The use of pumps working as turbines (PATs) to improve the energy efficiency of water networks has been studied in the last years. This recovery system is justified due to a low investment contrasting with the capacity to take advantage in certain points with low and medium recoverable heads. Analyses of water systems using simulation software and/or optimization algorithms need the characteristic curves (head and efficiency) of the machines, which should be known with minor error by the water managers. The knowledge of the best efficiency point (BEP) as a turbine is one of the major limitations when the user wants to choose PATs. In this sense, the present research defines new approach equations to estimate the BEP of the PAT, as well as to predict the characteristic curves, comparing the results with the rest of the published methods. The comparison demonstrated that the new proposal reduced the error indexes, improved the R 2 and increased the accuracy of the error ellipse using an experimental database of 181 different PATs.Water 2020, 12, 468 2 of 18 enable to quantify the recovered energy, and therefore, the improvement of the sustainability in the water systems [10][11][12].Although there are different methods to approach tasks (ii) and (iii) described in the previous paragraph, the majority of them use a low number of experimental data, and therefore, the committed error is high [13,14]. In this research line, the present research is focused on establishing a new analytical approach, to improve the prediction of the PAT parameters and on the simulation and energy analyses of the water systems. The research contains a deep review of experimental data of PATs that were already published (Figure 1). The database contains a high number of experimental uses; particularly, the research used 181 different PATs, 60% higher than previous studies [12]. The specific speed of the used machine was between 5.09 and 219.09 (m, kW).Water 2020, 12, 468 2 of 16Although there are different methods to approach tasks (ii) and (iii) described in the previous paragraph, the majority of them use a low number of experimental data, and therefore, the committed error is high [13,14]. In this research line, the present research is focused on establishing a new analytical approach, to improve the prediction of the PAT parameters and on the simulation and energy analyses of the water systems. The research contains a deep review of experimental data of PATs that were already published (Figure 1). The database contains a high number of experimental uses; particularly, the research used 181 different PATs, 60% higher than previous studies [12]. The specific speed of the used machine was between 5. 09 and 219.09 (m, kW)