Moment of momentum equation for curvilinear free-surface flow

Abstract

The control volume approach in fluid mechanics relies upon the conservation of energy, momentum and angular momentum. However, open channel flows are typically related to only conservation of energy and momentum. Thus, for flows of non-uniform velocity and non-hydrostatic pressure distributions, the number of unknowns is larger than that of equations for depth-averaged models. This gap resulted in semi-empirical approaches either using momentum or using energy conservation. However, a more fundamental depth-averaged model may be developed by accounting for angular momentum balance. This basic approach was largely overlooked in hydraulic practice. The generalized form of the control volume conservation laws in curvilinear flow are presented herein, including the angular momentum balance. The development is used to prove that the classical Boussinesq-type solution does not satisfy the angular momentum balance. A more general Boussinesq approach is considered and applied to the 2D free overfall, indicating its ability to reproduce the salient flow features.