GATE Exam > GATE Questions > A water pumping system is being driven by a p...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
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.
|
Explore Courses for GATE exam
|
|
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup