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For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its diameter is not to exceed 1m?
- a)40 kg
- b)51 kg
- c)62 kg
- d)73 k
Correct answer is option 'B'. Can you explain this answer?
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Problem Statement:
A solid disc flywheel is required for an engine to maintain a fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is 2 kJ. The diameter of the flywheel is not to exceed 1m. We need to determine the least possible mass of the flywheel.
Solution:
Given data:
Average speed of the engine = 1200 rpm
Fluctuation of speed = 2%
Fluctuation of kinetic energy per cycle = 2 kJ
Maximum diameter of the flywheel = 1m
We know that the kinetic energy of a solid disc flywheel is given by the formula:
KE = (1/2) I ω^2
Where,
KE is the kinetic energy of the flywheel
I is the moment of inertia of the flywheel
ω is the angular velocity of the flywheel
The fluctuation of kinetic energy per cycle is given by the formula:
ΔKE = KE_max - KE_min
Where,
ΔKE is the fluctuation of kinetic energy per cycle
KE_max is the maximum kinetic energy of the flywheel
KE_min is the minimum kinetic energy of the flywheel
We can calculate the minimum moment of inertia required to maintain the fluctuation of speed within 2% about the average speed as follows:
Δω = (2/100)ω_avg
Where,
Δω is the maximum fluctuation of angular velocity
ω_avg is the average angular velocity
Δω = (2/100) × (2π × 1200/60) = 2.513 rad/s
We know that the moment of inertia of a solid disc flywheel is given by the formula:
I = (1/2) m r^2
Where,
I is the moment of inertia of the flywheel
m is the mass of the flywheel
r is the radius of the flywheel
Since the diameter of the flywheel is not to exceed 1m, the radius of the flywheel is 0.5m.
Now, we can calculate the minimum mass of the flywheel as follows:
ΔKE = (1/2) I (Δω)^2
2 kJ = (1/2) × I × (2.513)^2
I = 0.316 kg m^2
m = (2 × I)/(r^2)
m = (2 × 0.316)/(0.5)^2 = 50.56 kg
Therefore, the least possible mass of the flywheel is 51 kg (option B).
A solid disc flywheel is required for an engine to maintain a fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is 2 kJ. The diameter of the flywheel is not to exceed 1m. We need to determine the least possible mass of the flywheel.
Solution:
Given data:
Average speed of the engine = 1200 rpm
Fluctuation of speed = 2%
Fluctuation of kinetic energy per cycle = 2 kJ
Maximum diameter of the flywheel = 1m
We know that the kinetic energy of a solid disc flywheel is given by the formula:
KE = (1/2) I ω^2
Where,
KE is the kinetic energy of the flywheel
I is the moment of inertia of the flywheel
ω is the angular velocity of the flywheel
The fluctuation of kinetic energy per cycle is given by the formula:
ΔKE = KE_max - KE_min
Where,
ΔKE is the fluctuation of kinetic energy per cycle
KE_max is the maximum kinetic energy of the flywheel
KE_min is the minimum kinetic energy of the flywheel
We can calculate the minimum moment of inertia required to maintain the fluctuation of speed within 2% about the average speed as follows:
Δω = (2/100)ω_avg
Where,
Δω is the maximum fluctuation of angular velocity
ω_avg is the average angular velocity
Δω = (2/100) × (2π × 1200/60) = 2.513 rad/s
We know that the moment of inertia of a solid disc flywheel is given by the formula:
I = (1/2) m r^2
Where,
I is the moment of inertia of the flywheel
m is the mass of the flywheel
r is the radius of the flywheel
Since the diameter of the flywheel is not to exceed 1m, the radius of the flywheel is 0.5m.
Now, we can calculate the minimum mass of the flywheel as follows:
ΔKE = (1/2) I (Δω)^2
2 kJ = (1/2) × I × (2.513)^2
I = 0.316 kg m^2
m = (2 × I)/(r^2)
m = (2 × 0.316)/(0.5)^2 = 50.56 kg
Therefore, the least possible mass of the flywheel is 51 kg (option B).
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For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its diameter is not to exceed 1m?a)40 kgb)51 kgc)62 kgd)73 kCorrect answer is option 'B'. Can you explain this answer?
Question Description
For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its diameter is not to exceed 1m?a)40 kgb)51 kgc)62 kgd)73 kCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its diameter is not to exceed 1m?a)40 kgb)51 kgc)62 kgd)73 kCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its diameter is not to exceed 1m?a)40 kgb)51 kgc)62 kgd)73 kCorrect answer is option 'B'. Can you explain this answer?.
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