Pressure

F = - \frac{P}{A} = - \nabla P

When saying pressure we usually refer to static pressure which is the pressure due to the random movement of the molecules on a certain speed V1

P = T (\frac{\partial S}{\partial V})_{E, N}

P = \frac{2}{3} n m < \frac{u^{2}}{2} >= \frac{2}{3} u

όπου
u : πυκνότητα εσωτερικής ενέργειας αερίου --> Internal energy

u = n m < \frac{u^{2}}{2} >

The pressure if we stopped the flow entirely V2=0
When local velocity is 0 the total pressure is the same with static pressure

q = \frac{1}{2} ρ V^{2}

The pressure due to the velocity

p o = p 1 + q o

Total pressure= Static pressure + Dynamic pressure
(only for Incompressible flow - derivates from Bernouli's Equation )

c p = \frac{p - p_{\infty}}{q_{\infty}}

C_{P} = C_{P} (V) = 1 - {\frac{V}{V_{\infty}}}^{2}

p = p_{\infty} + q_{\infty} C_{p}

For V=0 : Pressure coefficient at stagnation point: $C_{P} = 1$