Consider the flow of air through a wind turbine whose blades sweep an area of diameter D (in m). The average air velocity through the swept area is V (in m/s). On the bases of the units of the quantities involved, show that the mass flow rate of air (in kg/s) through the swept area is proportional to the air density, the wind velocity, and the square of the diameter of the swept area.

Question

There's no diagram or image, btw.

Answer 1

not very complicated
velocity v (do not use V, that is usually volume)
Area that air flows though= pi R^2 = pi D^2/4
so
Volume of air through/second = v (pi D^2/4)
but mass = density times volume so mass /second
= rho v D^2 (pi/4)