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An application of Computational Fluid Dynamics (CFD) using the Finite Element Method (FEN) for modeling the behavior of a 50 kW (Q = 120 l/s) Cross Flow Hydraulic Turbine is presented. H = 50 m and ω = 124.61 rad/s), with the objective of explaining in a numerical methodological way, the classical design principles and assumptions, as well as the search for their optimization. As results, pressure and velocity fields are obtained for different conditions (Q = 0 - 203.61 l/s, H = 9.40 - 580.71 m and ω = 25, 50, 100 and 125 rad/s) and regimes (laminar, transition and turbulent ) of operation, from which some indicators of turbine operation are quantified (distribution of velocity vectors in the intake section, efficiency and guideline injector coefficient, characteristic curves of the 50 kW turbine and of the unit turbine ). Finally, operating parameters of the turbine are projected for ...