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? $\rho$_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

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Quizplus · Accepted Answer

The power in the wind is given by the formula P = 0.5 * ρ * A * v^3, where ρ is the air density, A is the area swept by the blades, and v is the wind velocity. The area A = π * r^2 = π * (5)^2 = 78.54 m^2. The power in the wind is P = 0.5 * 1.25 * 78.54 * (10)^3 = 49.0875 kW. Since only 30% of the wind's energy can be extracted, the maximum power output is 0.3 * 49.0875 = 14.7 kW.

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