Abstract <p>Interest in a detailed study and simulation of the processes occurring in heat- and mass-transfer equipment is determined by the variety of designs and types of devices, as well as the variety of different ways to enhance the processes taking place in the equipment. The study of the hydrodynamics of technological media and the interaction of phases (components) in contact devices makes it possible to optimize the geometry of the designed equipment in order to enhance the efficiency of the heat- and mass-transfer processes. For simulation and analyzing of the processes taking place in technological equipment, computational fluid dynamics software systems based on finite-element analysis methods are often used, which allows obtaining velocity, concentration, temperature, and pressure distribution curves only for single-phase media. However, simulation of technological processes involves describing the hydrodynamics of multiphase media under the influencing conditions of centrifugal field and Coriolis acceleration on the nature of interaction, which today is a rather complex task requiring significant computing resources, machine time, as well as human resources. In connection with the above, it is of interest to develop an approach to simulation that combines the simplicity of analytical dependences and ensures sufficient accuracy in computations, verified by satisfactory agreement of the results obtained from the literature sources and the results of numerical studies performed using computational fluid dynamics software systems. The present paper proposes a mathematical description of the solution of a hydrodynamic problem related to determining the two-phase flow velocity in a profile nozzle of a centrifugal unit. The paper presents the basic differential equations and boundary conditions describing the flow of interacting phases in a profile nozzle.</p>