Problem of thin liquid layer distribution on angled surface

The article analyzes some features of the thin layer motion of inviscid incompressible fluid flowing along an inclined surface in the approximation of the theory of “shallow water.” Based on the proposed approach, we studied the influence of the surface inclination angle on fluid dynamics. To simplify the process of obtaining solutions, a generalized self-similar scheme is introduced, when the form of the time component is adopted without specification. Proposed substitution allows us to obtain analytical solutions in a number of special cases. The choice of the terms of the equation for the transformation enables obtaining a sufficiently large number of different solutions depending on the number of terms in the equation. Comparison with approximate solutions can be used to determine the range of variation of the special parameters obtained by using the method. The results obtained may be of interest, for example, in selecting the angle of inclination of the walls of the ditch, intercepting rainwater flowing from the hill to the road or from the roadway to the ditch.