水静力学中旋转抛物体问题的进一步分析

A Further Discussion on the Problem of Rotating Liquid within a Cylinder

通过力学分析,研究了绕中心轴等角速度旋转圆柱体容器内的液体平衡问题,给出了自由液面方程.随后,证明了旋转抛物体的体积为同底同高圆柱体体积的一半.其次,在柱坐标系下,给出了旋转抛物线与圆柱体的轴线和母线,以及原液面围成的两部分投影面积之间的数量关系.

Through mechanics analysis,the problem of liquid equilibrium within a rotating cylinder at a certain angular velocity is studied,and hence the free surface equation is given.What follows,it gives a proof that the volume of rotating parabolic body is half of a cylinder which has the same bottom and height.Later,under the cylinder coordinate,it gives numerical relation between two areas which are separated by cylinder’s axis,mother line and initial liquid surface.