In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are `70ms^(-1)` and `83ms^(-1)` respectively. What is the lift on the wing, if its area is `2.5m^(2)`? Take the density of air to be `1.3kgm^(-3)`

Explanation

We are given that, ` v_1 = 70 m//s , v _ 2 = 63 m//s rho = 1.3 kg//m^ 3 `, Area of the wing, ` A = 2.5 m ^ 2 `.
If ` P_1 and P_2 ` are the pressures on the upper and the lower surfaces of the wing, according to Bernoulli’s theorem, ` P_1 + (1)/(2) rho v _ 1 ^ 2 = P_2 + (1)/ (2) rho v _ 2 ^2 or P_2 - P_1 = (1)/(2) rho v _ 1 ^ 2 - (1)/(2) rho v _ 2 ^ 2 = (1)/(2) rho (v_1 ^ 2 - v _2^2 ) `
`therefore ` Force acting on the wing, ` F = (P_2 - P_1)A, F = (1)/(2) rho (v_1^ - v_2^ 2 ) A `
` = (1)/(2 ) xx (1.3) (70 ) ^2 - (63 ) ^ 2 (2.5 ) N = 1.5 xx 10 ^(3) N`