Hydraulic Mean Depth (Hydraulic Radius) — Full Circular Pipe For a circular pipe of diameter d flowing full, the hydraulic mean depth R = A/P equals:

Introduction:The hydraulic mean depth (hydraulic radius) R = A/P is a key parameter in flow formulas such as Chezy and Manning. For common sections, closed-form expressions exist, simplifying design checks.

Given Data / Assumptions:

• Circular conduit of diameter d flowing full.
• Area A = (pid^2)/4, Wetted perimeter P = pid.
• Steady uniform flow conceptually.

Concept / Approach:Apply the definition R = A/P directly to the circular section values.

Step-by-Step Solution:Compute A = (pid^2)/4.Compute P = pid.Then R = A/P = [(pid^2)/4]/(pid) = d/4.

Verification / Alternative check:Dimensional check: R has dimensions of length; d/4 has length, consistent. Known tables list R = d/4 for a full circular pipe, confirming.

Why Other Options Are Wrong:d/6 and d/2 and d are not obtained from A/P for the full circular case; they may appear in other hydraulic relations (e.g., depth to centroid), but not R.

Common Pitfalls:Confusing hydraulic radius with radius of the pipe; using diameter in place of wetted perimeter for partially full conditions; mixing up A/P with perimeter/area.

Final Answer:d/4