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 $\frac{1}{K}pv^{2}A.$ Find $K.$

Answer 1

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,
$p_{2}-p_{1}=\frac{1}{2}\rho \left(v_{1}^{2} - v_{2}^{2}\right)$
$=\frac{\rho }{2}\left(2 v^{2} - v^{2}\right)=\frac{\rho v^{2}}{2}$
$\therefore $ Force of dynamic lift $=\frac{1}{2}\rho v^{2} A_{1}$