A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.00 metres. What is the maximum power output if 30.0% of the wind's energy can be extracted? $\rho$air = 1.25 kg/m3.
A)7.20 kW
B)14.7 kW
C)21.3 kW
D)29.4 kW
E)39.6 kW

Question

Quizplus · Accepted Answer

The maximum power output of a wind generator is given by:
Pmax = (1/2) * rho * A * v^3 * Cp
where rho is the air density (given), A is the area swept by the blades (pi*r^2), v is the wind velocity (given), and Cp is the coefficient of performance or extraction (given as 30% or 0.3). 
Plugging in the values: 
Pmax = (1/2) * 1.25 * pi * (5.00)^2 * (10)^3 * 0.3
Pmax = 14.7 kW
Therefore, the best choice is B.

A Wind of Velocity 10 M/s Is Blowing Through a Wind