$(20$ pts$)$ A $4-$liter CSTR is being used for conducting a kinetic study for the enzyme$-$ catalyzed consumption of substrate $S.$ Five experiments are conducted using the same inlet substrate concentration, $S_O,$ of $80$mmo$\frac{l}{L}$ but five different volumetric flow rates. The enzyme concentration is kept constant in all experiments. Estimate the Michaelis kinetic parameters and the rate equation for this reaction.

$\backslash$table$[[$Flow rate $(\frac{L}{h}),0\mathrm{.}60,0\mathrm{.}80,1\mathrm{.}00,1\mathrm{.}20,1\mathrm{.}40],[$Exit substrate $(mmo\frac{l}{L}),3\mathrm{.}2,6\mathrm{.}5,9\mathrm{.}8,13\mathrm{.}5,22\mathrm{.}1]]$