Specific Momentum and Energy for Flow through a Wide Quasi-Rectangular Channel

Specific energy and momentum are two fundamental quantities to investigate associated water depths, i.e., subcritical and supercritical, for open channel flow passing through wide rectangular channels. Historically, alternative or sequent depths were often used because there were no analytical solutions for flow depths with clear mathematical steps. In this study, we provide primarily detailed derivation procedures of the analytic solutions for the two water depths in specific momentum and energy equations without using symbolic software. More importantly, we found reciprocal relationships between the water depths of the specific energy and momentum and generalized specific energy and momentum equations for the quasi-rectangular channel geometries with varying depths.