Most Efficient Depth for Circular Channel – Condition for Maximum Discharge The discharge through an open channel of circular section is maximum when the flow depth is approximately 0.81 times the diameter of the circular channel (y ≈ 0.81 D).

Introduction:
For partially full circular conduits used as open channels, one can find a depth that maximizes discharge for a given slope and roughness. This “most efficient” depth is a standard design datum in sewer and stormwater engineering.

Given Data / Assumptions:

• Steady, uniform open-channel flow in a circular section.
• Friction laws such as Manning or Chezy apply.
• Diameter D is fixed; depth y varies with the central angle of wetted segment.

Concept / Approach:

Discharge Q is proportional to A * R^(2/3) for a given slope and roughness (Manning’s equation), where area A and wetted perimeter P depend on the wetted central angle. Maximizing Q with respect to depth yields the condition y/D ≈ 0.81, a widely tabulated result.

Step-by-Step Solution:

Verification / Alternative check:

Design charts for circular conduits show peak Q near y/D ≈ 0.8–0.82 for typical friction laws, validating the rule of thumb 0.81.

Why Other Options Are Wrong:

0.34 and 0.50 are too shallow and reduce area. 0.67 under-utilizes the section. 0.95 is near full, where increased perimeter outweighs area gain.

Common Pitfalls:

Confusing the depth for maximum velocity with that for maximum discharge; neglecting that the optimum is insensitive to the exact friction law but not identical to the full-flow condition.

Final Answer:

0.81 times