GATE 2026 CE (CE1) – Question 63
An Activated Sludge Process (ASP) has an inlet wastewater flowrate of 20000 m$^3$/day with a Biochemical Oxygen Demand (BOD) concentration of 250 mg/l. It produces treated wastewater containing 20 mg/l BOD. The aeration tank has a working volume of 6000 m$^3$ and a biomass concentration of 3000 mg/l. Biological Sludge Residence Time (BSRT) of the system is 6 days. The influent wastewater and the treated effluent from the system have negligible concentrations of biomass. The sludge recycle line from the bottom of the Secondary Sedimentation Tank (SST) to the inlet of the aeration tank has a flowrate of 6000 m$^3$/day.
To maintain equilibrium, the flowrate (in m$^3$/day) of sludge that is to be wasted from the system is ______ (*in integer*).
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Correct answer: 1000
Explanation
The sludge residence time is $\theta_c = \frac{V X}{Q_w X_w + Q_e X_e}$. The effluent carries negligible biomass. Taking the waste to be drawn at the aeration tank concentration, $\theta_c = \frac{V}{Q_w}$, so $Q_w = \frac{6000}{6} = 1000$ m$^3$/day.