Calculation of water flow discharge using the truncated triangular prisms method

Abstract

The article describes the calculating method for the water flow discharge. This method is based on the “velocity-area” proportion. In the proposed method, the flow of water passing through the cross section of the channel is represented as a body, the volume of which consists of a set of elements in the form of truncated triangular prisms. The side edges of the prism are the velocity vectors measured at the corresponding points. The bases of these prisms are the areas of triangles, the vertices of which are the points of measurement of the corresponding velocities. The volume of every element is determined by the formula for calculating the volume of a truncated prism. As a reference body, as a model of the diagram of flow velocities, one fourth of a sphere with a unit radius is taken, the volume of which can be calculated with the high accuracy. There are 15 speed verticals (they are also taken as measurement verticals) with five speed measurement points on every vertical: “surface”, 0.2h, 0.6h, 0.8h, “bottom”. The velocity value is represented by the length of the vector directed perpendicularly from the velocity vertical, from the point of velocity measurement to the surface of the sphere. Three adjacent velocity vectors are the side edges of the prism. The method of calculating the flow rate according to the approved measurement procedure is chosen for comparison. The results obtained by both methods are compared. As a result, the volume of the model, as one fourth of a sphere with the unit radius, was 1.0472; the volume calculated by the standard method was 1.0279; and by the method of prisms - 1.0124. Despite the absence of correction factors, the volume obtained by the prism method is only 1.55% less than one with the standard method. To smooth the results obtained by the method of truncated triangular prisms, the range of correction factors of 1.03…1.07 was determined, depending on the number of velocity verticals.