In open-channel hydraulics and sewer design, the hydraulic mean radius (hydraulic radius) R is defined as which of the following?

Introduction / Context:
The hydraulic mean radius R = A/P (often called hydraulic radius) is a key parameter in Manning and Chezy formulations, representing an effective depth that couples area and boundary friction in open channels and partially full pipes.

Given Data / Assumptions:

• Any prismatic channel or conduit with wetted perimeter P.
• Steady, uniform flow approximations.

Concept / Approach:

By definition, R = A/P where A is the cross-sectional flow area and P is the wetted perimeter in contact with the fluid. For a full circular pipe, R = D/4, but this is a special case; for other shapes and partial flow, R must be computed from A and P directly.

Step-by-Step Solution:

Verification / Alternative check:

Dimensions: A has L^2, P has L, so A/P has L, consistent with a length scale for hydraulic resistance.

Why Other Options Are Wrong:

(a) and (c) are not standard definitions. (b) confuses head difference with geometry. (e) is only valid for full circular pipes; the question asks a general definition.

Common Pitfalls:

Blindly using D/4 for partial-full pipes; forgetting that roughness and geometry both influence P and thus R.

Final Answer:

Cross-sectional flow area divided by wetted perimeter (A/P)