The article presents a combined mathematical model that allows us to determine and investigate the dynamic characteristics of the latest type of non-contact sealing for pump and compressor shafts, which eliminates leakage of pumped products, which are important from the point of view of safe operation. The proposed method is based on the laws of conservation of energy and conservation of matter. The model is based on static and dynamic calculation of operation characteristics, while its key feature is the combination of analytical, variational and numerical solutions. The materials of the article may be useful to developers of new types of contactless seals of centrifugal machines.