Air is streaming past a horizontal air plane wing such that its speed is `120 ms^-1` over the upper surface and `90 ms^-1` at the lower surface. If the density of air is `1.3 kg m^-3`m find the difference in pressure between the top and bottom of the wing. If the wing is `10 m` long and has an average width of `2 m`, calculate the gross lift of the wing.

Explanation

According to Bernoulli's equation,
`P_(1)+(1)/(2)rhov_(1)^(2)=P_(2)+(1)/(2)rhov_(2)^(2)`
i.e., `P_(1)-P_(2)=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))`
`=(1)/(2)(1.3)(120^(2)-90^(2))=4.1xx10^(3)(N)/(m^(2))`
The net uplift due to the difference in pressure is
`F_(up)=DeltaPxxA=(4.1xx10^(3))(10xx2)=8.2xx10^(4)N`