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.

Answer

[`4095 Nm^(-20; 81900N`]

Explanation

Here, `v_(1)=120 ms^(-1), v_(2)=90 ms^(-1)`,
`rho=1.3 kf m^(-3), l=10.0m , b=2.0m ,`
Let `P_(1)` and `P_(2)` be the pressure of air at the upper and lower faces of plane respectively, then
`(P_(1))/(rho)+(1)/(2)v_(1)^(2)=(P_(2))/(rho)+(1)/(2)v_(2)^(2)`
`:. P_(2)-P_(1)=(1)/(2)rho (v_(1)^(2)-v_(2)^(2))`
`=(1)/(2)xx1.3xx(120^(2)-90^(2))=4095 Nm^(-2)`
Gross lift `=(P_(2)-P_(1))xxA=(A=(P_(2)-P_(1))xxlxxb`
`=4095xx10xx2=81900 N`