$($i$)$ Based on Bemoulli's equation, derive the orifice discharge rate based on

orifice area Aortos and water depth above the orfice h$.$

$[5/15$ marks$]$

$($ii$)$ Discuss the difference in the orfice discharge rates $Q_1$ and $Q_2$ from the two

containers in Figure Q$2$a$,$ assuming the initial water depth inside the contains

are at the same and the orifices are located at the same level below the water

surface, $h.$

$[2/15$ marks$]$

$($iii$)$ A vertical cylindrical tank, $2m$ diameter, has a sharp$-$edged orifice with

diameter $d=0\mathrm{.}05m$ near the bottom. The orifice has a discharge coefficient

of $0\mathrm{.}6$ as in Figure $Q2b.$ Water $($density of $1000k\frac{g}{m^3},$ gravitational

acceleration $g=9\mathrm{.}81\frac{m}{s^2})$ is also pulled into the tank at a constant rate On ${?}_{in}$ to

keep the water level inside the tank same.

If water enters the tank at a constant rate $Q_{in}$ of $0\mathrm{.}0095\frac{m^3}{s},$ find the depth of

water above the orifice when the level in the tank becomes stable.

marks$]$

$($a$)$

$($b$)$

Figure Q$2.$