For the design of hydraulic structures, it is necessary to use special methods for calculating the water flow to determine the kinetic energy acting on the structures. A mathematical model of a two-dimensional in terms of stationary open water flow and boundary conditions in the problem of free spreading are formulated. The main solved and to be solved problems of determining the flow parameters are determined, its reduction to a dimensionless form by various transformations of coordinates and flow parameters. The method proposed by I.A. Sherenkov. The solution of the problem is described, which depends on the dimensionless parameter - the Froude criterion at the outlet of the flow from the pipe. With Froude numbers exceeding one or close to it, it is required to build a series of graphs or develop a unified theory, an algorithm for solving the problem. The general conclusions on the work are as follows: - the need for further research has been proven theoretically and experimentally. - tasks are formulated that must be performed, solved in order to obtain a result adequate to the real process of solving the problem of free spreading of a turbulent flow to the entire spectrum of parameters. - substantiated the need to continue research to determine the entire spectrum of parameters of a stationary open two-dimensional potential flow in terms of its outflow from a free-flow pipe into a wide horizontal smooth channel. - the requirements for the model taking into account the conjugation of a uniform flow with a radial flow in the form of a simple wave are determined The work was written with a critical assessment of existing methods for solving the problem and to substantiate the relevance of further scientific research.