Velocity field of a liquid stream in a spiral channel of rectangular cross section

Abstract

The equations for the velocity distribution of an ideal incompressible liquid in a rectangular tube twisted along a spiral line are established within the framework of the theory of a uniform spiral stream [1]. On the basis of the equations obtained, a numerical calculation is made of the velocity field in a hydroseparator [2] designed for the enrichment of valuable minerals. The results obtained are compared with the available experimental data, indicating their satisfactory qualitative agreement. Secondary flows develop during the flow of a liquid in curvilinear channels. The liquid near the upper and lower walls flows toward the inner side wall while the liquid in the central part of the stream flows from the inner to the outer walls. A qualitative explanation of this phenomenon is given in [3, 4]. Despite the fact that viscous forces play an important role in the formation of the secondary flow, a correct description of the flow structure can be obtained within the framework of the Gromeka equation. Good qualitative and quantitative agreement between experimental data and theoretical calculations of vortex flows made on the basis of the Gromeka equation has been obtained in many reports ([1, 5], for example).