Question

An airplane has an effective wing surface area of 19.4 m2 that is generating the lift force. In level flight the air speed over the top of the wings is 67.0 m/s, while the air speed beneath the wings is 51.0 m/s. What is the weight of the plane?

Answer 1

Answer:

W =23807.68 N

Explanation:

given,

surface area of wing = 19.4 m²

speed over top wing = 67 m/s

speed under wing = 51 m/s

density of air =  1.3 kg/m³

weight of plane

From Bernoulli's principle

$P_1 + \dfrac{1}{2}\rho v_1^2 = P_2 + \dfrac{1}{2}\rho_2^2$

where 1 and 2 are two different locations at the same geo potential level  

so if we call 1 the lower surface and 2 the upper surface,

we find the pressure differential, P₁ -P₂

$\Delta P =\dfrac{1}{2}\rho (v_2^2-v_1^2)$

$\Delta P =\dfrac{1}{2}\times 1.3 \times (67^2-51^2)$

$\Delta P =1227.2\ N/m^2$

then the force acting on the plane is

F=P A

F=1227.2 x 19.4

F =23807.68 N

weight of the plane

W =23807.68 N