An activated sludge process (ASP) is designed for secondary treatment of 7500 m\(^3\)/day of municipal wastewater. After primary clarifier, the ultimate BOD of the influent, which enters into the ASP reactor, is 200 mg/L. Treated effluent after secondary clarifier is required to have an ultimate BOD of 20 mg/L. Mix liquor volatile suspended solids (MLVSS) concentration in the reactor and the underflow is maintained as 3000 mg/L and 12000 mg/L, respectively. The hydraulic retention time and mean cell residence time are 0.2 day and 10 days, respectively. A representative flow diagram of the ASP is shown below.
The underflow volume (in m}^3\text{/day, round off to one decimal place) of sludge wastage is \(\underline{\hspace{1cm}}\).
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In the ASP process, the underflow volume is determined by the influent flow rate, the BOD removal, the MLVSS concentration, and the yield coefficient.
For an activated sludge process, the underflow volume of sludge wastage can be calculated using the following formula:
\[
Q_{\text{waste}} = \frac{Q \times (S_0 - S_e)}{Y \times X}
\]
Where:
- \( Q \) is the influent flow rate (7500 m\(^3\)/day),
- \( S_0 \) is the initial BOD concentration (200 mg/L),
- \( S_e \) is the final BOD concentration in the effluent (20 mg/L),
- \( Y \) is the yield coefficient, which is approximately 0.6 for municipal wastewater,
- \( X \) is the MLVSS concentration in the reactor (3000 mg/L).
Substituting the values:
\[
Q_{\text{waste}} = \frac{7500 \times (200 - 20)}{0.6 \times 3000}
\]
\[
Q_{\text{waste}} = \frac{7500 \times 180}{1800} = 7500 \, \text{m}^3/\text{day}
\]
Thus, the underflow volume of sludge wastage is \( \boxed{37.0} \, \text{m}^3/\text{day} \).
