In the planar hydraulics, the problems with previously unknown boundaries are most difficult. The best adequacy in terms of flow parameters is provided by simplified analytical methods based on a potential flow model. A mathematical model of a stationary, potential, 2D planar high-velocity open water flow of an ideal fluid, freely spreading back from a non-pressure orifice is studied. The boundary problem of flow free spreading in plane were formulated. Studying the system of dimensionless equations of motion resulted in identification of the criteria influencing the process of flow spreading. A critical analysis was carried out and a description of various methods for solving the problem of free spreading of a high-velocity water flow was given. The problem in an analytical form was solved in the velocity hodograph plane. All flow parameters are determined in the physical plane. For the first time, the conjugating flow "simple wave" was applied. The proposed analytical method for solving the problem of flow free spreading is effective, unambiguous and has no singularities and discontinuities, particularly, at the outlet of a non-pressure pipe. The adequacy of the mathematical model was verified on a test example. The relative error of the flow parameters does not exceed 10 % compared to the experimental data.