How Is Lift Force Calculated for an Airplane?

[Jimkatz809]

Homework Statement

Consider an airplane of wing area 29 m^2 (both wings combined) flying through air of density0.549 kg/m^3 . From the plane’s point of view, the air flowing above the plane’s wings has
speed 178 m/s , but the air flowing below the wings has speed 140 m/s . What is the net upward lift force on the plane? Assume laminar air flow both above and below the plane’s wings. The plane is flying horizontally. Answer in units of kN.

Homework Equations

Pressure = F/A
Rho= m/volume

The Attempt at a Solution

I am so lost, my brother was sick so I had to pick him up from school and I missed the first part of lecture where he explained this. I'm not even sure what equations I can use. PLEASE HELP

 

[ehild]

Have you heard about Bernoulli' principle?

ehild

 

[kerimek]

As a scientist, it is important to understand the concept of pressure and its relationship to the lift force on an airplane. The lift force on an airplane is created by the difference in pressure between the air above and below the wings. The Bernoulli's principle states that as the speed of a fluid (in this case, air) increases, the pressure decreases. In this scenario, the air above the wings is moving faster than the air below, creating a lower pressure above the wings and a higher pressure below. This pressure difference results in an upward lift force on the plane.

To calculate the net upward lift force on the plane, we can use the equation F = P x A, where F is the lift force, P is the pressure, and A is the wing area. We can also use the equation P = ρ x V^2, where ρ is the density of the air and V is the speed of the air.

First, we need to calculate the pressure difference between the air above and below the wings. Using the equation P = ρ x V^2, we can calculate the pressure above the wings as P = (0.549 kg/m^3) x (178 m/s)^2 = 17,970 Pa. Similarly, the pressure below the wings is P = (0.549 kg/m^3) x (140 m/s)^2 = 9,708 Pa. The pressure difference is then 17,970 Pa - 9,708 Pa = 8,262 Pa.

Next, we can calculate the lift force using the equation F = P x A. The wing area is given as 29 m^2, so the lift force is F = (8,262 Pa) x (29 m^2) = 239,598 Pa or 239.6 kN.

In conclusion, the net upward lift force on the plane is 239.6 kN. It is important to note that this calculation assumes laminar air flow, which means that the air flows smoothly over the wings without any turbulence. In real life, there may be some turbulence which can affect the lift force and other factors, such as the shape and angle of the wings, also play a role in determining the lift force.