Abstract
This article studies ordinary differential equations modeling incompressible flow in rigid pipes that connect two distensible vessels, one of which is periodically forced. The forcing controls either the pressure or the volume of the excited vessel and---in part of the period---can be replaced by free relaxation. The pressure losses at the junctions of the pipes and vessels are quadratic with or without switches according to the direction of the flow. Stability and net flow of the equilibria of the unforced systems is investigated. Pumping solutions are defined and proven to exist in case of nonlinear pressure losses at the junctions. In contrast to often-quoted literature, it is shown that “impedance defined” piecewise linear models can not produce net flow with continuous solutions. For partial forcing models numerical simulations are reported.
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