Derivation of Dynamic Pressure

[arithhuh]

Dear All, I need your help with a present problem -

I am a student pilot, and want to see the derivation for the dynamic pressure formula - which is 1/2PV^2 where P - Density, V-Velocity

I was asked an interesting question by my a fellow student: Why is dynamic pressure directly proportional to v^2 and not just V?

Kindly explain to me these points.

Thank you,
~ Aditya.

 

[FredGarvin]

It comes from looking at Newton's Second Law for a fluid particle along a streamline. In a nutshell, the term is the result of an integration of the term
$$\rho V \frac{\partial{V}}{\partial{s}}$$

How much detail do you want to get into?

 

[Lojzek]

Here is a simple argument why the pressure is proportional to v^2:

The object flying through air must remove air in front of it. If you assume that the change of air velocity is proportional to the speed of the object, then the change of momentum of air (pushed away in a certain time) is proportional to v^2 (because the mass current is also proportional to v). Force equals the change of momentum/change of time, so force is also proportional to v^2.