Prandtl-Glauert compressibility corrections.

Consider flow over a thin aerofoil at Mach number,$$M_{\infty}=0.5$$ at an angle of attack of $$\alpha$$.Using the Prandtl-Glauert rule for compressibility correction find a formula for lift coefficient $$C_{L}$$.

Asked on 14th October 2019 in
Prandtl-Glauert Compressibility correction for a low speed flow is $c_{L}=\frac{c_{l,0}}{\sqrt{1-M_{\infty}^{2}}}$
We will get $$c_{l,0}$$ by using thin airfoil theory. Thin airfoil theory is $c_{l,0}=2\pi\alpha$
$$\Rightarrow c_{L}=\frac{2\pi\alpha}{\sqrt{1-\left ( 0.5 \right )^{2}}} \\\Rightarrow c_{L}=7.255\alpha\approx 7.26\alpha$$