Viscous gas flow in a vertical tube

We consider the viscous gas motion in a round tube under the gravity force. Gas pressure is supposed to be constant. (It is necessary to create a vacuum at the bottom (air suction by a pump) or air injection at the top for implementation of a such a flow.) The Sutherland formula is used for the viscosity coefficient and a similar formula with the same rate of accuracy is used for the thermal conductivity coefficient. With an appropriate choice of input parameters, the Poiseuille kind flow occurs such that its velocity, density and temperature depend only on the distance to the tube axis (velocity is directed along this axis). Thus the system of motion equations, which generally consists of partial derivatives equations, turns into the system of ordinary differential equations. An exact solution to this system is suggested for verification of viscous gas flow computational packages.