Considering only drag induced by the fluid P=F*v=0.5*(density of air)*(velocity)^3*(frontal area)*(coefficient of drag)
The truth is always in the equations. Power has a linear relationship with the coefficient of drag, all other variables being constant. The equation doesn't always really work out because of frontal area approximations for irregular shapes, Cd's are generally never exact, and density is truly variable depending on the fluid conditions and the boundary layer, both thermal and hydraulic.
(I know it's been said, but I and others may place our faith in the math)
