Dynamics of a Tube Conveying Fluid

A tube conveying a large amount of fluid with a free outlet does not sit still. We construct and analyze a nonlinear evolution equation describing such phenomena. Two types of boundary conditions at the inlet are considered, one for which it is clamped and one for which it is hinged. Analyzing the linear stability of the trivial solution, we find that with the former boundary conditions, it exhibits a ``flutter'' instability, while with the latter boundary conditions, it exhibits a ``rotation'' instability. These instabilities and the nonlinear behaviors of the system are also studied numerically.