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)?

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:

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