When is the equation FD = 1/4 AV^2 false and what is the error in the equation?

[jason bourne]

Homework Statement

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.

Homework Equations

FD = 1/4 AV^2

FD = 1/2 CD *ApV^2

The Attempt at a Solution

I searched everywhere on wikipedia and NASA site and no luck and I don't know integration yet so can't follow the complicated math. Please anyone can help me.

 

[RoyalCat]

Look closely at the second equation. It is a private case of the first.

The factor of $$\tfrac{1}{2}$$ is pretty weird too.

All you need to remember is what the drag force is proportional to, and that's fairly simple:
The higher the area perpendicular to the flow - the greater the drag.
The greater the density of the medium - the greater the drag.
The greater the square of the velocity of the object wrt the medium - the greater the drag
And then there's just some constant.

 

[jason bourne]

Thanks for your reply. But it was like a bonus question kind of thing, why 1/4 AV^2 instead of the other equation, he said the 1/4 will work for any speed less than speed of sound and uses normal air and something. And he said 1/4 is not the error that # is precise, so the problems got to be in the AV^2.hmm.