Question

The blades of a windmill sweep out a circle of area A. If the wind flows at a velocity v perpendicular to the circle and its density is $\rho$, what is the mechanical power received by the windmill?

Answer 1

Mass of air hitting the windmill per second, m $=Density\times Volumepersecond=Density\times Velocity\times Area$
$=\rho vA$
$\therefore$ Associated kinetic energy per second $=\frac{1}{2}\left(\rho vA\right)\times v^2=\frac{\rho A{v}^3}{2}$
This is nothing but the power received.