Air flows over the top of an aeroplane wing of area A with speed` v_1` and past the under side of the wing of area A with speed `v_2` Show that the magnitude of the upward in force on the wing L is L = ` (1)/(2) rho A ( v_1^(2) - v_2^(2))` where `rho` is the density of the alr.

Explanation

Bernouli.s equations
`P + (1)/(2) rho v^(2) +rho gh = a ` constant
The pressure difference across the upper and lower surface is` Deltap= p_2 -P_1`
` P_1 +(1)/(2) rho v_1^(2) = P_2 +(1)/(2) rho v_2^(2) ` because `rhogh` is a constane
` Delta P = P_2 - P_1 = (1)/(2) rho ( v_1^(2) -v_2^(2)) `
Lift on the plane ` = L= Delta P xx A = (1)/(2) rho A (v_1^(2) -v_2^(2))`