Design check for circular sewers at low flow depth: if a circular sewer flows at only 0.2 of its full depth, how is the nominal gradient commonly adjusted to maintain self-cleansing velocity?

Introduction / Context:
Sewers should achieve self-cleansing velocity to prevent deposition. At shallow depths, the hydraulic radius and velocity reduce; designers compensate by increasing the gradient (slope) relative to that required at half-full or full-flow reference conditions.

Given Data / Assumptions:

• Circular gravity sewer designed by Manning’s equation.
• Operating depth is only 0.2 of full diameter.
• Target is to maintain adequate velocity for self-cleansing.

Concept / Approach:

Velocity V ∝ R^(2/3) * S^(1/2) for a given roughness n. At y/D = 0.2, both hydraulic radius and area reduce; therefore, to recover target velocity, S must be increased compared to the “nominal” slope used at more favorable depths (e.g., 0.5D). Empirical practice tables suggest multiplying slope, and a common rule-of-thumb is to treble the nominal gradient for y/D ≈ 0.2.

Step-by-Step Solution:

Verification / Alternative check:

Use partial-flow charts/tables (ratio V/V_full vs y/D) to confirm that tripling the slope yields required V for the pipe size and roughness.

Why Other Options Are Wrong:

(a) Keeping slope unchanged would likely underperform; (b) doubling may still be insufficient; (d) overly pessimistic—proper design can achieve self-cleansing.

Common Pitfalls:

Ignoring minimum velocity criteria; using nominal slope without low-flow checks; not accounting for silt-laden inflows.

Final Answer:

Nominal gradient is trebled.