Dynamic Pressure

What is dynamic pressure ?

Dynamic pressure is that part of the total pressure which represents the fluid kinetic energy.
In many of the equations related to the study of aerodynamics we find the term ½ρV², this is known as the dynamic pressure, but why?
If we look at the term dimensionally

½ is a constant and has no dimensions
ρ is air density , it has dimensions of kg m^-3
V² is the relative velocity of the oncoming air, it has dimensions of m²s^-2

Pressure has dimensions of kg m^-1 s^-2.
If we multiply kg m^-3 by m²s^-2 we end up with dimensions of kg m^-1 s^-2, the dimensions of pressure.
So by dimensional analysis we can prove that we have calculated a pressure, but where does the ½ come from ?
Integration.

Calculating dynamic pressure.

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