b$)$ A cylindrical water tank whose top is open to the atmosphere is initially filled with water. Now the discharge plug near the bottom of the tank is pulled out, and water jet whose diameter is $0\mathrm{.}5$ in streams out $($Fig$.$ Q$5).$

i$.$ Derive an expression to calculate the average velocity of the jet where $h$ is the height of water in the tank measured from the center of the hole.

$[7$ Marks$]$

ii$.$ Determine an expression to find how long it would take the water level in the tank to drop to $0\mathrm{.}2m$ from the bottom.

$[7$ Marks$]$

$5$

Figure Q$5$: Water tank