$$

You are a chemical engineer employed at Distell $($Heineken Beverages Home$),$ and you are responsible for overseeing the distillation. You are tasked by your line manager to control the flow of wine on the trays of the distillation column. The figure below shows the schematic diagram of the tray. The flow of the tray is given by the Francis weir formula

$F(t)=0\mathrm{.}4w{h}^{1\mathrm{.}5}\sqrt[\phantom{2}]{(2g)}$

Where

$h(t)=$ liquid level $on$ tray above the top $of$ the weir, $ft$

$w=$ width $of$ the weir over which the liquid overflows, $ft$

$g=$ acceleration due $to$ gravity, $32\mathrm{.}2f\frac{t}{s^2}$

The steady$-$state inlet flow and process parameters are as follows:

Tray cross$-$sectional area $=11\mathrm{.}2f{t}^2$

$w=30ft$

$F_0(0)=30f\frac{t^3}{sec}$