You have assembled a modern three-bladed upwind WT with a rotor radius of \(5 \mathrm{~m}\) at sea level where the density is \(1.225 \mathrm{~kg} / \mathrm{m}^{3}\).

a. If the wind is blowing at an average speed of \(10 \mathrm{~m} / \mathrm{s}\), what is the power of the wind traveling through the swept area of the rotor?

b. What is the average actual power produced by a turbine of this type at this wind speed? Find \(C_{p}\)

Find the maximum power coefficient, \(C_{p}\), based on the following equation for axial induction.
\[ C_{p}=4 a(1-a)^{2} \]