|Model, 1. modul, 2006, id:346|
|Vejleder:||Johnny T. Ottesen|
|Findes på RUb:||Ja|
In this report a mathematical model describing a physical system consisting of a rubber tube placed in a fluidfilled tank is formulated and analysed. This experiment is not subjected to empirical inquiry, but our experiment has clear analogy to previous works. A pump is compressing the tube periodically at a place of asymmetry. The report has two main purposes: To formulate a model that investigates if a mean flow is existent, and to find out which mechanisms are responsible for creating a mean flow. The model is formulated in accordance to the compartment principle and consists of 11 1st order interdependent differential equations. The equations are formulated according to conservation of mass and Newtons 2. law. When the size of each compartment approaches zero the differential equations approksimates the equation of continuity and the linearized Euler equation in one dimension with a frictional term. In the final model inertans, resistance and compliance varies with the radius of the tube. These three terms are thought to contribute to the mean flow and we wish to find out which of the three contributes the most. The equations in the model are solved numerically in MatLab to establish a mean flow. Afterwards the inertans, resistance and compliance are kept constant in pairs. The report concludes that it is possible to create a frequency dependent mean flow, and that the inertans contributes primarily to the frequency dependent mean flow.