A Steady Flow of The Viscous Compressible Liquid in Vertical Pipe

Abstract

In the study of the flow of gas-liquid mixture over circular vertical pipe rising from the deep zone to ground level, it is observed that, the velocity on surface of tube is much more than in the center of flow. Such a picture is seen also in the water filtration process in sands ordering from high permeability zone to lower. Same phenomena occur in transportation of the water carbon nana-tubes.  In order to predict behavior of those processes in this paper, we have studied the compressible liquid flow over the circular vertical pipe ordered from the deep zone to the ground surface for some concrete inlet and outlet regimes of the pipe. The Navier-Stokes equations system as a model of study. For certain inlet and outlet regimes of the flow splitting the equation into the cross section and axes variables, the pressure and velocity distribution are found. The Lane-Emden equation arises for determining the pipe cross section velocity distribution, which is also justified by our calculations on the used model.