Understanding Drag Force: Standard Formula vs. Alternative Formula Explained

AI Thread Summary
The standard drag force formula, FD = 1/2 CD * ApV^2, incorporates the drag coefficient, cross-sectional area, fluid density, and velocity. An alternative formula, FD = 1/4 AV^2, provides an approximate relationship under specific conditions. This approximation assumes a constant drag coefficient and fluid density, which may not hold true in all scenarios. The simplified equation FD ∝ A⋅V^2 is applicable only when area and velocity change while maintaining a consistent profile in a uniform fluid. Understanding the limitations of these formulas is crucial for accurate drag force calculations.
jason bourne
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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.
 
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Such a simple equation assumes that CD⋅ρ = 0.5
Where ∝ means proportional to; FD ∝ ¼⋅A⋅V2
can be further simplified to; FD ∝ A⋅V2
That can only be applied where changes to area or velocity occur, while maintaining a constant profile in a constant density fluid.
 

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