Question

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

• 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 \%$