大学物理 ›› 2021, Vol. 40 ›› Issue (4): 19-21.doi: 10. 16854 / j. cnki. 1000-0712. 200143

• 物理实验 • 上一篇    下一篇

器壁旋转模式下液体平衡状态的分析

雷 奕,石立红,张俊成,潘建澎   

  1. 长江大学 石油工程学院,湖北 武汉 430100
  • 收稿日期:2020-04-15 修回日期:2020-09-04 出版日期:2021-04-13 发布日期:2021-04-21
  • 通讯作者: 石立红,E-mail: 29918451@ qq. com
  • 作者简介:雷奕( 1997—) ,男,江西九江人,长江大学石油工程学院 2019 级研究生.
  • 基金资助:
    长江大学大学生创新创业训练计划项目( 编号: 2017096) 资助.

Analysis of liquid equilibrium state under the rotating mode

LEI Yi,SHI Li-hong,ZHANG Jun-cheng,PAN Jian-peng   

  1. Institute of Petroleum Engineering ,Yangtze University,Wuhan,Hubei 430100,China
  • Received:2020-04-15 Revised:2020-09-04 Online:2021-04-13 Published:2021-04-21

摘要: 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,存在的极限值为槡3 +1,当液体旋转角速度超过临界角速度时,旋转

液面分为中部的抛物面和边缘增长的水膜两部分.

关键词: 流体力学, 器壁旋转, 平衡液面, 恒等式, 临界值

Abstract: 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 in- crease 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槡3 +1,when the liquid

rotation angular veloci- ty 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.

Key words: fluid mechanics, wall rotation, equilibrium liquid level, identity, critical value