Find the pressure difference on an airplane wing where air flows over the upper

Question

Find the pressure difference on an airplane wing where air flows over the upper surface with a speed of 125 m/s, and along the bottom surface with a speed of 102 m/s. kPa (b) If the area of the wing is 34 m^2, what is the net upward force exerted on the wing? kN During a thunderstorm, winds with a speed of 47.9 m/s blow across a flat roof with an area of 672 m^2. (a) Find the magnitude of the force exerted on the roof as a result of this wind. kN (b) Is the force exerted on the roof in the upward or downward direction?

Explanation / Answer

According to the given problem,

1.)

a)P1- P2= 0.5(1.29)(125)^2 - 0.5(1.29)(102)^2 = 3367.545 Pa

b) F = PA = (3367.545)(34) = 111496.53 N

2.)

Given:

v = 47.9 m/s
A = 672 m^2
= 1.292 kg/m^3 (standard sea level air density)


Solve using Bernoulli's principle, difference between lift above and below the surface. I'm going to have to assume that this is an enclosed roof, and thus no wind beneath it.

P1 = * [ (v2) / 2 ]
P1 = (1.292 kg/m^3) * [ (47.9 m/s)2 ] / 2 ]
P1 = 1,482.2 Pa

P2 = 0, because there is no wind across it.

So force

F = A * P1
F = (672 m2) * (1,482.2 Pa)
F = 996030.91 N

b) The force is directed upward. Stationary air exerts a larger pressure than air moving rapidly past the outside of the roof.

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