Effects of Flow Parameters on Flow Variables of a Newtonian Fluid through a Cylindrical Collapsible Tube

Abstract

In this study the effects of longitudinal tension, tube stiffness and volumetric flow rate on the cross sectional area of a collapsible tube, flow velocity and internal pressure of a Newtonian fluid through a cylindrical collapsible tube have been determined. The tube was considered collapsible in the transverse direction, taken to be perpendicular to the main flow direction. Collapse happens when external pressure exceeds internal pressure and hence the tube results to a highly noncircular cross sectional area. The fluid flow in consideration was steady and incompressible. Equations governing the flow are non-linear and cannot be solved analytically. Therefore an approximate solution to the equations was determined numerically. In this case, finite difference method was used. A computer program then was used to generate the results which were presented in form of graphs. The results show that the longitudinal tension and tube stiffness are directly proportional to both the cross sectional area and internal pressure and inversely proportional to the flow velocity and that change in volumetric flow rate has no effect on the cross sectional area but it is directly proportional to the flow velocity and inversely proportional to the internal pressure.