Question

In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70m/s$ and $63m/s$ respectively. What is the lift on the wing, if its area is $2.5m^2$ ? Take the density of air to be $1.3kg/m^3$.

• A. $5.1\times 10^{2}N$
• B. $6.1\times 10^{2}N$
• C. $1.6\times 10^{3}N$
• D. $1.5\times 10^{3}N$

Answer 1

Answer: (D)

Let the lower and upper surface of the wings of the aeroplane be at the same height $h$ and speeds of air on the upper and lower surfaces of the wings be $v_1$ and $v_2$.
Speed of air on the upper surface of the wing $v_1=70m/s$
Speed of air on the lower surface of the wings $v_2=63m/s$
Density of the air $\rho =1.3kg/m^3$
Area $A=2.5m^2$
According to Bernoulli's theorem,
$p_1+\frac{1}{2}\rho v_1^2+\rho gh=p_2+\frac{1}{2}\rho v^2+\rho gh$
or $p_2-P_1=\frac{1}{2}\rho \left(v_1^2-v_2^2\right)$
$\therefore$ Lifting force acting on the wings,
$F=\left(p_2-p_1\right)\times A=\frac{1}{2}\rho \left(v_1^2-v_2^2\right)\times A$
$[\because$ Pressure $=\frac{\text{ Force }}{\text{ Area }}]$
$=\frac{1}{2}\times 1.3\times \left[(70{)}^2-(63{)}^2\right]\times 2.5$
$=\frac{1}{2}\times 1.3[4900-3969]\times 2.5$
$=\frac{1}{2}\times 1.3\times 931\times 2.5=1.51\times 10^{3}N$