Extending the Validity of Basic Equations for One-dimensional Flow in Tubes with Distributed Mass Sources and Varying Cross Sections

Flow problems are solved using so-called fundamental equations and the corresponding initial and boundary conditions. The fundamental equations are the motion equation, the continuity equation, the energy conservation equation, and the state equations. In our paper, we extend the validity of the equation of motion used to describe one-dimensional, steady-state tubular flow to a case in which the mass flow of the medium changes along the tubular axis during the flow. Such flows occur in perforated and/or porous pipes and air ducts. The research in this direction was motivated by the fact that the extension and formulation of the equation of motion in this direction has not been carried out with completely general validity. In the equation of motion used to solve the problems, the isochoric and isotherm nature were assumed. In our paper, we present fundamental equations that formulate differential equations to describe polytrophic and expanding flows.