Two vertical tanks placed on a platform are connected by a horizontal

pipe with a radius $r$ as shown in Figure $2.$ Each tank has a length $L$ and a radius $R.$ Consider the fluid volume in the connecting pipe negligble. At first, the valve on the pipe is closed and one tank is full while the other is empty. When the valve is opened, the average velocity through the pipe is given by $u=\frac{\sqrt[\phantom{2}]{h}}{2},$ where $u$ is the average velocity in

$s$ and $h$ is the difference between the levels in the two tanks in meter.

$($a$)$ Derive an expression for the time when the levels in the two tanks become equal.

$($b$)$ If $r=1cm,L=2m,$ and $R=1m.$ Evaluate the time for the levels in the two tanks to become equal.