Primary settling tank sizing: A rectangular tank 24 m long, 6 m wide, and 3 m deep is designed for a detention time of 2 hours. What is the allowable sewage flow rate (m^3 per hour)?
Civil Engineering
Waste Water Engineering
Difficulty: Easy
Choose an option
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A204 cu m
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B208 cu m
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C212 cu m
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D216 cu m
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E220 cu m.
Answer
Correct Answer: 216 cu m
Explanation
Introduction / Context:
Sedimentation tank detention time is a fundamental design check linking tank volume to flow. Given geometry and detention time, we can directly compute the allowable volumetric flow rate.
Given Data / Assumptions:
- Length L = 24 m, Width B = 6 m, Water depth H = 3 m.
- Detention time t = 2 hours.
- No allowance for sludge storage is requested; use gross volume for this calculation check.
Concept / Approach:
Detention time t = V / Q. Therefore, Q = V / t. Compute the tank volume from its rectangular plan and depth.
Step-by-Step Solution:
V = L * B * H = 24 * 6 * 3 = 432 m^3.t = 2 hours, so Q = V / t = 432 / 2 = 216 m^3 per hour.Match with the closest option: 216 cu m.Verification / Alternative check:
Unit check: m^3 divided by hours gives flow in m^3/h, which is correct. A quick sense-check shows that halving the volume would halve the detention time, matching proportional expectations.
Why Other Options Are Wrong:
- 204, 208, 212, 220 m^3/h are numerical distractors; only 216 m^3/h equals 432/2.
Common Pitfalls:
- Mistakenly using area instead of volume in the formula.
- Mixing minutes and hours, causing unit errors (e.g., 120 minutes vs 2 hours).
Final Answer:
216 cu m