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 fractional 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

For a being aircraft in a level flight, the weight of aircraft is balanced by the upward force due to pressure difference
`triangle P xx A=mg`
`=3.3 xx 10^(5) xx 9.8`
`rArr triangle P=(3.3 xx 10^(5) xx 9.8)/(500)`
`=6.5 xx 10^(3) N//m^(2)`
(b) Let `v_(1) and v_(2)` are the speeds of air on the lower and upper surfaces of the wings of aircraft, respectively and `p_(1) and p_(2)` are their corresponding pressures. Using Bernoulli.s principle. `p_(1)+1/2 pv_(1)^(2)=p_(2)_1/2 pv_(2)^(2)`
`rArr p_(1)-p_(2)=1/2 p(v_(2)^(2)-v_(1)^(2))`
`=1/2 p(v_(2)+v_(1)) (v_(2)-v_(1))`
`=p ((v_(2)+v_(1))/(2)) (v_(2)-v_(1))`
`=pv_(av) (u_(2)-v_(1))`
where `u_(av)=1/2 (v_(2)+v_(1))=960 km//hr`
`=266.67m//s cong 267 m//s`
`(v_(2)-v_(1))//v_(av) =(p_(1)-p_(2))/(pv_(av)^(2))`
`=(6.5 xx 10^(3))/(1.2 xx (267)^(2)) cong 0.08`
So, the spped of air above th wing only needs to be 8% higher than below.