Hi, I hope that this clarifies the maths.
The velocity induced at the rotor is
Vi = SQRT((Thrust)/(Disc Area * 2 * airdensity))
(Sorry I can't get a formula editor to work ...)
Thrust/Disc Area is the same as disc loading so
Vi = SQRT (discloading/(2*airdensity))
standard air density is 0.002378 slug/ft3
(1/standard air density) is 420.5 which, when divide by the 2 is where the 210 factor comes into the equation. This is the bit that would change for different air densities. Take the invert of the air density and divide by 2.
This gives the induced velocity at the rotor, as you already pointed out lucaberco, the velocity downstream increases.