On the equations of open channel flow

The traditional equations for describing open channel flow have appeared in the literature for decades and are so ingrained that they might seem to be statements of settled science. Careful derivations that detail assumptions and approximations relied upon in the formulation are mostly absent. We derive mass, momentum, and energy equations by averaging their small-scale counterparts and formulate forms that are Galilean invariant as required by continuum mechanics. Averaging is over a time increment and a spatial region in a single step, clarifying the need for closure relations. The derivation leads to the Boussinesq tensor and Coriolis vector as rigorous generalizations of the Boussinesq and Coriolis coefficients typically proposed. Examples are provided for the computation of these coefficients from published data. The approach employed here can be extended to systems such as pipe flow or shallow water equations, and the Galilean invariant forms are also suitable for entropy generation analyses.