The selection of pumps as turbines (PATs) for their respective use in energy optimisation systems is a complicated task, because manufacturers do not provide the characteristic curves. For this reason, some research has been carried out to predict them with computational fluid dynamics (CFD) and mathematical models. The purpose of this study is to validate these two prediction methodologies of flow (Q) vs. head (H) curves through numerical modelling using the computational package OpenFOAM, together with a comparison with the experimental data obtained from a PAT for the case in which the nominal rotation speed of the machine varies. Depending on the configuration and working conditions of the PAT, the simulation performed with OpenFOAM was validated by calibrating it with the nominal curve of the pump and with another simulation performed with CFD workbench SOLIDWORKS FloEFD. Subsequently, the second methodology related to the analyses and mathematical models proposed to predict the Q vs. H curves were also validated with new models in OpenFOAM and the experimental data. The results show that these prediction methods are effective when a machine’s operating point is close to the BEP (best efficient point). The absolute error ranges obtained with these two prediction methodologies for rotation speeds of 880 rpm, 1020 rpm, 1200 rpm, and 1500 rpm are between 5 and 24%, 2 and 17%, 0 and 12%, and 1 and 24%, respectively.