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Modern methods of computational fluid dynamics have been used to study flows with mass supply in axisymmetric channels of solid-propellant rocket motor charges. The studies were carried out with the aim of increasing the accuracy of predicting the intraballistic parameters for performing engineering calculations. The analysis of changes in intraballistic characteristics in the flow part of the channel charge in the classical and nozzleless solid propellant rocket motors is carried out for different rates of mass supply from the combustion surface. For an isobaric combustion chamber, a characteristic velocity profile is shown along a tubular charge path and a charge with sudden expansion. It is shown that for a steady cosine profile of axial velocity after sudden expansion of the channel, a length of more than three gauges is required. For a high-speed combustion chamber, a comparison of the axial velocity profile is carried out depending on the flow velocity under different conditions of mass supply. The tendency of the influence of flow velocity on the character of the profile is noted. It is shown that at a Mach number over 0.5, an increase in the mass flow rate from the combustion surface provides a less filled velocity profile tending to cosine. The differences between the pressure losses in the flow passage of the channel charge, calculated in the axisymmetric approximation, and the losses determined using gas-dynamic functions, are shown. An increase of the mass flow rate in the charge channel of a nozzleless solid-propellant rocket motor leads to a decrease in pressure losses at Mach number over 0.8.