Abstract
The purpose of the research was to create an adequate mathematical apparatus to establish the interrelation between surface and drainage waters, since the need of interconnection between surface and drainage waters in the field of environmental safety, reclamation and hydrology arises regularly. At the same time, conducting field studies that determine this interrelation is a very costly and time-consuming event, therefore, the development of a mathematical apparatus that adequately describes the relationship between surface and drainage waters is an urgent task. Materials and methods. The developed mathematical apparatus is based on the compilation of the classical theory, namely: the Chezy, Darcy formulas, the water table, the water balance equation and the expression for the water surface slope. Results. As a result of the research, the drainage water runoff zone was divided into a finite number of elements, and the average velocity of the filtration flow interacting between the canal and drainage water was determined. Numerical verification of the modeling results was carried out on the basis of data obtained during field studies at the inter-farm canal section near the village Swamp Belevsky district Tula region. In the process of research, an algorithm and a program were developed for calculating the drainage water flow rate for the considered section of the inter-farm canal. Based on the simulation results, a hydrograph of drainage water flow rate was constructed in the inter-farm canal near the village Swamp, while the hydrograph of drainage water flow, built on the basis of modeling results, practically coincides with the hydrograph, built on the basis of data provided from the results of field studies. Conclusions. Approbation of the results of the developed mathematical apparatus and mathematical model showed the correlation between theoretical and experimental studies with a determination coefficient value of 90.22 %.
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