A useful approximation for the \(x\) component of velocity in an incompressible laminar boundary layer is a cubic variation from \(u=0\) at the surface \((y=0)\) to the freestream velocity, \(U\), at the edge of the boundary layer \((y=\delta)\). The equation for the profile is \(u / U=\) \(\frac{3}{2}(y / \delta)-\frac{1}{2}(y / \delta)^{3}\), where \(\delta=c x^{1 / 2}\) and \(c\) is a constant. Derive the simplest expression for \(v / U\), the \(y\) component of velocity ratio. Plot \(u / U\) and \(v / U\) versus \(y / \delta\), and find the location of the maximum value of the ratio \(v / U\). Evaluate the ratio where \(\delta=5 \mathrm{~mm}\) and \(x=0.5 \mathrm{~m}\).