A fully loaded Boeing aircraft has a mass of `3.3xx10^(5) kg`. Its total wing area is `500 m^(2)` . It is in level flight with a speed of `960 km//h`.
(a) Estimate the pressure difference between the lower and upper surfaces of the wings
(b) Estimate the fracitional increases in the speed of the air on the upper surfaces of the wing relative to the lower surface. The density of air is `1.2 kg//m^(3)`.

Explanation

(a) When Boeing aircraft is in level flight, then upward force due to difference of pressure `(delta P)` on area A of the wings is equal to weight of wings. I.e.
`Delta P xx A = mg = 3.3 xx 10^(5) xx 9.80`
or `Delta P = (3.3 xx 10^(5) xx 9.80)/(500) = 6.468 xx 10^(3)Pa`.
(b) If `upsilon_(1), upsilon_(2) ` are the speed of air on the lower and upper surface of the wings of aeroplane, and `P_(1), P_(2)` are the pressure there then using Bernoulli's theorem, we have
`P_(1)+1/2 rhoupsilon_(1)^(2) + P_(2) + 1/2 rho_(2) upsilon_(2)^(2)`
or `P_(1) - P_(2) = (rho)/(2) (upsilon_(2)^(2)-upsilon_(1)^(2))`
`Delta P = rho ((upsilon_(2)+upsilon_(1))/(2)) (upsilon_(2)-upsilon_(1))`
`=rho upsilon_(av) (upsilon_(2)-upsilon_(1))`
here, `upsilon_(av) = (upsilon_(2)+upsilon_(1))/(2)`
`= 960 km//h = 267 ms^(-1)`
`:. (upsilon_(2)-upsilon_(1))/(upsilon_(av)) = (DeltaP)/(rho upsilon_(av)^(2)) = (6.468 xx 10^(3))/(1.2 xx (267)^(2))`
`~~0.08 = 8%`.
It means the speed of air above the wings should be `8% more than below the wings.