Open-Channel Design – Meaning of “Most Economical” Cross-Section A channel section is said to be most economical when, for a given cross-sectional area and bed slope, it conveys the maximum discharge, which equivalently corresponds to a minimum wetted perimeter and often results in less excavation for the required discharge.

Introduction:Hydraulic engineers seek channel geometries that carry the largest flow for a given area and slope, thereby reducing friction losses. Such sections are called “most economical” or “most efficient” and are central to irrigation, drainage, and flood conveyance design.

Given Data / Assumptions:

• Uniform open-channel flow on a given bed slope and roughness.
• Fixed flow area (or design discharge and slope).
• Wetted perimeter influences frictional resistance via hydraulic radius.

Concept / Approach:

For Manning or Chezy relations, discharge Q is proportional to A * R^(2/3) (Manning) or A * sqrt(R) (Chezy) for a given slope, where R = A / P is hydraulic radius, A is area, and P is wetted perimeter. Maximizing Q at fixed A is therefore equivalent to maximizing R, which in turn means minimizing P. Practical excavation volumes also drop when the perimeter is minimized for the same area, translating to less lining and earthwork.

Step-by-Step Solution:

Verification / Alternative check:

Known optimal proportions (e.g., b = 2y for rectangular channels) arise from minimizing P for a given A, confirming the equivalence of the criteria.

Why Other Options Are Wrong:

Selecting any single statement ignores the equivalence among these conditions under standard friction laws; hence “all of the above” is most appropriate.

Common Pitfalls:

Confusing “most economical” with “cheapest” in absolute cost without hydraulic equivalence; forgetting roughness and side-slope constraints can modify the geometric optimum.

Final Answer:

all of the above