Substantiation of the influence of the channel shape and the roughness of machine canals on the pressure loss of irrigation pumping stations

To take into account the influence (on the value of head losses) of the channel cross-sectional shape and the presence of a flow with a free surface in it, additional correction factors are introduced (when using the concept of hydraulic radius), as well as new dependencies and formulas for determining the coefficient of hydraulic friction are presented, taking into account the influence of the morphometric elements of the channel on the hydraulic resistance of the machine channels of pumping stations. The article presents the results of hydraulic studies in free-flow and pressure water pipelines, the results of which showed that the dependencies obtained for calculating hydraulic resistance in round pressure pipes cannot be extended without appropriate adjustments to the pressure-free channels (provided that the pipe diameter is replaced in the corresponding calculations D-value 4R, where R-hydraulic radius). This position is justified by the presence of a number of factors that distinguish the pressure movement of liquid in pipes from its free-flow movement in the channels, where there is a free flow surface, a wider range of roughness of the channel bottom and walls, a different (than in pipes) distribution of tangential stresses along the wetted perimeter, the possibility of two different flow states (depending on the slope of the channel bottom). The work also considers the general equation of fluid motion in free-flow channels and the functional dependences of the hydraulic friction coefficient on the Reynolds number, relative roughness and on the shape of the free section of the channel; resistance formulas, first for the simplest channels with respect to the cross-sectional shape (round and infinitely wide rectangular), and then for channels with a more complex cross-sectional shape.