Abstract
In this research study, fluid flow through a cylindrical collapsible tube has been investigated. Of particular interest is the effect of flow parameters on the cross sectional area of a collapsible tube, flow velocity and internal pressure of the fluid. The flow parameters considered are longitudinal tension and volumetric flow rate. The tube is 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 is steady and incompressible. Equations governing the flow are non-linear and cannot be solved analytically. Therefore an approximate solution to the equations has been determined numerically. In this case, finite difference method has been used. A computer program has then been used to generate the results which are presented in form of graphs. The results show that the longitudinal tension is 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.
Highlights
Fluid is a type of matter which undergoes continuous deformation when some external force is applied
2.1.1 Effect of varying Longitudinal Tension on the cross sectional area of the collapsible tube In order to determine the effect of longitudinal tension on the cross sectional area of the collapsible tube, other parameters were held constant while the longitudinal tension was varied
2.2 Discussion The objective of this study was to do an analysis of the flow parameters of a Newtonian fluid through a cylindrical collapsible tube
Summary
Fluid is a type of matter which undergoes continuous deformation when some external force is applied. It is said to undergo deformation if the distance between any two neighboring molecules change. The viscosity does not change with the rate of flow. A collapsible tube is any tube with sufficiently flexible walls that it can elastically accommodate deformation to a highly noncircular cross section when the external pressure exceeds the internal pressure. The study of flow through collapsible tubes is of utmost importance in biological studies as well as in industries. Collapse occurs when high external pressures are applied, such as when an artery is compressed by a sphygmomanometer cuff during blood pressure measurement. In the industry, collapse may be experienced during cementing operations, trapped fluid expansion, or well evacuation, among many others.
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