Question

Use the worked example above to help you solve this problem. An airplane has wings, each with area 3.95 m2, designed so that air flows over the top of the wing at 249 m/s and underneath the wing at 225 m/s. Find the mass of the airplane such that the lift on the plane will support its weight, assuming the force from the pressure difference across the wings is directed straight upwards.

Answer 1

here,

the area of wings ,A = 3.95 m^2

the speed over the top of wings , vt = 249 m/s

the speed undreneath the wing , vb = 225 m/s

using Bernauli's equation

the pressure difference , dP = 0.5 * p * (vt^2 - vb^2)

dP = 0.5 * 1020 * ( 249^2 - 225^2) Pa

dP = 5.802 * 10^6 Pa

let the mass of the airplane be m

equating the forces vertically

m * g = dP * A

m * 9.81 = 5.802 * 10^6 * 3.95

solving for m

m = 2.34 * 10^6 kg

the mass of airplane is 2.34 * 10^6 kg