Flow Pattern near the Outlet of a Straight Long Circular Tube : 2nd Report, Theoretical Calculation

A theoretical study was carried out to investigate such a flow that a liquid of low viscosity issues downward from a vertical tube into the atmosphere. Numerical calculations were performed by using both vorticity transfer and momentum theory. From the study the following results were obtained: (1) Inside of the tube, velocity profile gradually becomes different from that of the Poiseuille flow as the flow comes close to the tube outlet. For Re=753, Fr=9.75 ×10-2, the velocity on the tube axis at the tube end becomes 1.23 times as large as that of the Poiseuille flow. Accordingly, the flow pattern at the tube end is no longer that of the Poiseuille flow. Issuing from the tube outlet, downstream, and the flow at a position by one tube-diameter downstream from the tube end settles to uniformity. These tendencies becomes remarkable with an increase of the ratio of the Reynolds number to the Froude number. (2) The pressure on the tube wall takes a minimum value at a position by the tube-radius times 0.7 from the tube end. This value is lower than the atmospheric pressure.