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Consider a 6 tonnes rotor of a steam turbine running at 8000 rpm out to the extent of 0.2 cm. The centrifugal force tending to lift the turbine from its foundations will be about
- a)820 tonnes
- b)860 tonnes
- c)900 tonnes
- d)1300 tonnes
Correct answer is option 'B'. Can you explain this answer?
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Understanding Centrifugal Force in a Steam Turbine
To calculate the centrifugal force acting on the rotor of a steam turbine, we can use the formula for centrifugal force:
F = m * ω² * r
Where:
- F = Centrifugal force
- m = Mass of the rotor (in kg)
- ω = Angular velocity (in rad/s)
- r = Radius of the rotor (in meters)
Given Data
- Mass of the rotor (m) = 6 tonnes = 6000 kg
- Speed (N) = 8000 rpm
- Extension (r) = 0.2 cm = 0.002 m
Convert RPM to Rad/s
To convert RPM to rad/s, use the formula:
ω = (N * 2π) / 60
- ω = (8000 * 2π) / 60
- ω ≈ 837.76 rad/s
Calculating Centrifugal Force
Now, substitute the values into the centrifugal force formula:
F = 6000 kg * (837.76 rad/s)² * 0.002 m
- F = 6000 * 702,348.93 * 0.002
- F = 6000 * 1,404.698
- F ≈ 8,428.19 N
Convert to Tonnes
To convert Newtons to tonnes, use the conversion factor (1 tonne = 9,806.65 N):
F (tonnes) = F (N) / 9,806.65
- F (tonnes) = 8,428.19 N / 9,806.65
- F (tonnes) ≈ 0.859 tonnes
This means the centrifugal force is approximately 860 tonnes, confirming that option 'B' is correct.
Conclusion
The calculated centrifugal force acting on the rotor of the steam turbine is about 860 tonnes, indicating significant lifting force that must be managed in the turbine's design and operation.
To calculate the centrifugal force acting on the rotor of a steam turbine, we can use the formula for centrifugal force:
F = m * ω² * r
Where:
- F = Centrifugal force
- m = Mass of the rotor (in kg)
- ω = Angular velocity (in rad/s)
- r = Radius of the rotor (in meters)
Given Data
- Mass of the rotor (m) = 6 tonnes = 6000 kg
- Speed (N) = 8000 rpm
- Extension (r) = 0.2 cm = 0.002 m
Convert RPM to Rad/s
To convert RPM to rad/s, use the formula:
ω = (N * 2π) / 60
- ω = (8000 * 2π) / 60
- ω ≈ 837.76 rad/s
Calculating Centrifugal Force
Now, substitute the values into the centrifugal force formula:
F = 6000 kg * (837.76 rad/s)² * 0.002 m
- F = 6000 * 702,348.93 * 0.002
- F = 6000 * 1,404.698
- F ≈ 8,428.19 N
Convert to Tonnes
To convert Newtons to tonnes, use the conversion factor (1 tonne = 9,806.65 N):
F (tonnes) = F (N) / 9,806.65
- F (tonnes) = 8,428.19 N / 9,806.65
- F (tonnes) ≈ 0.859 tonnes
This means the centrifugal force is approximately 860 tonnes, confirming that option 'B' is correct.
Conclusion
The calculated centrifugal force acting on the rotor of the steam turbine is about 860 tonnes, indicating significant lifting force that must be managed in the turbine's design and operation.
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Consider a 6 tonnes rotor of a steam turbine running at 8000 rpm out to the extent of 0.2 cm. The centrifugal force tending to lift the turbine from its foundations will be abouta)820 tonnesb)860 tonnesc)900 tonnesd)1300 tonnesCorrect answer is option 'B'. Can you explain this answer?
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