# An airplane has a mass of 18,000 kilograms, and the total wing is 50 m2. during level flight, the pressure on the lower wing surface is 5.25 x 104 pa. what is the pressure on the upper wing surface?

Jul 7, 2014

An airplane's ability to fly is dependent upon three things. First, the thrust generated by the engine propels the plane forward. Second, the angle of the wing provides an initial surface for the passing air to push the airplane up into the air. Finally, a simple fluid mechanics principle known as "lift" allows the airplane to remain in the sky for the duration of the flight.

Lift is simply a pressure differential between the bottom of the wing and the top of the wing. An airplane wing will see a positive lift because the static pressure on the bottom of the wing is greater than the static pressure on the top of the wing. Bernoulli's principle is the guiding principle for this phenomenon, and is shown below:

$P + \frac{1}{2} p {v}^{2} = C$

This is not Bernoulli's complete form, but since the hydrostatic head differential over an airfoil is negligible, it is sufficient. This question can be answered in the following manner:

1) Assume the plane has reached a cruising altitude and is not changing elevation. Then sum the forces in the vertical direction, which I will call "y":

$\sum {F}_{y} = {W}_{p} + {F}_{L} = 0$

where ${W}_{p}$ is the weight of the plane, and ${F}_{L}$ is the lift pushing up on the plane.

2) Next, solve for F_L since the mass of the plane is given:

${W}_{p} + {F}_{L} = 0$

${F}_{L} = - {W}_{p}$
${F}_{L} = - \left(- m g\right) = - \left(- 9.8 \frac{m}{s} ^ 2 \cdot 18 , 000 k g\right) = 176 , 400 N$

${F}_{L}$ should be positive since it is opposing the weight of the plane.

3) Equate ${F}_{L}$ to the pressure differential multiplied by the area of the wings:

${F}_{L} = \left({P}_{b} - {P}_{t}\right) \cdot A$

where ${P}_{b}$ and ${P}_{t}$ are the static pressures on bottom and top of the wings, respectively.

${P}_{b} - {P}_{t} = {F}_{L} / A = \frac{176 , 400 N}{50 {m}^{2}} = 3 , 528 P a$
${P}_{b} - {P}_{t} = 3 , 528 P a$
$- {P}_{t} = 3 , 528 P a - {P}_{b}$
${P}_{t} = {P}_{b} - 3 , 528 P a$
${P}_{t} = 5.25 x {10}^{4} P a - 3 , 528 P a$
${P}_{t} = 4.90 x {10}^{4} P a$

Note that this answer makes sense because the pressure on the top of the wing should be less than the pressure on the bottom of the wing.