Author(s): Sergei Sokolov

Linked Author(s): Sergei Sokolov

Keywords: Shallow water; Long wave; Unsteady fluid flow; Water discharge; Mean flow velocity

Abstract: In the paper, an analytical solution for the problem of long waves in shallow water is proposed. A simple wave in a horizontal cylindrical channel is considered. The area ω of the cross-section is approximated by the relationship ω=Ah^n, where h is the depth of water in the lowest point of the cross-section, А and n are the numerical parameters. The expression describes wide range of cross-sectional shape of cylindrical channels as well as two variants of prismatic ones. For instance, values of factor n=1 and n=2 correspond to rectangular and triangular cross-section, respectively. Also the cross-section contour is limited by a parabola of general view such as y=ax^k where y, x are the water edge coordinates, k and a are the parabola parameters. The wave is generated by a vertical plate under the action of a constant force. The movement of the fluid tends to a steady and uniform flow. Earlier, a general solution for the wave velocity was obtained for this problem. The proposed solution is its development. It makes possible to calculate the mean water velocity and the water discharge in the steady- flow phase depending on the value of the driving force and the shape of the channel cross-section. The solutions are independent of the fluid viscosity. The solution is general. It allows one to analyze the influence of the cross-sectional shape on the flow parameters. The results of calculations of the flow velocity and the water discharge for several variants of channels with a rectangular cross-section are presented. It was found that the channel width is more significant than the flow depth for the capacity of channel

DOI: https://doi.org/10.3850/IAHR-39WC2521711920221728

Year: 2022