U字管マノメータの液面の振動
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概要
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The problem of oscillation of an incompresible fluid in an open-ended U-tube is frequently discussed in the textbooks of hydraulics, vibrations, and automatic control, etc. Most of them usually give the term of viscous resistance in the kinematic equation of fluid column by using a skin frictional force derived from Hagen-Poiseuille law, which is only applicable to the laminar flow in steady, fully developed motion. But as the flow is dependent on time, it is doubtful if the theoretical equation given in the usual textbooks can explain the experimental results. Therefore, the theoretical kinematic equations using the term of viscous resistance which is derived from not only the case Of laminar flow, but also the case of turbuient flow in steady motion are presented in this paper. And these equations show it impossible to explain the experimental results. Then what sort of explanation for the oscillations of an incompressible fluid in an open-ended U-tube is there? In fact, many theoretical and experimental studies which are different from those in usual textbooks have been taken hitherto, and a brief perspective of the study between 1911 and 1967 is given by J C Biery. And recently a new theoretical study has been presented by D A P Jayasinghe and others. However, it does not secm that tbe definitive solution of this problem has been given. So a new attempt is presented in this paper. On the basis of our experimental results, it is assumed that the deviation from equilliblium fluid level in U-tube is expressed as a second order ordinary differential equation with constant coefficients and the damping factor depends only on Valensi Number. Under these assumptions, it is shown that the approximate formula of the damping factor which may be utilized, at least, in the case of Valensi Numbers ranging from 20 to 180, can be established.
- 山形大学の論文
- 1976-02-20