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I'd like to calculate the force of drag on a small plate when high speed air is coming into contact with it. I understand the force of drag equation is:

$$F = {1\over2}\rho v^2C_dA$$

for $\rho $ = density of air, $v$ = velocity, $C_d$ = drag coefficient, and $A$ = area

However, I have a concern:

When air speed is $475$ m/s, does compressibility of air become an issue when calculating drag?

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That's above the speed of sound, so the compressibility of air definitely matters.

In general, the speed at which compressibility becomes important depends on the shape of the object. When an object exceeds its critical mach number (the speed at which air flowing over some part of its surface exceeds the speed of sound), its drag increases dramatically.

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