Drag force on a sphere moving through a fluid

[Tulatalu]

A body moves through a fluid, a retarding force due to turbulence may be experienced. In case of a sphere of radius R moving with speed v through a stationary fluid of density p which it at rest, this force is given by
F = kp (R^2) (v^2)
k is a constant.
Why F is proportional to kp (R^2) (v^2) ?

 

[Nugatory]

Google for "drag force calculation" and you'll find many good derivations. In practice, with real objects moving through real fluids, the calculations are hairy enough that we often resort to simulations.