# Does static pressure(p - p∞) at wing surface change exponentially, with square of the velocity?

Integration of static pressure over wing we get lift.

and

Formula for lift is L= 1/2 x Cl x A x V2 x ro; that implies that static pressure (p - p∞) change exponentially(as square of velocity), becuase A, Cl and ro dont change with velocity in attached flow regime.

One end of differential manometer I connect to small hole that I drill at upper wing surface(hole is drilled perpedicular to wing surface), other end connect to static port. Manometer show -400Pa at 100km/h, does it mean at 150km/h will be -900Pa, at 200km/h = -1600Pa etc ?

Does static pressure (p - p∞) change as square of velocity, in attached flow regime?

• Static pressure is constant w.r.t. velocity (by definition). Do you mean dynamic pressure? Or total pressure? Mar 22 at 19:31

Indicated static pressure changes proportionally to the square of velocity. Static pressure around an airfoil depends on which point the pressure is measured, and is described as pressure coefficient at a location on the chord. The pressure coefficient is:

$$c_p = \frac{p - p_∞}{q_∞} => p = c_p * q_∞ + p_∞$$

p is the local pressure a particular point on the wing surface. The dynamic pressure $$q_∞$$ changes with the square of the velocity, but the static pressure has quite a large contribution to the equation. At sea level, with $$p_∞$$ = 101325 N/m^2 and $$\rho$$ = 1.225 kg/m$$^3$$:

• Is pressure coeficient constant with velocity? If yes, differential manometer show "delta pressure"(static pressure wing - static pressure freestream) = Cp x dynamic pressure, so If Cp is constant then " delta pressure" rise with square of velocity. Am I correct? Mar 25 at 18:13
• Indeed, delta pressure rises with the square of velocity, and then the surrounding pressure is added. Mar 26 at 5:00
• Yes only if we assume that Cp remain constant with velocity. But Cp change with Re number so this is not 100% accurate.. Mar 26 at 7:02
• You can edit your answer because differential manometer show delta pressure (p - p∞). Mar 27 at 7:04