Wind Energy - Physics

Wind Power

The power P of a wind-stream, crossing an area A with velocity v is given by

 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P=\frac{1}{2}\rho A v^3}

It varies proportional to air density $\rho$, to the crossed area A and to the cube of wind velocity v. 

The Power P is the kinetic energy

$E={\frac {1}{2}}mv^{2}$

of the air-mass crossing the area A during a time interval

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dot{m}=A \rho \frac{dx}{dt}=A\rho v}