In the liquid$-$level system shown in Figure $2,$ assume that the outflow rate Q$($m$^(3))/($s$)$ through the outflow valve is related

to the head H$($m$)$ by Q$=0\mathrm{.}01*$sqrt$($H$).$

Also, assume that when the inflow rate Q$\_($i$)$ is $0\mathrm{.}015($m$^(3))/($s$)$ the head stays constant. For t$<mn>0</mn>$ the system is at steady state

$($Q$\_($i$)=0\mathrm{.}015($m$^(3))/($s$)).$ At t$=0$ the inflow valve is closed and so there is no inflow for $\{$:t$>=0).$

Scenario I:

$($i$)$ Develop a mathematical model for this liquid$-$level system.

Hint: Accumulation $=$ Input $-$ Output