Consider a steady two-dimensional zero pressure gradient laminar flow of air over a flat plate as shown below. Find the ratio of displacement thickness to momentum thickness of the boundary layer at a distance of 2m from the leading edge.
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.
Blasius solution for 2D zero pressure gradient laminar flow of air over a flat plate is \[\frac{\delta ^{*}}{x}=\frac{1.721}{Re_{x}^{1/2}}
\\\frac{\theta}{x}=\frac{0.664}{Re_{x}^{1/2}}
\\\Rightarrow \frac{\delta ^{*} }{\theta}=\frac{1.721}{0.664}
\\=2.59\]
