# Windmill Power Problem

#### tandoorichicken

I had trouble with this, probably because there are no numbers in it:

"The power P delivered by a windmill whose blades sweep in a circle of diameter D by a wind speed v is proportional to the square of the diameter and the cube of the wind speed. Show that this dependence on diameter and wind speed is what you would expect in the case of 100% efficient energy transfer by showing that the energy transferred per unit time is equal to

P = &pi;/8 * &rho; * D^2 * v^3. (&rho; is the density of air, approx. 1.25 kg/m^3)

I have no clue how or where to start.

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#### HallsofIvy

Imagine a column of air passing through the circle "swept out" by the blades of the windmill at speed v. In unit time, that will be a cylinder with diameter D and length v. Calculate the volume of that cylinder and multiply by the density to get its mass. Now, what is the kinetic energy of that mass of air?

"Windmill Power Problem"

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