Calculate the electric power produced by a wind mill, when the wind speed is 10 m/s and the radius of the rotor circle (wing length) is 15 m. The density of air is 1.25 kg/m3. The e�efficiency of the wind mill is 45%.
To calculate the electric power produced by a windmill, we can use the following formula:
Power = 0.5 * (density of air) * (π * (radius of rotor circle)^2) * (wind speed)^3 * (efficiency)
Let's plug in the given values into the formula:
Density of air = 1.25 kg/m^3
Radius of rotor circle = 15 m
Wind speed = 10 m/s
Efficiency = 45% or 0.45 (as a decimal)
Now we can calculate the power:
Power = 0.5 * 1.25 * (π * 15^2) * 10^3 * 0.45
First, let's calculate the value of (π * 15^2):
(π * 15^2) ≈ 706.86
Now, let's calculate the power:
Power ≈ 0.5 * 1.25 * 706.86 * 10^3 * 0.45
Power ≈ 0.5 * 1.25 * 706.86 * 10^3 * 0.45 ≈ 177,772,500 Watts
Therefore, when the wind speed is 10 m/s and the radius of the rotor circle is 15 m, the electric power produced by the windmill is approximately 177,772,500 Watts.