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Is there any equation that calculates the $C_d$ value in the formula of air drag ? $$F_d = \rho C_d v^2 A$$ I have found that there are tables for this constant but I am looking for the equation that evalutes it.

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I thought Cd was shape-specific and depended only on shape. Like, that was the point of the parameter. – AlanSE Oct 19 '11 at 19:25

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$C_d$ has to depend on the fluid, the surface shape, and texture of the object. In addition, that formula is only valid in the laminar flow regime, so when $v$ is sufficient to cause turbulent eddies, you get different behavior. You need to read up on Reynolds numbers and so on.

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actually I am developing a simulation of a projectile motion and I am studying the effect of drag on it.So I am supposed to include many objects (i.e ball, box, cannon projectile, etc) in my simulation project. – Creative Oct 19 '11 at 20:02
In this case, for simplicity I would reccomend using a simplistic approach for drag on the object. Some thing like $D = -\lambda v^{2}$, where $D$ is the drag force, $\lambda$ is some simple approximate coefficent and $v$ is the projectile velocity. – Killercam Oct 29 '11 at 10:39
@Manishearth The number is named after Reynolds, not Reynold. – Bernhard Mar 15 '12 at 7:46
@Bernhard: Whoops; forgot. Fixed, thanks! – Manishearth♦ Mar 15 '12 at 7:51
I woudn't say that the formula is only valid in the laminar flow regime. It is usually applied for higher Reynolds numbers, as opposed to Stokes drag. However, we need to remember that the formula is 1) only approximate and 2) often less helpful then it seems, as for large class of objects $C_d$ depends an awful lot on the velocity – malina Mar 15 '12 at 11:13
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For most ordinary shapes your Cd will be approximately 1/2, so that the force is just the velocity head of the fluid multiplied by the cross-sectional area of the body.

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