The mathematical model of the process of separation for the liquid-solid system in the hydrocyclone battery is considered, at that the devices are equipped with replaceable pairs of inserts for varying the diameters of the inlet and outlet pipes. It is established that when assessing the overall degree of purification of the suspension in the hydrocyclone battery with the same diameter of the corpuses and replaceable diameters of the pipes, it is necessary to take into account not only the separation factor, but also the average residence time of the liquid in the separation zone. In this connection, it is proposed the parameter P, equal to the product of these indicators. In this interpretation, increase the total degree of purification of the suspension concomitantly with increase the number of hydrocyclones in the battery is consistent with the corresponding value of the parameter R. © 2019 IOP Publishing Ltd. All rights reserved.