International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

The paper considers a way of the numerical solution of a system of partial differential equations describing the nonstationary flow of a viscous liquid along a vertical straight pipe of circular cross-section. The result obtained is not final, because the proposed approximation scheme is the simplest and provides only the first order of accuracy. Computer modeling has shown that such an approximation is suitable only for a small time interval.

In the paper a mathematical model of the non-stationary motion of a viscous liquid mixture through the vertical straight pipe of the circular cross section is proposed. During the model construction weak compressibility of the mixture is considered. The Navier-Stokes equations system is taken as a basis. Such model can be used in the description of oil motion in a vertical well.