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Introduction. An analysis of mathematical models of two-dimensional planned flows was carried out. Such flows are characterized by local depth-averaged velocities and local depths at each point of the flow. The mathematical model formation of the water flow is based on its division into several sections. There is a section where the flow parameters (velocity, depth, width) are kept constant at the stage of flow exit from the pipe — the inertial front. The purpose of the article and its relevance are defined.Materials and methods. By introducing dimensionless complexes on the basis of π-theorem, the formula for the length of inertial front of the water flow at its spreading from a rectangular pipe into a wide diverting channel is derived. An analogy from gas dynamics is used, namely, the transition to the plane of the velocity hodograph. Using the velocity hodograph, the distribution of depths and velocities of the flow along its longitudinal axis of symmetry and along the extreme line of current was obtained. The main computation tasks for the flow parameters have been formulated.Results. Numerical calculations of the formulated main tasks for determining flow parameters are described. Comparison with experimental data is given and the adequacy of the refined mathematical model of a two-dimensional planned flow is confirmed.Conclusions. The resulting formula for the length of the inertial front makes it possible to achieve the desired error in calculating the parameters of the water flow. With flow expansions up to 5, the relative error of the ordinates and flow velocities does not exceed 7–10 %. Calculation formulas and implemented programs will allow HTS designers to quickly and accurately determine the boundaries, speed and depth of free flow on the culvert.