Most Economical (Hydraulically Efficient) Channel Shape Among common prismatic open-channel sections used in practice, which cross-section is generally considered the most hydraulically efficient for conveying discharge (given similar area and roughness)?

Introduction:
A channel section is termed “most economical” or “most hydraulically efficient” when it carries the maximum discharge for a given area, bed slope, and roughness—equivalently, when the wetted perimeter is minimized, maximizing the hydraulic radius R = A / P.

Given Data / Assumptions:

• Comparison limited to practical prismatic sections used in fieldwork.
• Similar roughness and slope; steady uniform flow conditions.
• Feasible constructability and stability of banks are considered.

Concept / Approach:
The theoretically best (maximum R) is a semicircular channel, but it is rarely used at scale. Among common practical forms, the trapezoidal section—optimized with the condition that one-half of the top width equals one of the equal side lengths—yields the least wetted perimeter for a given area, providing superior efficiency over rectangular/triangular forms.

Step-by-Step Solution:
Define hydraulic radius R = A / P; larger R reduces frictional resistance.For a given area A, minimize P. The trapezoid allows both bottom width and side slopes to be tuned to minimize P.Optimal trapezoid (most economical) satisfies: hydraulic mean depth = half the flow depth, and side slopes chosen so one side equals half the top width; this increases R beyond rectangular/triangular shapes.

Verification / Alternative check:
Design handbooks list conditions for most economical trapezoidal and rectangular channels; the trapezoid consistently offers better efficiency and bank stability in practice.

Why Other Options Are Wrong:
Rectangular and square are special cases with higher wetted perimeter for the same area when not at their own “most economical” proportions; triangular channels are typically less efficient and less stable.

Common Pitfalls:
Confusing theoretical semicircular optimum with practical sections; ignoring side-slope stability and erosion criteria.

Final Answer:
trapezoidal