Chapter 4, Problem 36P

Viscous liquid from a circular tank. D = 300 mm in diameter, drains through a long circular tube of radius R = 50 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 How 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 m/s.