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Dimensionless and criterial complexes are successfully used in many technical fields. They play an important role in research and design. There are a large number of dimensionless and criterial complexes, which have their advantages and are chosen depending on the topic and specific objectives of the study. The article considers dimensionless and criterial complexes most often used in studies of turbomachines, in particular vortex expansion machines - relative internal (isoentropic) efficiency, degree of pressure drop, adjusted wheel speed, speed coefficient, adjusted diameter, flow factor and coefficient. The authors processed the data of the experimental study of the turbogenerator with a peripheral-side channel and presented them in the form of graphical dependences using these complexes. The improvement of these energy-saving turbogenerators is important because they are used to generate electricity from excess gas pressure, are considered environmentally friendly and are needed for the development of distributed energy. Vortex expansion machines with a peripheral-lateral channel are also poorly understood, so the topic is relevant. In this study, their area of use was determined and reflected in the ns - Ds diagram among radial and other vortex expansion turbomachines to facilitate their comparison and design.