Investigation of the propagation of waves of sudden change in mass flow rate of fluid and gas in a “short” pipeline approach

The problem of the propagation of waves of sudden change in mass flow rates originated at the ends of a pipeline of a finite length is formulated and solved analytically in the paper. In the process of modeling, it was assumed that the route change in pressure is due to the local component of the inertia force, and the velocity of propagation of waves of small pressure disturbances depends on the elastic properties of the pipeline material and fluid. The Dirichlet problem with respect to mass flow rate is solved by the Fourier method and a periodic solution is obtained in the form of a functional series. Instead of solving the Neumann problem with respect to hydrostatic pressure, a pressure solution is obtained by integrating the mass conservation equation over time, where the known solution of the problem with respect to mass flow is used. The options for using the solution for cases of low and super compressible fluids, as well as for studying the propagation of longitudinal waves in an elastic rod, are discussed. According to analytical solutions, a series of calculations was carried out for the problems of instantly closing the inlet and/or outlet sections of the functioning area, as well as for the problem of gas pumping into the elementary section of the pipeline. The features of the propagation of compression and rarefaction waves in the context of the above tasks are investigated. Some graphical results are presented and analyzed.