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The velocity of flow through a Kaplan turbine is 10 m/s. The outer diameter of the runner is 4 m and the hub diameter is 2 m. Find the volume flow rate of the turbine in m3/s?
- a)95
- b)75
- c)85
- d)105
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The velocity of flow through a Kaplan turbine is 10 m/s. The outer dia...
To find the volume flow rate of the turbine, we need to calculate the cross-sectional area of flow and multiply it by the velocity of flow.
Given data:
Velocity of flow (v) = 10 m/s
Outer diameter of the runner (D) = 4 m
Hub diameter (d) = 2 m
To calculate the cross-sectional area of flow, we need to subtract the area of the hub from the area of the runner.
1. Calculate the area of the runner (A_r):
The area of a circle is given by the formula A = πr^2, where r is the radius.
The radius of the runner (R_r) is half the diameter, so R_r = D/2 = 4/2 = 2 m.
Therefore, the area of the runner is A_r = π(2)^2 = 4π m^2.
2. Calculate the area of the hub (A_h):
The radius of the hub (R_h) is half the hub diameter, so R_h = d/2 = 2/2 = 1 m.
Therefore, the area of the hub is A_h = π(1)^2 = π m^2.
3. Calculate the cross-sectional area of flow (A_flow):
A_flow = A_r - A_h
A_flow = 4π - π
A_flow = 3π m^2.
4. Calculate the volume flow rate (Q):
Q = A_flow * v
Q = 3π * 10
Q ≈ 30π m^3/s
Approximating the value of π as 3.14:
Q ≈ 30 * 3.14
Q ≈ 94.2 m^3/s
Rounding off to the nearest whole number, the volume flow rate of the turbine is approximately 94 m^3/s.
Therefore, the correct answer is option A: 95.
Given data:
Velocity of flow (v) = 10 m/s
Outer diameter of the runner (D) = 4 m
Hub diameter (d) = 2 m
To calculate the cross-sectional area of flow, we need to subtract the area of the hub from the area of the runner.
1. Calculate the area of the runner (A_r):
The area of a circle is given by the formula A = πr^2, where r is the radius.
The radius of the runner (R_r) is half the diameter, so R_r = D/2 = 4/2 = 2 m.
Therefore, the area of the runner is A_r = π(2)^2 = 4π m^2.
2. Calculate the area of the hub (A_h):
The radius of the hub (R_h) is half the hub diameter, so R_h = d/2 = 2/2 = 1 m.
Therefore, the area of the hub is A_h = π(1)^2 = π m^2.
3. Calculate the cross-sectional area of flow (A_flow):
A_flow = A_r - A_h
A_flow = 4π - π
A_flow = 3π m^2.
4. Calculate the volume flow rate (Q):
Q = A_flow * v
Q = 3π * 10
Q ≈ 30π m^3/s
Approximating the value of π as 3.14:
Q ≈ 30 * 3.14
Q ≈ 94.2 m^3/s
Rounding off to the nearest whole number, the volume flow rate of the turbine is approximately 94 m^3/s.
Therefore, the correct answer is option A: 95.
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Community Answer
The velocity of flow through a Kaplan turbine is 10 m/s. The outer dia...
The volume flow rate is given by
Substituting the given values in the above equation, we get Q = 95 m3/s.
Substituting the given values in the above equation, we get Q = 95 m3/s.
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The velocity of flow through a Kaplan turbine is 10 m/s. The outer diameter of the runner is 4 m and the hub diameter is 2 m. Find the volume flow rate of the turbine in m3/s?a)95b)75c)85d)105Correct answer is option 'A'. Can you explain this answer?
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