Abstract
In this work, a mathematical model of the movement of the water flow and an optimal unified design of a hydro turbine are developed, which is protected by an innovative patent of the Republic of Kazakhstan. Thus, as a result of the research, a new empirical−analytical mathematical model of the primary energy converter for low−capacity hydroelectric power plants was obtained. The study of the model has shown its sufficient adequacy and the possibility of using it to analyze the operation of the installation in both static and dynamic modes. The results obtained in this work can be used as part of a model of hydroelectric power plants of different types and capacities.