THE MODEL OF FREE SPREADING A FLOW RAPID BEHIND A RECTANGULAR PIPE

Abstract

The article considers the free spreading of a turbulent stationary two-dimensional open potential water flow into a wide diverting riverbed behind a non-pressure pipe of a rectangular section. A system of nonlinear partial differential equations of motion has been adopted as the mathematical model of the flow in the physical plane. When moving to the plane of the velocity hodograph, the nonlinear system of equations is transformed into a linear system with respect to partial derivatives. Using the obtained system of equations, various problems along the flow of two-dimensional water streams have been solved analytically. The paper determines the flow kinetics parameter t and the angle q characterizing the direction of the local flow velocity vector at the intersection points of an arbitrary equipotential and an arbitrary current line. The X, Y coordinates of these points are found. The peculiarities of changing the angle θ during the transition of the vertical front of the XD are taken into account. Article proposes a module for the transition from a two-dimensional water flow model to a one-dimensional one. This module is necessary for using the laws of flow resistance and taking into account the resistance forces. The model proposed in this paper is a development of analytical methods for calculating potential flows with previously unknown boundaries and before the flow expands. It allows determining the entire range of geometric and kinematic parameters of the flow with an error not exceeding 10%. The adequacy of the model for all flow parameters improves the accuracy of previously existing methods. This allows the designers of road culverts to increase its reliability.

Keywords

• mathematical model, two-dimensional flow, motion equations, resistance forces, flow energy equations, line flow, hydrodynamic pressure, flow spread parameters, free spreading of the flow into the diverting riverbed