A wastewater plant must meet a discharge standard of $20m\frac{g}{l}$ BOD. The design flow rate is $1000\frac{m^3}{d}$ with an expected influent BOD of $280m\frac{g}{l}.$ For anticipated conditions the $1^{st}$ order reaction rate constant will be $0\mathrm{.}45d^{-1}.$ To achieve this rate, the reactor cannot be more than $1\mathrm{.}5m$ deep. With a $($totally subjective$)$ criteria that CSTR$\text{'}$s are optimized when square in plan and PFR$\text{'}$s are optimized when the L:W ratio is $6$:$1,$ determine the dimensions for a PFR and single CSTR$.$ Re$-$determine the system dimensions if the single CSTR were divided into $4$ equally$-$sized CSTR$\text{'}$s$.$ Sketch a plan footprint of the PFR system that maintains the required dimensions, but allows the system to be constructed on an approximately square footprint.