Oscillation of Viscous Liquid in a U Tube

概要

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The problem of damped oscillation of viscous liquid in a U tube is described in many hydraulics and fluid mechanics textbooks. In these textbooks the velocity distribution across the tube is assumed to be parbolic for the unsteady oscillating flow just like for the steady Poiseuille's flow and thus it is necessarily derived that the damped constant is inversely proportional to the second power of radius. However, our theoretical results are as follows. When the motion of the liquid in the U tube is oscillatory, the velocity distribution across the tube is represented by Bessel's function of order O, and the damped constant is inversely proportional to the first power of radius. When the velocity distribution is parabolic, the motion of the liquid is non-oscillatory and damped. Our theoretical study is quite consistent with our exprimental results.
東海大学の論文