Question

It is desired to design an aeroplane with a lift of $1000N/m^2$ of wing area. If the velocity of streamline flow part of the lower wing surface is $100m/s$, then the required velocity over the upper surface is (given density of air is $1.3kg{m}^{-3}$):

• A. $57m/s$
• B. $77.4m/s$
• C. $107.4m/s$
• D. $127.2m/s$

Answer 1

The correct option is C $107.4m/s$

Using Bernoulli's theorem,

$\begin{array}{c}{P}_1+\frac{1}{2}\rho {v_1}^2=P_2+\frac{1}{2}\rho {v_2}^2\\ \frac{1}{2}\rho \left({v_2}^2-{v_1}^2\right)=P_1-P_2\\ {v_2}^2=\frac{2\left(P_1-P_2\right)}{\rho }+{v_1}^2\\ {v_2}^2=\frac{2000}{1.3}+{\left(100\right)}^2\\ v_2=107.4m/s\end{array}$