Question

The lift force acting on the wing of an aeroplane is $2275\text{N}$. If the area of the wing is $5{\text{m}}^2$ and velocity of air on the lower surface of the wing is $30\text{m/s}$, velocity of air on the upper surface of the wing is (density of air is $1.3{\text{kg/m}}^3)$

• A. $20\text{m/s}$
• B. $25\text{m/s}$
• C. $35\text{m/s}$
• D. $40\text{m/s}$

Answer 1

The correct option is D $40\text{m/s}$

We know that
uplift on aeroplane is
$F=\left(\Delta P\right)A$

Using Bernoulli's theorem,

$P_1+\frac{1}{2}\rho v_1^2=P_2+\frac{1}{2}\rho v_2^2$

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

$F=\frac{1}{2}\rho (v_2^2-v_1^2)A$

$2275=\frac{1}{2}\times 1.3\times (v_2^2-{30}^2)\times 5$

$v_2^2-{30}^2=\frac{2\times 2275}{1.3\times 5}=700$

$v_2=\sqrt{900+700}=\sqrt{1600}$

$v_2=40{\text{ms}}^{-1}$