A fully loaded boeing aircraft has a mass of `3.3 times 10^5 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 increase in the speed of the air on the surface of the wing relative to the lower surface.[ The density of air is p=`1.2 kg m^-3`]

Explanation

(a) The weight of the Boeing aircraft is balanced by the upward force due to the pressure difference
`DeltaPxxA=3.3xx10^(5)kgxx9.8`
`DeltaP=(3.3xx10^(5)kgxx9.8ms^(-2))//500m^(2)`
`=6.5xx10^(3)Nm^(-2)`
(b) We ignore the small height difference between the top and bottom sides in Eq. The pressure difference between them is then
`Delta=(rho)/(2)(v_(2)^(2)-v_(1)^(2))`
Where `v_(2)` is the speed of air over the upper surface and `v_(1)` is the speed under the bottom surface.
`(v_(2)-v_(1))=(2Deltarho)/(rho(v_(2)+v_(1)))`
Taking the average speed
`v_(av)=(v_(2)+v_(1))//2=960km//h=267ms^(-1)`, we have
`(v_(2)-v_(1))//v_(av)=(DeltaP)/(rhov_(av)^(2))~~0.08`
The speed above the wing needs to be only 8% higher than that below.