Question

Calculate the theoretical power generated by a wind rotor of 5 m diameter with wind velocity of 7.2 km.h\(^{-1}\). Assume air density as 1.4 kg.m\(^{-3}\).

• A. 100 W
• B. 110 W
• C. 200 W
• D. 220 W

Hint:

The theoretical power of wind is given by:
P = 0.5 \(\times\) \(\rho\) \(\times\) A \(\times\) V\(^3\).
Some questions might use P = \(\rho\) \(\times\) A \(\times\) V\(^3\) for simplicity.
Always check the units: \(\rho\) in kg/m\(^3\), A in m\(^2\), V in m/s.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We need to calculate the theoretical power generated by a wind rotor.
We have the diameter, wind velocity, and air density.

Step 2: Key Formula or Approach:
Theoretical power = \(\rho\) \(\times\) A \(\times\) V\(^3\).
Where \(\rho\) is air density, A is the swept area, V is the wind velocity.

Step 3: Detailed Explanation:
Diameter = 5 m.
Radius = 2.5 m.
Area A = \(\pi\) \(\times\) r\(^2\) = \(\pi\) \(\times\) 2.5\(^2\) = 19.635 m\(^2\).
Wind velocity = 7.2 km/h = 7.2 \(\times\) 1000 3600 = 2 m/s.
\(\rho\) = 1.4 kg/m\(^3\).
Power = 1.4 \(\times\) 19.635 \(\times\) 2\(^3\).
Power = 1.4 \(\times\) 19.635 \(\times\) 8.
Power = 1.4 \(\times\) 19.635 = 489.
489 \(\times\) 8 = 219.912 W.
This is approximately 220 W.

Step 4: Final Answer:
The theoretical power generated is 220 W.
Hence, the correct option is (D).