A fully loaded boeing aircraft has a mass of $5.4\times10^5\ \text{kg}$. Its total wing area is $500\ \text{m}^2$. It is in level flight with a speed of $1080\ \text{km h}^{-1}$. If the density of air $\rho$ is $1.2\ \text{kg m}^{-3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be ($g=10\ \text{m s}^{-2}$)
Answer: (D) 10
In level flight the pressure difference supports the weight:
$$\Delta P=\frac{mg}{A}=\frac{5.4\times10^6}{500}=1.08\times10^4\ \text{Pa}$$
Bernoulli: $\Delta P=\tfrac12\rho(v_2^2-v_1^2)\approx\rho v\,\Delta v$, with $v=1080\ \text{km h}^{-1}=300\ \text{m s}^{-1}$:
$$\frac{\Delta v}{v}=\frac{\Delta P}{\rho v^2}=\frac{1.08\times10^4}{1.2\times9\times10^4}=0.10=10\%$$
Solution by Sreeraj P, M.Sc Physics