# 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 \(C_{L}\).

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\)