In a recent paper, a consistency correction for the water flux using multiple flow direction (MFD) algorithms that account for exchanges between a cell and its neighbors was proposed, thanks to a reinterpretation of the MFD as a well chosen discretization of the Gauckler-Manning-Strickler continuous equation. Building on those results, we introduce here a general framework allowing to derive consistent expressions of the water flux for the most commonly used multiple/single flow direction (MFD/SFD) water flow routines, including versions in which water is flowing from a node to its neighbors. This general framework is shown to be sufficiently general to encompass the alternative continuous definition of the unit catchment area of the literature. Numerical examples illustrate the consistency and convergence of the proposed water flux reconstructions.