Parameter & design criteria* Equation* & obtained value BOD5/BODu = 0.666% BODu/Xb = 1.42% Desired effluent SS = 25 mg/l Biodegradable fraction (generating solids) = 0.65 Desired effluent BOD = 20mg/l ${S}_{ss}=\frac{{\text{BOD}}_{\text{5}}}{{\text{BOD}}_{\text{u}}}\ast \left[\frac{{\text{BOD}}_{\text{u}}}{{X}_{b}}*S{S}_{b}/S{S}_{e}\right]=15.4\text{mg/l}$ ${S}_{\text{sol}}={S}_{\text{total}}-{S}_{\text{ss}}=4.6\text{mg/l}$ Sludge age, θc = 10 days S0 = 212.8 mg/l Yield coefficient, Y = 0.5 MLVSS concentration = 3500 mg/l Endogenous respiration coefficient, Kd = 0.057d−1 at (15˚C) $V=\frac{Y{\theta }_{c}{Q}_{ave}\left({S}_{o}-{S}_{sol}\right)}{\text{MLVSS}\left(1+{K}_{d}{\theta }_{c}\right)}=5,684{\text{m}}^{3}$ Return sludge ratio Qr/Q = 0.8 Concentration of recycle sludge, Xr = 10,000 mg/l ${\theta }_{c}=\frac{V\ast X}{\left({Q}_{W}\ast {X}_{r}\right)+\left({Q}_{e}\ast {X}_{e}\right)}$ $\to \text{sludgewasterate},{Q}_{W}=174{\text{m}}^{\text{3}}\text{/}d$ Hydraulic detention time, $\text{HRT}=V/\left(Q\right)=0.19d$ $\frac{F}{M}=\frac{{S}_{0}}{\text{HRT}\ast \text{MLVSS}}=0.32{d}^{-1}$