The researches on sloshing of the free surface flow in containers carrying liquid are of theoretical and practical significance. Numerical solutions often involve some approximations of the boundary condition, when considering the wide-range movement or the nonlinearity of the free surface flow. In this paper, under partial slip boundary conditions, the high-order nonlinear differential equations of a cylinder-shaped partially filled liquid container are numerically solved. The influences of the contact line and the fluid height of liquid and the partial slip boundary conditions on the macroscopic radius of the fluid layer are discussed. The results may serve a reference for treating similar boundary conditions of free surface flow for partially filled liquid carrying containers.%摘要数值方法进行相关问题的研究就以圆柱形储液罐为例，考虑部分滑移边界条件，对所得的高度非线性微分方程进行了数值求解，讨论了贮液腔体内液面接触线和液体高度线，及部分滑移条件对流体层微观半径的影响；所得结论对自由液面晃动问题数值研究中的边界条件处理有参考意义．
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