### THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

## A MATHEMATICAL MODEL OF VISCOUS LIQUID MIXTURE MOTION THROUGH A VERTICAL CYLINDRICAL PIPE

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.