Purpose. To increase the level of environmental safety of enterprises by improving the quality of air purification from polydisperse dust in two-circuit closed systems, in particular, to obtain the basic design relations for the engineering calculation of such systems. Methodology. The aim of the study was realised by mathematical and numerical modelling of hydrodynamic processes in the elements of a closed double-circuit purification system. Findings. A methodology for hydraulic calculation of a closed two-circuit cleaning system was proposed by drawing up a pressure balance of individual circuits, and a dependence for the complex coefficient of hydraulic losses of the collection-return apparatus was determined. Originality. The hydraulic calculation of two-circuit closed cleaning systems is proposed to be carried out by compiling the pressure balance of individual circuits. To calculate a specific element of the system – the collection-return apparatus – the concept of a complex hydraulic loss coefficient is introduced, which takes into account both local pressure losses and losses along the length, and also indirectly reflects the effect of flow swirl on the hydraulic resistance of this element. For the complex coefficient of hydraulic losses, the quantitative results necessary for engineering calculations were obtained by numerical modelling of hydrodynamic processes of the swirling flow in an annular pressure channel. Practical value. The obtained results make it possible to design two-circuit closed cleaning systems for different production conditions, which, in turn, makes it possible to replace typical and inefficient direct-flow systems with a system in which the efficiency of polydisperse dust capture is significantly increased due to separate cleaning.