A steady CSTR receives 300 L/hour with substrate concentration 150 mg/L. Required treatment efficiency is 76%. Substrate decay is half-order with $k=.05\,(\mathrm{mg/L})^{1/2}/\mathrm{hour}$. Find reactor volume in integer m³.
A completely mixed reactor has the effluent concentration throughout its contents: $S=150(1-.76)=36$ mg/L. Half-order removal rate is $r=kS^{1/2}=.05\sqrt{36}=.3$ mg/L/hour. Steady balance gives $V=Q(S_0-S)/r=300(150-36)/.3=114000$ L. Dividing by 1000 gives **114 m³**.
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