Difficulty: Medium
Correct Answer: all the above
Explanation:
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:
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
Discussion & Comments