The maximum power that can be extracted by a wind turbine from an air stream is approximately

Question:

The maximum power that can be extracted by a wind turbine from an air stream is approximately
P = kd2v3
Where d is the blade diameter, u is the wind speed, and the constant k = 0.5 W· s3/m5.
(a) Explain the dependence of P on d and on u by considering a cylinder of air that passes over the turbine blades in time t (Fig. 20.31). 'This cylinder has diameter d, length L = ut, and density p.
(b) The Mod-5B wind turbine at Kahaku on the Hawaiian island of Oahu has a blade diameter of 97 m (slightly longer than a football field) and sits atop a 58-m tower. It can produce 3.2 MW of electric power. Assuming 25% efficiency, what wind speed is required to produce this amount of power? Give your answer in m/s and in km/h.
(c) Commercial wind turbines are commonly located in or downwind of mountain passes. Why?

L= ut