Air is streaming past a horizontal aeroplane wing such that the speed of air is 120 m/s over the upper surface and 90 m/s at the lower surface, with respect to the plane. If the density of air is 1.3kg/`m^(3)` , find the difference in pressure between the top and bottom of the wing. If the wing is 10m long and has an average width of 2m, calculate the gross lift of the wing.

Explanation

Neglecting the difference in gravitational potential energy across the thickness of the wing, accoring to Bernouli.s equation,
`P_(1)+(1)/(2)rhoV_(1)^(2)` i.e. `P_(1)-P_(2)=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))`
`=(1)/(2)(1.3 kg//m^(3))(120^(2)-90^(2))(m//s)^(2)=4.1xx10^(3)N//m^(2)`
Now, the net uplift due to the difference in pressure is `F_(up)=DeltaPxxA`
`=(4.1xx10^(3)N//m^(3))(10xx2m^(2))=8.2xx10^(4)N`
Note that this is not force of buoyancy (B) as B is a fluid static force.