Question

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.

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)