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The article presents the results of experimental studies of the uneven distribution of the distances between the wires of the warp and weft in woven wire meshes with square cells used to clean gases and liquids from mechanical impurities in various branches of technology. On the basis of experimental data using the methods of probability theory, the regularity of the size distribution of the cells of these grids is determined. The length of its minimum side is chosen as the determining size of a square cell. The results of the conducted studies were used to estimate the fractional coefficient of the leakage of spherical particles through the mesh in the sieve mechanism of separation of these particles from the fluid flow. The probability of particle breakthrough through the grid is assumed to be equal to the fraction of the fluid flow passing through the cells, which determines the size of which is larger than the particle diameter. For experimental verification of the calculated values of the leakage coefficient for the sieve filtering mechanism, a preliminary analysis of the influence of the parameters of the hydrodynamic mode of fluid flow through the grid and the level of fluid contamination on the filtering mechanism was carried out. The results of experimental studies of the fractional leakage coefficient values obtained by the sieve filtering mechanism are compared with the calculated data.