An aircraft of mass `4 xx 10^(5)kg` with total wing area `500m^(2)` in level flight at a speed of 720 `km h^(-1)`. The density of a at its height is `1.2 kgm^(-3)`. The fractional increases in the speed of the air on the upper surface of its wings relative to the lower surface is (take `g = 10 ms^(-2)`)

Options

A. 0.04
B. 0.08
C. 0.17
D. 0.32

Answer

C

Explanation

Weight of the aircraft is balanced by the upward force due to the pressure difference
`Delta P xx A` = mg
`implies Delta P=(mg)/(A)=(4xx10^5xx10)/(500)=4/5 xx 10^4 N/m^2`
Let `v_1` and `v_2` are the speed of air lower and upper surface of the wings
Using Bernoulli theorem -
`P_1+1/2 rho v_1^2=P_2+1/2 rho v_2^2`
`implies Delta P=rho ((v_2^2-v_1^2))/(2)=rho ((v_1+v_2)/(2))(v_2 - v_1)`
`implies Delta P=rho v_("avg")(v_2-v_1)`
`((v_2-v_1))/(v_("avg"))=(DeltaP)/(rho v_("avg")^2)=(4/5 xx 10^4)/(1.2 xx (200)^2)=0.17`