Solution of equation of extreme streamline with free flowing of a torrential stream behind rectangular pipe

Abstract

The article discusses the methods of modeling two-dimensional in terms of turbulent flows. Their difference and advantages are described. The equations of flow motion in the plane of the hodograph are given, as well as the velocity and depth of the flow in the entire region of its flow. Next, a new method is proposed, the purpose of which is to solve a system of differential equations. Using a differential equation connecting the physical cavity of the flow stream and the plane of the travel time curve, a simple model of the flow of a steady, vortex-free water flow in a wide horizontal, smooth outlet channel is proposed. The flow model in the vicinity of the outlet from the pressureless pipe uses the fact that the resistance forces of the flow to the bottom of the outlet channel are small compared with the forces of inertia. The obtained solutions allow us to calculate the flow parameters with an accuracy sufficient for the design of hydraulic structures of the drainage system from the upper pool to the lower one under roads and railways. This model allows you to identify the basis of the laws of the real spreading of the flow and on its basis there is an opportunity for further building models taking into account the resistance forces in order to increase the correspondence of the mathematical model to the real flow.