# Find the ratio of displacement thickness to momentum thickness of the boundary layer.

Consider a steady two-dimensional zero pressure gradient laminar flow of air over a flat plate as shown below.The free stream conditions are $$u_{\infty}=100\;m/s,\rho_{\infty}=1.2\;kg/m^{3},p_{\infty}=1\;atm$$ and $$\mu_{\infty}=1.8\times 10^{-5}\;kg/m-s$$.Find the ratio of displacement thickness to momentum thickness of the boundary layer at a distance of $$2\;m$$ from the leading edge.

Asked on 15th October 2019 in
Blasius solution for 2D zero pressure gradient laminar flow of air over a flat plate is $\frac{\delta ^{*}}{x}=\frac{1.721}{Re_{x}^{1/2}} \\\frac{\theta}{x}=\frac{0.664}{Re_{x}^{1/2}} \\\Rightarrow \frac{\delta ^{*} }{\theta}=\frac{1.721}{0.664} \\=2.59$