An industrial waste with an inlet $BO{D}_5$ of $800m\frac{g}{L}$ must be treated to reduce the exit $BO{D}_5$ level to less than $20m\frac{g}{L}.$ The inlet flow rate is $400\frac{m^3}{h}.$ Kinetic parameters have been estimated for waste as ${}_{\text{m}\text{a}\text{x}}=0\mathrm{.}20h^{-1},K_s=50m\frac{g}{L}$ of $BO{D}_5,Y_{\frac{x}{s}}=0\mathrm{.}5mgMLVS\frac{S}{m}gBO{D}_5,$ and $k_d=0\mathrm{.}005h^{-1}.$ A waste treatment unit of $3200m^3$ is available. Assume a recycle ratio of $0\mathrm{.}40$ and no biomass in the effluent stream.

If the system is operated at a value of ${}_c=120h,$ find $BO{D}_5$ in effluent stream.

What is the cell mass concentration at the outlet of the sludge reactor?

What will be the sludge production rate from this process?