Theoretical Stable Hydraulic Section based on the Principle of Least Action

Despite decades of effort, stable hydraulic geometry for an open channel water flow has hardly been established because of too many unknown variables for too few rational relationships. This article derives the most efficient channel cross section using calculus of variations for the given flow area at the minimum wetting perimeter length, which is equivalent to the principle of least action. Analysis indicates that water can most efficiently flow in a semi-ellipse section channel with minimum friction and erosion. Anisotropy in channel erodibility was found to be necessary in the natural stable channel characterization because gravitation force and channel bank consolidation cannot be ignored in earth surface material. This channel cross section, based on the principle of least action, may be regarded as the theoretical stable hydraulic section for erodible bed, which was comparable to the observed river cross-sections during high flow periods.