A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.00 meters. What is the maximum power output if 30.0% of the wind's energy can be extracted? ρ_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 power output of a wind turbine is given by the formula P = 0.5 ρ A v^3, where ρ is the density of air, A is the area swept out by the blades, and v is the velocity of the wind. Here, we are given ρ = 1.25 kg/m^3, A = πr^2 = 25π m^2, v = 10 m/s, and a efficiency of 30% or 0.3. Therefore, the power output is:

P = 0.5 ρ A v^3 × 0.3 = 0.5 × 1.25 × 25π × 10^3 × 10^3 × 10^3 × 0.3 = 14.7 kW.

The best choice is B, 14.7 kW, because it correctly uses the formula for power output of a wind turbine and takes into account the given values of ρ, A, v, and efficiency.

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