$F(t)=0\mathrm{.}4w^{155}\sqrt[\phantom{2}]{(2g)}$

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 $=11\mathrm{.}2f{t}^2$

$w=30ft$

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

DEPARTMENT OF CHEMICAL ENGINEERING

$2024$ PCI$360$S$-$PROCESS CONTROL AND INSTRUMENTATION

GRADUATE ATTRIBUTE ASSESSMENT ASSIGNMENT

GA$2-$ Application of scientific and engineering knowledge

Start Date: $24$ April $2024$

End Date: $8$ May $2024$

You perform a unit step change to the inflow to monitor the change in the height. The following changes of height were observed during your investigation.

$\backslash$table$[[$Time $($s$),$Change in Height $($m$)],[0,0\mathrm{.}0081],[0\mathrm{.}05,0\mathrm{.}00837],[0\mathrm{.}1,0\mathrm{.}0085],[0\mathrm{.}15,0\mathrm{.}00852],[0\mathrm{.}2,0\mathrm{.}0086],[0\mathrm{.}25,0\mathrm{.}0088],[0\mathrm{.}3,0\mathrm{.}0089],[0\mathrm{.}35,0\mathrm{.}00897],[0\mathrm{.}4,0\mathrm{.}00894],[0\mathrm{.}45,0\mathrm{.}00897],[0\mathrm{.}5,0\mathrm{.}00898],[0\mathrm{.}55,0\mathrm{.}008975],[0\mathrm{.}6,0\mathrm{.}008998],[0\mathrm{.}65,0\mathrm{.}00899],[0\mathrm{.}7,0\mathrm{.}008999],[0\mathrm{.}75,0\mathrm{.}00897],[0\mathrm{.}8,0\mathrm{.}00895],[0\mathrm{.}85,0\mathrm{.}00898],[0\mathrm{.}9,0\mathrm{.}00899],[0\mathrm{.}95,0\mathrm{.}00899],[1,0\mathrm{.}009]]$

Develop an empirical model for a first order system from the process data, that relates the change height in the tank to the inlet flow.