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 wing is given by:

Let $p_1$ and $p_2$ be the air pressures on the upper and lower surfaces of the wing. Then from Bernoulli's theorem we have
$p_1+\frac{1}{2}\rho v_1^2=p_2+\frac{1}{2}\rho v_2^2$
where $v_1=\sqrt{2}v$ and $v_2=v$. Therefore, the pressure difference is
$p_2-p_1=\frac{1}{2}\rho \left(v_1^2-v_2^2\right)=\frac{\rho }{2}\left(2v^2-v^2\right)=\frac{\rho v^2}{2}$
Force of dynamic lift = pressure difference $\times$ surface area of wing
                                $=\frac{1}{2}\rho v^{2}A$