Merging and splitting flows in a tee: the Pavlovsky method

Introduction. The Pavlovsky method is employed to consider the flows that merge and split inside a tee. Materials and methods. The problem of flows, merging and splitting inside a simple straight tee, is reduced to the problem of limits in a theory of functions applied to the characteristic function of a flow. The influence of the geometric parameter of a tee (a module), head losses and an external power source, produced on the flow rate coefficient in a tee, is identified in the work. Results. The co-authors identified a relation between the geometric parameters of a tee and its capacity in case of an isoenergetic flow and an external mechanical power supply. Conclusions. As for practical tasks, it is sufficient to reproduce a pentagon, stylizing a simple straight tee, on a strip having a ledge, while preserving the correspondence of points of polygons. The following conclusions are made: dissipation does not reduce the flow rate coefficient when flows merge, neither does it reduce the flow rate coefficient when flows split; minimum values of flow rate coefficient q = Q0/Q1 in case of merging flows are attained in the absence of dissipation, and they do not exceed the maximum value of the flow rate coefficient in case of splitting flows is attained in the absence of dissipation and it is not less than dissipation in a tee is explained by the flow separation from the vertex of angle B when flows merge and by the flow separation from the vertex of angle C when flows merge. Hydraulic losses do not reduce flow rate coefficient q = q+ when flows merge and do not increase flow rate coefficient q = q– when flows split. flow rate coefficient q+ goes down if a source of external mechanical power (a pump) is connected to a tee when flows merge; if flows split, the flow rate coefficient goes up and varies within the 1 < q– < 2 interval, and it doesn’t go up if q– > 2.