Question

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

Answer 1

$P=\frac{Kineticenergy}{Time}$
Mass of wind hitting per sec $=Density\times vol.=Density\times Vel.\times area$
$=\int .V.A$
$\therefore$ Associated energy per sec $=\frac{1}{2}(\int VA).V^2=\frac{\int A{V}^3}{2}$
This is nothing but power received.