GATE 2019 CE (CE1) – Question 52
Wastewater is dosed with 35 mg/L chlorine for 99% microorganism kill. Survival follows $N_t=N_0e^{-kt}$, where k = 0.23 min⁻¹. Flow is 36 m³/h. A chlorination tank has depth 1.5 m and width 1.0 m. Find its length (m), to two decimal places.
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Correct answer: 7.95 to 8.15
Explanation
For 99% kill, surviving fraction is 0.01. From $0.01=e^{-0.23t}$, $t=\ln100/0.23=20.0225$ min. Flow is 0.6 m³/min, so volume is 12.0135 m³. Tank length is $12.0135/(1.5\times1)=$ **8.01 m**. The chlorine dose does not enter once the rate constant is supplied.