$[10$ points$]$

A CMBR reactor is being designed to remove $80\%$ of BOD by weight from a surface water body for

potable water treatment. The body of water produces an influent water stream with a $S_0=0\mathrm{.}75\frac{g}{m^3}.$

Total surface area of the reactor upon which biofilm grows is $5,000m^2.$ The reactor is known to have a

specific loss rate of $1\mathrm{.}4$ days ${?}^{-1}$ and a solid retention time of $20$ hours. Biofilm mass density is $15\frac{g}{m^3}$

and average biofilm thickness is $0\mathrm{.}3mm.$ The treatment process yields $0\mathrm{.}333g$ of volatile suspended

solids per $g$ of BOD.

a$)$ Determine appropriate flow rate to achieve the desired BOD reduction.

b$)$ Determine active biomass in the CMBR bulk liquid $(\{$:$x_a).$