Viscous liquid from a circular tank, \(D=300 \mathrm{~mm}\) in diameter, drains through a long circular tube of radius \(R=50 \mathrm{~mm}\). The velocity profile at the tube discharge is

\[u=u_{\max }\left[1-\left(\frac{r}{R}\right)^{2}\right]\]

Show that the average speed of flow in the drain tube is \(\bar{V}=\frac{1}{2} u_{\max }\). Evaluate the rate of change of liquid level in the tank at the instant when \(u_{\max }=0.155 \mathrm{~m} / \mathrm{s}\).