Residential colony sewers of 100 mm, 150 mm, and 225 mm diameters are all laid at a gradient of 1 in 120. Which size is least likely to choke in due course (i.e., maintains better self-cleansing at this slope)?

Introduction / Context:
Sewer self-cleansing depends on achieving sufficient shear stress at the pipe invert to transport solids. For a given slope, larger diameters tend to have larger hydraulic radii, affecting velocity and shear. Designers choose sizes and slopes to limit deposition and choking.

Given Data / Assumptions:

• Common gradient: S = 1/120 for all three pipes.
• Same roughness and similar flow regime expectations.
• Comparative question: which size is least likely to choke at this slope.

Concept / Approach:

With Manning’s relation, V ∝ R^(2/3) * S^(1/2) for a given roughness. At the same slope, increasing diameter increases hydraulic radius R for partially full flows typical in sewers. Greater R generally gives higher velocity and bed shear, improving self-cleansing conditions and reducing choking risk, all else equal.

Step-by-Step Solution:

Verification / Alternative check:

Practical experience confirms that very small sewers (e.g., 100 mm) are prone to deposition unless steeper slopes or frequent connections (creating turbulence) are present.

Why Other Options Are Wrong:

100 mm and 150 mm diameters have lower hydraulic radii and are more vulnerable to deposition at the same slope; “All of these” is incorrect because size influences self-cleansing; “None” is also incorrect.

Common Pitfalls:

Assuming velocity is independent of pipe size at the same slope; ignoring partial-flow behavior and solids transport criteria.

Final Answer:

225 mm diameter