Most economical circular channel for maximum velocity (open-channel flow) For a circular channel carrying water (not running full), the section that gives maximum mean velocity satisfies which of the following conditions?

Introduction / Context:For a given circular conduit running partially full as an open channel, there is a specific depth that maximizes the mean velocity (equivalently minimizes hydraulic losses per unit area). This is often called the most economical circular section for velocity in open-channel hydraulics.

Given Data / Assumptions:

• Circular conduit flowing with a free surface (not pressurized).
• Resistance described by Manning or Chezy; objective is to maximize V ∝ R^(2/3) for given slope and roughness.
• Geometry relates depth, area, and wetted perimeter via the central angle of the wetted segment.

Concept / Approach:

By differentiating V with respect to depth (or equivalently maximizing R = A/P), the optimal depth occurs at y ≈ 0.81 D. The corresponding geometric relations yield R ≈ 0.304 D and wetted perimeter P ≈ 2.245 D.

Step-by-Step Solution:

Verification / Alternative check:

Standard hydraulics tables list the same ratios for the most economical circular section for maximum velocity, confirming the results.

Why Other Options Are Wrong:

Each item (a), (b), and (c) is individually correct; therefore, any single selection is incomplete. The comprehensive correct choice is “all the above.”

Common Pitfalls:

Confusing “maximum velocity” with “maximum discharge” depth (which has a different optimal ratio); applying full-pipe relations to free-surface flow.

Final Answer:

all the above