 9 liters of
fuels and developed a constant power of 3 kW. If the fuel contains 34,636MJ/m3, what is the
approximate thermal efficiency?
Solution:
W 3kW
ηth = = = 17.32%
Q 17.318kW
(9 liters/5hrs) (34636MJ/m3 )
Q= = 17.318 KW
(1000 lit) (3600 sec)
7. A pony brake test of an engine shows that the crankshaft rotates at 1530 rpm. The brake arm
length is 0.75m and the net load on the scales is 20kgf. What if the power developed?
Given: N = 1530 rpm, a = 0.75 m, F = 20kgf
, Solution:
2π(20kgf)(1530rpm)(0.75m) m 9.8N
P = 2πFNa = = (2403.3kgf. ) ( )
60sec s kgf
m J
= 23552.52 N − or 23552.52 or 23.55 kW
s s
= 23.55 kW x 1.34hp
= 31. 56hp
8. Determine that brake thermal efficiency of an engine if its mechanical efficiency if 87% and the
indicated thermal efficiency is 45%
Given: ME = 87%, ITE = 45%
Solution:
BTE = 0.87 x 0.45 x 100 = 39%
9. What is the rim speed of a 9 in diameter flywheel turning at 1800 rpm?
Given: D = 9 in, N – 1800rpm
Solution:
9in
V = πDN = π ( ) (1800rpm) = 4241.1ft/min
12in
10. What is the speed ratio of the transmission unit to give the tractor a speed of 3.5kph? The engine
speed is 2200 rpm and a rear wheel diameter of 55 cm.
Given: S = 3.5kph, N = 2200 rpm, D = 55cm
Solution:
60sec
V = πDN = π(0.55m)(2200rpm) ( ) = 228.08kph
1000
228.08kph
SR = = 65.2: 1
3.5kph
11. What is the efficiency of the transmission if the input speed is 2000 rpm, input torque of 220lb.ft
and an output of torque at the final drive is 19lb-ft at 17,000rpm?
Solution:
(17,000rpm)(19lb − ft)
Efficiency = = 73.4%
(2000rpm)(220lb − ft)
12. How much power is actually received by a pump run by a 7.5hp engine running at 2800 rpm? If a
3% slip is allowed between bolt and pulley.
Solution:
P = 7.5hp – (7.5hp x 0.03) = 7.3hp
13. Determine the brake thermal efficiency of a 5hp gasoline engine consuming 2 liters of fuel in an
hour?
Solution:
5 hp 5hp
BTE = = = 19%
2lit 34330MJ 1m 1hr 26hp
( )( )( )( )
hr m3 31000lit 3600sec
14. A gasoline engine has a thermal efficiency of 23%. Test shows it uses 1.2 liter of premium gasoline
fuel per hour. What is the approximate power it generates?
Solution:
liter 34330MJ
(1.2 .) ( ) J
P = hr m3 = 11443.30 x 0.23 = 2.632 kW
(1000lit) (3600sec) s
,15. If clearance volume of 3.5 x 4 in gasoline engine is 7 cubic inches, what is the compression ratio?
Solution:
TV πD2 L π(3.5)2 (4in)
CR = ; TV = PD + CV = + 7in3 = + 7in3 = 45.48in3
CV 4 4
TV 45.48in3
CR = = = 6.5: 1
CV 7in3
16. A diesel engine produces 100kW of brake power while it is running at 2000rpm rated speed and
consuming 37kg/hr. of fuel. Calculate the specific fuel consumption.
Solution:
37kg
( .)
SFC = hr = 0.37kg/kW − hr
(100kW)
17. An engine is tested on a dynamometer and produced 450 N-m of torque at a speed of 2400 rpm.
Calculate the power output.
Solution:
2π(2400rpm) (450N − m)
P = 2πNT = = 113kW
(1000) (60sec)
18. The firing interval and firing order of a 4 stroke, 3 cylinder in-line engine?
Solution:
(360) (2)
FI = = 240o
3
3 1
19. What is the engine displacement of an 3 x4 in 4 cylinder engine?
4 4
Solution:
πD2 L π(3.75in)2 (4.25in)(4)
PD = = = 187.8 in3
4 4
20. What should be the number of teeth to be meshed with T3 to combine the linear speed of a 2
wheel tractor running at 2.175mph given the following data?
Ground wheel
1st reduction 2nd reduction 3rd reduction
diameter
N1 = 2000rpm T3 = 13t T5 = 30t D = 500mm
D1 = 300mm T4 =? T6 = 90t
D2 = 600mm
Solution:
Forward speed = πDN = 2.175mph, N or N6 = 37.15rpm
N5T5 = N6T6, N5 = 111.44rpm, N5 = N4
N1D1 = N2D2, N2 = 1000rpm
T3N3 = T4N4,
T4 = 108t
21. Determine the time in hours to plow a 3 ha field using 200mm animal drawn plow with an average
depth of cut of 100mm traveling at a speed of 1.554mph and efficiency of 85%. What is the total
distance traveled in kilometer by the farmer upon completion of the plowing operation?
Given:
A = 3 ha; d = 100mm; Efficiency = 85%
W = 200mm; S = 1.554mph
, Solution:
SWEff (1.554mphx1.609km)(0.2m)(0.85) ha
EFC = = = 0.0425 .
10 10 hr
3ha
T = = 70.5 hrs
0.0425ha
.
hr
D = 1.554mph x 1.609x70.5 = 176.3km
22. The application rate of a certain chemical is recommended at 5 kg/ha. The calibration test of a 15
liter knapsack sprayer is as follows: Nozzle discharge = 1.5 lit/min, Swath = 2700mm and walking
speed = 18m/min. Determine the total volume of water applied per hectare?
Given:
𝑄𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑒𝑑= 5kg/ha = 5lit/ha
Capacity = 15 liters
𝑄𝑠𝑝𝑒𝑒𝑑 = 1.5 lit/min
W = 2.7m
S = 18m/min
Solution:
(1min)(10,000m2 )(1.5lit)
Vt = = 308.6 lit/ha
18m x2.7m
23. Determine the efficiency of a 64V starting system if the rate for the battery when the engine crank
is 190 ampere and the maximum power required for the cranking of the engine is 5hp.
Given:
V = 64 I = 190amp P = 5hp
Solution:
P = EI = (64V)(190amp) = 12,160W = 16.29hp
5hp
Eff = = 31%
16.29hp
24. Compute the velocity of a windmill having 9ft diameter wheel and an efficiency of 25%. The actual
power output is said to be 0.7235hp.
Solution:
ρAV 3 0.7235hp m m
P= ;P = = 540N − = 55.1kg −
2 1.34hp s s
2
9ft
1.2kg π (3.28ft)
m ( 3 )( )V 3
m 4
(55.1kg − ) =
s 2
110.2 2.50 9.98m
V =( )= =
(1.2)(5.91) 0.25 s
25. A drawer dynamometer show that the average pull required for a certain machine is 2460lbs. if
the tractor travels 1,670ft in 55 min, what is the rate of travel in mph?
Solution:
(1,670ft)(60min)(1km)(1mile)(1m)
V= = 0.345mph
(55min)(3.28ft)(1000m)(1.609km)(1hr)
26. What would be the operating efficiency of an engine if its size to operate a 120V direct current
electric generator is 18,91hp? Assume that it has maximum output of 65 amperes.
Solution:
