Difficulty: Easy
Correct Answer: 1
Explanation:
Introduction / Context:
The hydraulic radius R = A/P (flow area divided by wetted perimeter) is a key geometric parameter in resistance equations such as Manning or Chezy. Comparing R across shapes running full helps benchmark frictional performance per unit area.
Given Data / Assumptions:
Concept / Approach:
Compute R for each shape: R = A/P. For the circle, A_c = π D^2/4 and P_c = π D ⇒ R_c = D/4. For the square, A_s = D^2 and P_s = 4D ⇒ R_s = D/4. The ratio is therefore 1.
Step-by-Step Solution:
Verification / Alternative check:
Dimensional consistency holds; both yield the same characteristic depth scale under full flow.
Why Other Options Are Wrong:
All other ratios differ from unity and contradict the direct A/P computation.
Common Pitfalls:
Accidentally using hydraulic depth A/T (open-channel concept) instead of hydraulic radius A/P for full-closed conduits.
Final Answer:
1
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