A Boeing 737 airliner has a mass of 20,000 kg and the total area of both wings (top or bottom) is 100 m2. What is the pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude?

a. 1960 N/m2
b. 7840 N/m2
c. 4560 N/m2
d. 3920 N/m2
e. 3070 N/m2

The correct option is A = 1960 N/m²

Explanation:

Given that,

Mass m= 20,000kg

Area A = 100m²

Pressure different between top and bottom

Assume the plane has reached a cruising altitude and is not changing elevation. Then sum the forces in the vertical direction is given as

∑Fy = Wp + FL = 0

where

Wp = is the weight of the plane, and

FL is the lift pushing up on the plane.

Let solve for FL since the mass of the plane is given:

Wp + FL = 0

FL = -Wp

FL = -mg

FL = -20,000× -9.81

FL = 196,200N

FL should be positive since it is opposing the weight of the plane.

Let Equate FL to the pressure differential multiplied by the area of the wings:

FL = (Pb −Pt)⋅A

where Pb and Pt are the static pressures on bottom and top of the wings, respectively

FL = ∆P • A

∆P = FL/A

∆P = 196,200 / 100

∆P = 1962 N/m²

∆P ≈ 1960 N/m²

The pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude is approximately 1960 N/m². Option A is correct