GATE 2025 ES – Question 39
The ASP diagram labels flow Q, substrate S, microorganisms X, and aeration volume V. Subscripts 0,r, w, e, i denote influent, recycle, waste, effluent, and aeration-to-settling flow. Influent contains microorganisms. Find net volumetric microorganism formation at steady state.
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Correct answer: (A) $[(Q-Q_w)X_e+Q_wX_r-QX_0]/V$
Explanation
Take the aeration/settling/recycle system as one control volume. Recycle is internal and cancels. At steady state, net formation equals external biomass outflow minus influent biomass: $(Q-Q_w)X_e+Q_wX_r-QX_0$. Dividing by aeration volume V gives the volumetric formation rate in **A**. The influent term cannot be omitted because the question explicitly gives nonzero influent microbes.