Given that the mass flow rate equation for a rotameter (variable area flowmeter) is show that for a float height, h, in a rotameter tube of cone angle, α, this becomes where m is the mass flow rate,...

Given that the mass flow rate equation for a rotameter (variable area flowmeter) is

show that for a float height, h, in a rotameter tube of cone angle, α, this becomes

where m is the mass flow rate, ao is the area of the annulus, Vf is the volume of the float, ρ is the density of the fluid, ρf is the density of the float, Af is the impact area of the float, Cd is the coefficient of discharge, and g is the gravitational acceleration.