Understanding Drag Force: Standard Formula vs. Alternative Formula Explained

[jason bourne]

I know that standard formula is, FD = 1/2 CD *ApV^2


FD = Drag Force. SI: N
CD = Drag Coefficient. SI: Dimensionless (Typical Values)
A = Coss-sectional Area perpendicular to the flow. SI: m2
r = Density of the medium. SI: kg/m3
v = Velocity of the body relative to the medium. SI: m/s

But our prof also said there's another formula for drag force,

FD = 1/4 AV^2

(Its is not supposed to be equal but approximately)

So the question is when is the equation above false, what's the error in the equation that makes it approximate.

 

[Baluncore]

Such a simple equation assumes that C_D⋅ρ = 0.5
Where ∝ means proportional to; F_D ∝ ¼⋅A⋅V²
can be further simplified to; F_D ∝ A⋅V²
That can only be applied where changes to area or velocity occur, while maintaining a constant profile in a constant density fluid.