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For the complete mixed activated sludge system shown below, given $S_0=400m\frac{g}{L},Q_0=400\frac{L}{s},Q_R$

$=150\frac{L}{s},V_r=1000m^3,S_1=S_2=30m\frac{g}{L},U=2\mathrm{.}25{10}^{-4}m\frac{g}{m}g.s,$

a$)$ Write a mass balance on substrate under steady$-$state conditions and derive equations for the concentration

of biomass $x$ in each reactor as a function of the food uptake rate $U.$

b$)$ Calculate $S,$ in $m\frac{g}{L}.$ ANSWER: $S=300m\frac{g}{L}$

c$)$ Calculate $x_1$ and $x_2,$ in mg$/$L$.$ ANSWER: $x_1=219\mathrm{.}3m\frac{g}{L},x_2=438\mathrm{.}5m\frac{g}{L}$