In this paper an analysis of the viscous incompressible flow has been carried out, from the very definition of the governing equations, up to the resolution of some practical problems, passing through the comprehensive study of the stabilized finite element techniques used in their resolution. As a consequence of this analysis, a code based upon a realistic interpretation of the forces has been written, which allows for the modelling of the open channel flow, with optimum results in the resolution of some benchmark and real flow problems related with the wastewater industry.