GATE 2017 CE (CE1) – Question 65

Water and Waste Water Quality and Treatment · Primary, secondary and tertiary treatment, effluent standards · 2 marks · Numerical answer

Wastewater of organic concentration 54 mg/L flows at 0.8 m³/day through a tank of dimensions 2 m × 4 m × 2 m. The contents are completely mixed and the first-order decay constant is 0.1 per day. Find steady outlet concentration in mg/L, to one decimal place.

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Correct answer: 17.9 to 18.1

Explanation

Tank volume is $V=2(4)(2)=16$ m³. A steady completely mixed balance gives $QC_{in}=QC+kVC$, so $C=C_{in}/(1+kV/Q)$. Here hydraulic residence time is $V/Q=16/0.8=20$ days. Thus $C=54/[1+0.1(20)]=18.0$ mg/L. A plug-flow exponential would be the wrong reactor model.

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