GATE 2019 CE (CE2) – Question 52

Water and Waste Water Quality and Treatment · Unit processes and operations · 2 marks · Numerical answer

The shown reactor handles flow Q m³/h, with influent and effluent concentrations C0 and C mg/L. First-order degradation occurs. Mixing can make it either a completely mixed flow reactor (CMFR) or plug-flow reactor (PFR). Adjust length for each while holding cross-section fixed. At steady state and C/C0 = 0.8, find LCMFR/LPFR, to two decimal places.

Diagram for GATE 2019 CE (CE2) question 52

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Correct answer: 1.10 to 1.15

Explanation

With equal flow and cross-section, length is proportional to residence time. First-order CMFR time is $(C_0/C-1)/k=0.25/k$. PFR time is $\ln(C_0/C)/k=\ln1.25/k$. Ratio is $0.25/\ln1.25=$ **1.12**.