An engine flywheel has a mass of 6.5 tonnes and the radius of gyration is 2 m. If the maximum and minimum speeds are 120 r. p. m. and 118 r. p. m. respectively, find maximum fluctuation of energy. [Ans. 67. 875 kN-m]
An engine flywheel has a mass of 6.5 tonnes and the radius of gyration is 2 m. If the maximum and minimum speeds are 120 r. p. m. and 118 r. p. m. respectively, find maximum fluctuation of energy. [Ans. 67. 875 kN-m]
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![An engine flywheel has a mass of 6.5 tonnes and the radius of gyration is 2 m. If the maximum and
minimum speeds are 120 r. p. m. and 118 r. p. m. respectively, find maximum fluctuation of energy.
[Ans. 67. 875 kN-m]
1.
A vertical double acting steam engine develops 75 kW at 250 r.p.m. The maximum fluctuation of
energy is 30 per cent of the work done per stroke. The maximum and minimum speeds are not to vary
more than 1 per cent on either side of the mean speed. Find the mass of the flywheel required, if the
radius of gyration is 0.6 m.
2.
[Ans. 547 kg]
In a turning moment diagram, the areas above and below the mean torque line taken in order are 4400,
1150, 1300 and 4550 mm² respectively. The scales of the turning moment diagram are:
Turning moment, 1 mm = 100 N-m ; Crank angle, 1 mm = 1°
3.
Find the mass of the flywheel required to keep the speed between 297 and 303 r.p.m., if the radius of
gyration is 0.525 m.
[Ans. 417 kg]
The turning moment diagram for a multicylinder engine has been drawn to a scale of 1 mm =
4500 N-m vertically and 1 mm=2.4° horizontally. The intercepted areas between output torque curve
and mean resistance line taken in order from one end are 342, 23, 245, 303, 115, 232, 227, 164 mm²,
when the engine is running at 150 r.p.m. If the mass of the flywheel is 1000 kg and the total fluctuation
of speed does not exceed 3% of the mean speed, find the minimum value of the radius of gyration.
[Ans. 1.034 m]
4.
An engine has three single-acting cylinders whose cranks are spaced at 120° to each other. The turn-
ing moment diagram for each cylinder consists of a triangle having the following values:
5.
Angle
0°
60°
180°
180° – 360°
Torque (N-m)
200
Find the mean torque and the moment of inertia of the flywheel to keep the speed within 180±3 r.p.m.
[Ans. 150 N-m; 1.22 kg-m²]
The turning moment diagram for a four stroke gas engine may be assumed for simplicity to be repre-
sented by four triangles, the areas of which from the line of zero pressure are as follows:
Expansion stroke = 3550 mm²; exhaust stroke = 500 mm²; suction stroke = 350 mm²; and compres-
sion stroke = 1400 mm². Each mm² represents 3 N-m.
6.
Assuming the resisting moment to be uniform, find the mass of the rim of a flywheel required to keep
the mean speed 200 r.p.m. within + 2%. The mean radius of the rim may be taken as 0.75 m. Also
determine the crank positions for the maximum and minimum speeds.
[Ans. 983 kg; 4° and 176° from I. D. C]
A single cylinder, single acting, four stroke cycle gas engine develops 20 kW at 250 r.p.m. The work
done by the gases during the expansion stroke is 3 times the work done on the gases during the
compression stroke. The work done on the suction and exhaust strokes may be neglected. If the
flywheel has a mass of 1.5 tonnes and has a radius
energy and the coefficient of fluctuation of speed.
7.
gyration of 0.6m, find the cyclic fluctuation of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc87d0f4-333e-44bc-a95c-b1a8bb0aae15%2F25762bbb-40c4-4e4a-8188-9c0709807362%2Fofvgkgr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:An engine flywheel has a mass of 6.5 tonnes and the radius of gyration is 2 m. If the maximum and
minimum speeds are 120 r. p. m. and 118 r. p. m. respectively, find maximum fluctuation of energy.
[Ans. 67. 875 kN-m]
1.
A vertical double acting steam engine develops 75 kW at 250 r.p.m. The maximum fluctuation of
energy is 30 per cent of the work done per stroke. The maximum and minimum speeds are not to vary
more than 1 per cent on either side of the mean speed. Find the mass of the flywheel required, if the
radius of gyration is 0.6 m.
2.
[Ans. 547 kg]
In a turning moment diagram, the areas above and below the mean torque line taken in order are 4400,
1150, 1300 and 4550 mm² respectively. The scales of the turning moment diagram are:
Turning moment, 1 mm = 100 N-m ; Crank angle, 1 mm = 1°
3.
Find the mass of the flywheel required to keep the speed between 297 and 303 r.p.m., if the radius of
gyration is 0.525 m.
[Ans. 417 kg]
The turning moment diagram for a multicylinder engine has been drawn to a scale of 1 mm =
4500 N-m vertically and 1 mm=2.4° horizontally. The intercepted areas between output torque curve
and mean resistance line taken in order from one end are 342, 23, 245, 303, 115, 232, 227, 164 mm²,
when the engine is running at 150 r.p.m. If the mass of the flywheel is 1000 kg and the total fluctuation
of speed does not exceed 3% of the mean speed, find the minimum value of the radius of gyration.
[Ans. 1.034 m]
4.
An engine has three single-acting cylinders whose cranks are spaced at 120° to each other. The turn-
ing moment diagram for each cylinder consists of a triangle having the following values:
5.
Angle
0°
60°
180°
180° – 360°
Torque (N-m)
200
Find the mean torque and the moment of inertia of the flywheel to keep the speed within 180±3 r.p.m.
[Ans. 150 N-m; 1.22 kg-m²]
The turning moment diagram for a four stroke gas engine may be assumed for simplicity to be repre-
sented by four triangles, the areas of which from the line of zero pressure are as follows:
Expansion stroke = 3550 mm²; exhaust stroke = 500 mm²; suction stroke = 350 mm²; and compres-
sion stroke = 1400 mm². Each mm² represents 3 N-m.
6.
Assuming the resisting moment to be uniform, find the mass of the rim of a flywheel required to keep
the mean speed 200 r.p.m. within + 2%. The mean radius of the rim may be taken as 0.75 m. Also
determine the crank positions for the maximum and minimum speeds.
[Ans. 983 kg; 4° and 176° from I. D. C]
A single cylinder, single acting, four stroke cycle gas engine develops 20 kW at 250 r.p.m. The work
done by the gases during the expansion stroke is 3 times the work done on the gases during the
compression stroke. The work done on the suction and exhaust strokes may be neglected. If the
flywheel has a mass of 1.5 tonnes and has a radius
energy and the coefficient of fluctuation of speed.
7.
gyration of 0.6m, find the cyclic fluctuation of
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