In this article, a theoretical mathematical model of gas flow through a duct in the case of local mass and momentum sources and sinks is presented. The continuity equation and motion equation with one-dimensional, density-stable gas flows were used to create this model. The size of sources and sinks and their locations have an effect on the size of gas stream flows in the duct, gas energy losses, and the parameters of the mechanical source energy that is causing the flow. In the traditional approach to describing the gas flow in the duct, the concept of resistivity and the equivalent resistance of the conduit is used. In the case of flow in the duct with local mass and momentum sources and sinks, the transport resistance depends on a bigger number of parameters than the concept of specific resistance usage. The location and size of the source flux or mass and momentum sinks and the fan work (suction, blowing) were taken into account in the presented model. The model gives the opportunity to determine the mechanical energy losses and efficiency of gas transport in the duct.

In this article, the analysis of mechanical energy changes in a gas medium flow with stable and variable density was presented. To determine the energy losses, the various sources of momentum and mass were used, which had an influence on air flow through the conduit in the system without heat exchange with the environment. The occurrence of varying density gas flow in the conduit (caused by local inflow of mass and momentum) in inclined pipes generates a natural depression–internal mechanical energy. The local momentum sources can facilitate or hinder the gas flow through the conduit. This phenomenon often appears in the network of underground mine workings and in ventilation and air conditioning installations. The characteristic for gas flow through a pipe or mining excavation is the equivalent aerodynamic resistance, the value of which is influenced by the mass and momentum of local sources. This value determines the facilitation or difficulty in gas transport through a section of conduit in relation to the mass stream of the medium. In this article, the dependency of mass flow and gas momentum with different densities on the value of the gas medium flow resistance in the conduit was analyzed. On the basis of the obtained results, the loss of mechanical energy and energy efficiency of flows were determined. In this work, two cases of fan work in suction and blowing modes were analyzed. For these examples, a gas inflow with three different mass streams, a density higher than the main stream density, and with a zero momentum value for this stream was modeled. Ten cases of mass inflow sources were considered. The results of the gas mass flow calculation through the fan m˙w and gas m˙0 and the coefficient of transport efficiency are graphically presented in the paper.