Dynamics of oscillation processes in siphon U-tubes

Abstract

The dynamics of oscillation processes in a siphon U-tube is studied for the system of connected vessels filled with homogeneous liquid. The equations and phase paths describing the motion of non-viscous liquid and fountain effects are given, oscillation frequencies are considered. Oscillations are nonlinear in general case, but they turn into linear by setting special parameters of the system. Phase portraits are obtained and their dependences on parameters of the system are analyzed for the linear and non-linear cases. It is shown that the behavior of the deep and shallow water in such a system could be discussed using analogy with the propagation of elastic waves in condensed matter. Some interesting analogies between a siphon U-tube and hydrodynamic, mechanical, electromagnetic phenomena, wave motion are also analyzed.