We investigate the flow of fluid through an elastic tube and compare the flow of a Newtonian and a non-Newtonian fluid. When fluid flows through a pipe, a pressure difference between the inlet and outlet of the pipe is created due to the flow and the viscosity of the fluid itself. As a result, stresses are induced in the pipe that lead to its deformation. We first derived the deformation equations for a fixed and a freely-deformable, nonlinearly elastic tube, and second the flow equations for the Newtonian and non-Newtonian fluids in tubes with a circular cross-section. Using a program, written in Python, we calculated the deformations of two differently clamped tubes for two different materials: rubber and human vein tissue, using water and blood as a reference for the Newtonian and non-Newtonian fluid, respectively. We later compared the velocity profile of water and blood, where we established the behaviour of the fluid is strongly dependent on its viscosity.
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