A wind power generator converts wind energy to electrical energy. For wind speed v the electrical power will be proportional to
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Consider a circular plane of unit area perpendicular to the wind velocity. Wind crossing this plane in unit time would be trapped in the cylinder having this plane as its base and length V. (volume of this cylinder = Vx(unit area) = V)
=> Energy crossing the circular plane per unit time = Power of wind = ((1/2)xdxV2)xV
(since K.E. of wind per unit volume = ((1/2)xdxV2 and other forms of energy carried by wind are independent of V.)
=> Power of generator would be proportional to V3.
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