GATE 2023 CE (CE1) – Question 64
The wastewater inflow to an activated sludge plant is 0.5 m$^3$/s, and the plant is to be operated with a food to microorganism ratio of 0.2 mg/mg-d. The concentration of influent biodegradable organic matter of the wastewater to the plant (after primary settling) is 150 mg/L, and the mixed liquor volatile suspended solids concentration to be maintained in the plant is 2000 mg/L. Assuming that complete removal of biodegradable organic matter in the tank, the volume of aeration tank (in m$^3$, in integer) required for the plant is _____.
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Correct answer: 16200
Explanation
The food to microorganism ratio is $\frac{F}{M} = \frac{QS_0}{VX}$. The flow is $0.5 \times 86400 = 43200$ m³/d. So $V = \frac{QS_0}{(F/M)X} = \frac{43200 \times 150}{0.2 \times 2000} = 16200$ m³ (the units of mg/L and g/m³ cancel).