Question

An aeroplane wing has an area $50m^2$. The speed of air flowing above the wing is $100{ms}^{-1}$ and below the wings is $80{ms}^{-1}$. The aerodynamic lifting force acting on the aeroplane wing if density of air is $1.3kg{m}^{-3}$ is _____ N.

• A. $156\ast {10}^3$
• B. $324\ast {10}^3$
• C. $256\ast {10}^3$
• D. $117\ast {10}^3$

Answer 1

The correct option is D $117\ast {10}^3$

Apply Bernoulli equation at lower wing and at upper wing points

point 1 is at lower wing and point 2 is at upper wing

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

net upward pressure is

$P_1-P_2=\frac{1}{2}\rho (v_2^2-v_1^2)$

Aerodynamic lifting force is

$(P_1-P_2)A=\frac{1}{2}\rho A(v_2^2-v_1^2)$

$F=\frac{1}{2}\times 1.3\times 50\times ({100}^2-{80}^2)$

$F=117\times {10}^{3}N$