Possible Scheme of Turbulent Potential Flow Free Expansion Below the Non-Pressure Pipe

Abstract

The paper substantiates a general scheme for solving two-dimensional free spreading problem in terms of open water potential flow below the non-pressure pipe. The first link. Since a uniform flow at its outlet from a rectangular pipe with its free spreading is coupled with a non-uniform flow of a general form, then, using a theorem from the general theory of two-dimensional in terms of turbulent water potential flows, the conclusion is given: since a straight-line characteristic is always the boundary between a uniform and non-uniform flow, then only a simple wave can directly adjoin the uniform flow area. Simple waves serve as a transitional form from the uniform flow to the general non-uniform flow. Therefore, it is not entirely correct to pose the free flow spreading boundary problem, trying to satisfy only the boundary conditions and obtain an analytical solution without taking into account the intermediate flow “simple wave”. The second important link in solving the problem is a general flow choice. And it can be selected from the intermediate flow condition found by the authors in the velocity hodograph plane. Let us call this flow the “type A flow”. “Type A flow” satisfies all the requirements of the flow spreading process function. When increasing, i.e. τ tends to 1, flow depth h tends to 0; velocity V tends to the maximum. The flow depth is greater on the symmetry axis than when moving along the equipotential to the flow free boundary. Using these two links, it is possible to apply a flow coupling scheme and solve the boundary problem of determining the entire spectrum of parameters for the potential flow spreading. The results obtained in this work can be used by the designers of hydraulic structures, which length is relatively short and where the flow resistance forces can be neglected.