器壁旋转模式下液体平衡状态的分析

基于器壁带动液体旋转稳定后形成的抛物面,推导出器壁斜率为K(K≠0)时的恒等式.得出K→∞时,随着转速增加,液位的变化是无限的,液位的上升高度与下降深度恒相等,旋转抛物体与同底同高圆柱体积关系为定值;当K＞0时,容器为上大下小的圆筒,旋转抛物面导致的液位变化是有限的,存在的极限值为√3+1,当液体旋转角速度超过临界角速...

Analysis of liquid equilibrium state under the rotating mode

This paper studies equilibrium liquid level formed by the rotation of liquid on the wall,the equation is deduced when the slop of the wall is K(K≠0).When K→∞,the change of liquid level is infinite with the increase of rotating speed,but the rise height of liquid level is equal to the fall depth of liquid level,and the volume relationship is a constant.when K>0,the container is a round table with large top and small bottom.The liquid level change caused by rotating paraboloid is limited,and the limit value is √3+1,when the liquid rotation angular velocity exceeds the critical angular velocity,the rotating liquid surface is divided into two parts:the paraboloid in the middle and the water film with growing edge.