Question

A fully loaded boeing aircraft has a mass of $5.4\times 10^{5}kg$. Its total wing area is $500m^2$. It is in level flight with a speed of $1080km/h$. If the density of air $\rho$ is $1.2kg{m}^{-3}$, 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 $\left(g=10m/s^2\right)$

• A. 16
• B. 6
• C. 8
• D. 10

Answer 1

Answer: (D)

$P_{2}A-P_{1}A=5.4\times 10^5\times g$
$P_2-P_1=\frac{5.4\times 10^6}{500}=5.4\times 2\times 10^2\times 10$
$=10.8\times 10^3$
$P_2+0+\frac{1}{2}\rho V_2^2=P_1+0+\frac{1}{2}\rho V_1^2$
$P_2-P_1=\frac{1}{2}\rho \left(V_1^2-V_2^2\right)=\frac{1}{2}\rho \left(V_1-V_2\right)\left(V_1+V_2\right)$
$10.8\times 10^3=\frac{1}{2}\times 1.2\left(V_1-V_2\right)\times 2\times 3\times 10^2$
$10.8\times 10=3.6\left(V_1-V_2\right)$
$V_1-V_2=30$
$\left(\frac{V_1-V_2}{V}\right)\times 100=\frac{30}{300}\times 100=10\%$