a plant has a primary effluent flow of 3.1 mgd with a tss of 68 mg/l. it flows into an aeration tank with a capacity of 340,000 gal. what is the sludge age if the mlss concentration is 2400 mg/l?

3.9 days
5.9 days
6.7 days
4.4 days

Question

a plant has a primary effluent flow of 3.1 mgd with a tss of 68 mg/l. it flows into an aeration tank with a capacity of 340,000 gal. what is the sludge age if the mlss concentration is 2400 mg/l?

3.9 days
5.9 days
6.7 days
4.4 days

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Applied Math Calculations", "Unit Conversion" ], "new_concepts": [ "Sludge Age Calculation", "Wastewater Process Control" ], "current_concepts": [ "Applied Math Calculations", "Unit Conversion", "Sludge Age Calculation", "Wastewater Process Control" ] } ## Calculate the mass of MLSS in the aeration tank $$ \begin{aligned} V_{\text{tank}} &= 340,000\text{ gal} = 0.34\text{ MG} \ \text{MLSS mass} &= V_{\text{tank}}\text{ (MG)} \times \text{MLSS concentration (mg/L)} \times 8.34\text{ lbs/gal} \ \text{MLSS mass} &= 0.34 \times 2400 \times 8.34 = 6805.44\text{ lbs} \end{aligned} $$ ## Calculate the daily mass of TSS entering the aeration tank $$ \begin{aligned} \text{TSS mass flow} &= Q\text{ (MGD)} \times \text{TSS concentration (mg/L)} \times 8.34\text{ lbs/gal} \ \text{TSS mass flow} &= 3.1 \times 68 \times 8.34 = 1758.072\text{ lbs/day} \end{aligned} $$ ## Calculate the sludge age $$ \begin{aligned} \text{Sludge Age} &= \frac{\text{MLSS mass (lbs)}}{\text{TSS mass flow (lbs/day)}} \ \text{Sludge Age} &= \frac{6805.44}{1758.072} \approx 3.87\text{ days} \approx 3.9\text{ days} \end{aligned} $$

(A) 3.9 days

(B) 5.9 days

(C) 6.7 days

(D) 4.4 days

{ "subject": "Natural Science", "question_type": "Multiple Choice", "knowledge_point": [ "Natural Science", "Environmental Science", "Wastewater Treatment Calculations" ] }

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Question

Explanation:

Calculate the mass of MLSS in the aeration tank

Calculate the daily mass of TSS entering the aeration tank

Calculate the sludge age

Answer: