(a) If this jet is in horizontal flight, determine the pressure difference betwe

Question

(a) If this jet is in horizontal flight, determine the pressure difference between the lower and upper surfaces of the wings.
Pa

(b) When the speed of air traveling over the wing is 227 m/s, determine the speed of air under the wing.  Use 1.29 kg/m3 as the density of air.

m/s

A small jet airplane has a total wing area of 87.5 m2 and a mass of 7.83 Times 104 kg. If this jet is in horizontal flight, determine the pressure difference between the lower and upper surfaces of the wings. Pa When the speed of air traveling over the wing is 227 m/s, determine the speed of air under the wing. Use 1.29 kg/m3 as the density of air. m/s

Explanation / Answer

a)
The net force due to pressure on the wing must counter the weight of the plane.

Weight of the plane :
W = m * g
= 7.83*10^4*9.8
= 767340 N

Now, pressure is force spread over an area
P = F / A

And the force must be equal to the weight of the plane
P = W / A
= 767340 / 87.5
= 8769.6 Pa

b)
From Bernoulli's equation:
p1 + 1/2*rho*v1^2 = p2 + 1/2*rho*v2^2
for points 1 and 2 along the same path in steady, incompressible flow.

We assume that the air on top and bottom of the wing starts upstream at the same conditions.

pt + 1/2*rho*vt^2 = pb + 1/2*rho*vb^2
where t = top
b = bottom

1/2*rho*vt^2 - 1/2*rho*vb^2 = pb - pt
0.5 * 1.29 * (227)^2 - 0.5 * 1.29 * vb^2 = 8769.6
33236.205 - 0.645 vb^2 = 8769.6
24466.605 = 0.645 vb^2
vb^2 = 37932.72

vb = 194.76 m/s

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