Chezy application to a full circular sewer: In Chezy’s relation V = C √(R * S) for a circular sewer of diameter D running full, the hydraulic mean radius R equals:

Introduction / Context:The hydraulic mean radius R (also called hydraulic radius) is A/P, where A is the cross-sectional area of flow and P is the wetted perimeter. It is fundamental in Chezy and Manning equations used for sewer design.

Given Data / Assumptions:

• Circular sewer of diameter D is flowing full.
• Chezy formulation uses R = A / P.
• Standard geometry of a circle applies.

Concept / Approach:For a full circular pipe, calculate A and P, then form their ratio to obtain R. This value is constant for full-flowing circular sections and is frequently used in uniform flow calculations.

Step-by-Step Solution:Area, A = π D^2 / 4Wetted perimeter, P = π DHydraulic radius, R = A / P = (π D^2 / 4) / (π D) = D / 4

Verification / Alternative check:Dimensional reasoning confirms that R must scale with length, and D/4 is consistent with known results for a full circular conduit.

Why Other Options Are Wrong:D and D/2: overestimate R; ratio A/P does not support such large values.D/8 and D/16: underestimate R; computation shows D/4 exactly.

Common Pitfalls:

• Using hydraulic diameter (4A/P) instead of hydraulic radius (A/P).
• Confusing part-full and full-flow geometry; R varies with depth for part-full flow.

Final Answer:D/4