Q$8.$ A $300m\frac{3}{d}$ wastewater with a soluble COD concentration of $180m\frac{g}{L}$ is to be treated in a completely activated$-$sludge process for BOD removal with nitrification at $15C$ and $2500m\frac{g}{L}$ MLVSS concentration, assuming $70$ percent BOD removal. Mechanical surface aerotors are used to provide a DO concentration in the aeration zone of $2\mathrm{.}0m\frac{g}{L}.$ Using the kinetic coefficients and assumptions provided below determine,

a$)$ Effluent $NH4-N$ concentration $(m\frac{g}{L})(10)$

b$)$ Hydraulic retention time $($HRT$)($hour$)(10)$

$\backslash$table$[[$Parameter$,$Unit,Value$],[$sCOD$/$BOD$,\frac{g}{g},1\mathrm{.}6],[$TKN$,m\frac{g}{L},40],[{}_{\text{N}\text{m}\text{a}\text{x}},gVS\frac{S}{g}VSS.d,0\mathrm{.}75],[K_{o2},m\frac{g}{L},1\mathrm{.}4],[K_N,gN{H}_4-\frac{N^2}{m^3},0\mathrm{.}74],[Y,gVS\frac{S}{g}CO{D}^3$ removed,$0\mathrm{.}6],[Y_N,gVS\frac{S}{g}N{H}_4-N,0\mathrm{.}12],[k_d,gVS\frac{S}{g}VSSd,0\mathrm{.}08],[k_{dN},gVS\frac{S}{g}VSS.d,0\mathrm{.}05],[$Safety factor,$-,1\mathrm{.}5],[pH,,7\mathrm{.}2]]$