Hydraulic radius comparison – full circular pipe vs full square conduit If a circular pipe runs full and a square conduit runs full with its side equal to the pipe diameter D, what is the ratio R_pipe / R_square of their hydraulic radii?

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:

• Circular pipe of diameter D, running full.
• Square conduit with side equal to D, running full.
• Wetted perimeter equals the entire inner boundary for both, because they are full.

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