An aircraft of mass $4\times {10}^5$ kg with total wing area $500m^2$ in level flies at a speed of 720 $km{h}^{-1}.$ The density of air at that height is $1.2kg/m^3.$ The fractional increase in the speed of the air on the upper surface of its wings relative to the lower surface is:  $(Take g=10m/s^2)$

The weight of the air croft is balanced by the upward force due to the pressure difference $\Delta P=\frac{mg}{A}=\frac{4\times {10}^5\times 10}{500}=\frac{4}{5}\times {10}^4 N/m^2$

By the beroulli’s theorem, $p_1+\frac{1}{2}\rho v_1^2=p_2+\frac{1}{2}\rho v_2^2$

$\Delta p=\frac{1}{2}\rho (v_2^2-v_1^2)$

$\Delta p=\frac{1}{2}\rho (v_2+v_1)(v_2-v_1)$

$\Delta p=\rho v_{av}(v_2-v_1)\Rightarrow v_2-v_1=\frac{\Delta p}{\rho v_{av}}$

$v_{av}=\frac{v_1+v_2}{2}=720km/n=200m/s\Rightarrow \frac{v_2-v_1}{v_{av}}=\frac{\Delta p}{\rho {\left(v_{av}\right)}^2}=\frac{\frac{4}{5}\times {10}^4}{1.2\times {\left(200\right)}^2}=0.17$