Question

In a test experiment on a model aeroplane in a wind tunnel the flow speeds on the lower and upper surfaces of the wing are $v$ and $\sqrt{2}v$ respectively. If the density of air is $\rho$ and the surface area of the wing is $A,$ the dynamic lift on the wings is given by $\frac{1}{K}p{v}^{2}A.$ Find $K.$

Answer 1

Answer: 2

Let $p_1$ and $p_2$ be air pressure on upper and lower surfaces of wing. From Bernoulli's theorem.
$p_1+\frac{1}{2}\rho v_1^2=p_2+\frac{1}{2}\rho v_2^2$
where $v_1=\sqrt{2}v$ Let $v_2=v$
$\therefore$ Pressure difference,
$p_2-p_1=\frac{1}{2}\rho \left(v_1^2-v_2^2\right)$
$=\frac{\rho }{2}\left(2v^2-v^2\right)=\frac{\rho v^2}{2}$
$\therefore$ Force of dynamic lift $=\frac{1}{2}\rho v^2{A}_1$