A crude approximation for the \(x\) component of velocity in an incompressible laminar boundary layer is a linear variation from \(u=0\) at the surface \((y=0)\) to the freestream velocity, \(U\), at the boundary-layer edge \((y=\delta)\). The equation for the profile is \(u=U y / \delta\), where \(\delta=c x^{1 / 2}\) and \(c\) is a constant. Show that the simplest expression for the \(y\) component of velocity is \(v=u y / 4 x\). Evaluate the maximum value of the ratio \(v / U\), at a location where \(x=0.5 \mathrm{~m}\) and \(\delta=5 \mathrm{~mm}\).