In a food industry plant, two immiscible fluids are pumped through a tube such that fluid \(1\left(\mu_{1}=0.5 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\right)\) forms an inner core \(\mathrm{r}=D / 4\) and fluid \(2\left(\mu_{2}=5 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\right)\) forms an outer annulus. The tube has \(D=5 \mathrm{~mm}\) diameter and length \(L=5 \mathrm{~m}\). Derive and plot the velocity distribution if the applied pressure difference, \(\Delta p\), is \(5 \mathrm{MPa}\).