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A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s-1 respectively. Mean wind velocity is 18 km h-1 and the density of air is 1.2 kg m-3. The required diameter of the propeller in m is _________
Correct answer is between '7.5,7.8'. Can you explain this answer?
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A water pumping system is being driven by a propeller type wind turbin...
Given:
- Power coefficient (Cp) = 0.4
- Total pumping head (H) = 20 m
- Rate of discharge (Q) = 7.0 L/s
- Mean wind velocity (V) = 18 km/h = 5 m/s
- Density of air (ρ) = 1.2 kg/m^3
To find:
The required diameter of the propeller.
Formula:
The power output of the wind turbine can be calculated using the formula:
P = 0.5 * Cp * ρ * A * V^3
The rate of discharge can be calculated using the formula:
Q = P / (ρ * g * H)
The area of the propeller can be calculated using the formula:
A = Q / (V * 1000)
Solution:
Step 1: Calculate the power output (P) of the wind turbine.
P = 0.5 * 0.4 * 1.2 * A * (5^3)
P = 10.8 * A
Step 2: Calculate the rate of discharge (Q) using the power output.
Q = (10.8 * A) / (1.2 * 9.81 * 20)
Q = 0.0459 * A
Step 3: Calculate the area of the propeller (A) using the rate of discharge.
A = (Q * V * 1000) / 7
A = 71.43 * Q
Step 4: Substitute the value of A from Step 3 into Step 2.
Q = 0.0459 * (71.43 * Q)
Q = 3.28 * Q
Step 5: Solve for Q.
Q = 0.0459 * 71.43 * Q
1 = 0.0459 * 71.43
Q = 1 / (0.0459 * 71.43)
Q = 3.28 m^2/s
Step 6: Calculate the diameter of the propeller (D) using the area.
A = π * (D^2) / 4
3.28 = π * (D^2) / 4
D^2 = (4 * 3.28) / π
D^2 = 4.15
D = √4.15
D ≈ 2.04 m
Therefore, the required diameter of the propeller is approximately 2.04 meters.
- Power coefficient (Cp) = 0.4
- Total pumping head (H) = 20 m
- Rate of discharge (Q) = 7.0 L/s
- Mean wind velocity (V) = 18 km/h = 5 m/s
- Density of air (ρ) = 1.2 kg/m^3
To find:
The required diameter of the propeller.
Formula:
The power output of the wind turbine can be calculated using the formula:
P = 0.5 * Cp * ρ * A * V^3
The rate of discharge can be calculated using the formula:
Q = P / (ρ * g * H)
The area of the propeller can be calculated using the formula:
A = Q / (V * 1000)
Solution:
Step 1: Calculate the power output (P) of the wind turbine.
P = 0.5 * 0.4 * 1.2 * A * (5^3)
P = 10.8 * A
Step 2: Calculate the rate of discharge (Q) using the power output.
Q = (10.8 * A) / (1.2 * 9.81 * 20)
Q = 0.0459 * A
Step 3: Calculate the area of the propeller (A) using the rate of discharge.
A = (Q * V * 1000) / 7
A = 71.43 * Q
Step 4: Substitute the value of A from Step 3 into Step 2.
Q = 0.0459 * (71.43 * Q)
Q = 3.28 * Q
Step 5: Solve for Q.
Q = 0.0459 * 71.43 * Q
1 = 0.0459 * 71.43
Q = 1 / (0.0459 * 71.43)
Q = 3.28 m^2/s
Step 6: Calculate the diameter of the propeller (D) using the area.
A = π * (D^2) / 4
3.28 = π * (D^2) / 4
D^2 = (4 * 3.28) / π
D^2 = 4.15
D = √4.15
D ≈ 2.04 m
Therefore, the required diameter of the propeller is approximately 2.04 meters.
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A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s-1respectively. Mean wind velocity is 18 km h-1 and the density of air is 1.2 kg m-3. The required diameter of the propeller in m is _________Correct answer is between '7.5,7.8'. Can you explain this answer?
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A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s-1respectively. Mean wind velocity is 18 km h-1 and the density of air is 1.2 kg m-3. The required diameter of the propeller in m is _________Correct answer is between '7.5,7.8'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s-1respectively. Mean wind velocity is 18 km h-1 and the density of air is 1.2 kg m-3. The required diameter of the propeller in m is _________Correct answer is between '7.5,7.8'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s-1respectively. Mean wind velocity is 18 km h-1 and the density of air is 1.2 kg m-3. The required diameter of the propeller in m is _________Correct answer is between '7.5,7.8'. Can you explain this answer?.
A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s-1respectively. Mean wind velocity is 18 km h-1 and the density of air is 1.2 kg m-3. The required diameter of the propeller in m is _________Correct answer is between '7.5,7.8'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s-1respectively. Mean wind velocity is 18 km h-1 and the density of air is 1.2 kg m-3. The required diameter of the propeller in m is _________Correct answer is between '7.5,7.8'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s-1respectively. Mean wind velocity is 18 km h-1 and the density of air is 1.2 kg m-3. The required diameter of the propeller in m is _________Correct answer is between '7.5,7.8'. Can you explain this answer?.
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