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In this article the equations of channel flow of fluid are considered. They are described by the continuity equation and the momentum equation depending on the rate of flow and cross-sectional area of flow. It is shown that natural phenomena significantly affect the flow stability and received a condition that ensures the stability of unstated flow at perturbation in initial and boundary conditions. Conditions of stability are checked on test examples, which depend on the following parameters: established movement parameters and middle and bottom slope angles. It is shown that in such assumptions the system of equations of channel flow of fluid is stable, if received conditions is executed.

INVESTIGATION OF THE STABILITY FOR ESTABLISHED FLOWS IN OPEN PSEUDOPRISMATIC CHANNELS