Problem#$1$:

A complete mix$-$activated sludge process is being proposed to treat a municipal wastewater at a design flow rate of $8000\frac{m^3}{d}.$ Influent soluble BOD must be reduced to an effluent total $B^2{D}_5$ of $10m\frac{g}{L}.$ Influent wastewater characteristics and design requirements include the following.

soluble $BO{D}_5=235m\frac{g}{L}$

effluent soluble $BO{D}_5=0\mathrm{.}3$ effluent total $BO{D}_5$

mixed liquor volatile suspended solids $=3000m\frac{g}{L}$

temperature $=20C$

growth rate constant $=2\mathrm{.}7d^{-1}$

half$-$saturation constant $=63m\frac{g}{L}$

endogenous decay rate coefficient $=0\mathrm{.}05d^{-1}$

yield coefficient $=0\mathrm{.}23\frac{g}{g}$

design mean cell residence time $=12d$

a$)$ What is the required hydraulic residence time?

b$)$ What is the required reactor volume?

c$)$ What is the $\frac{F}{M}$ ratio?