Abstract:
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.
Keywords:thin layer of liquid, angle of inclination, shallow water, incompressible fluid, non-viscous liquid.
Fulltext:
PDF file (523 kB)