fdmid = fdeqn[[1,1,2]] /. f[d rho v/m] -> 0.5
Then FD equals k2 v^2, where
k2 = 0.25 a rho
or, expressing the area of a circle, a, in terms of the diameter, d
k2 = k2 /. a -> 1/4 Pi d^2
Up to 3. Two Models for the Drag Force