泥沙在动水中的沉淀运动(一)——圆球在流体中运动时所受的阻力

在河道动力学中,一般在讨论泥沙和水的相对速度时,都应用斯笃克斯公式。但是这样一个假定是没有经过严格证明的,它的正确性必须仔细地加以讨论。本文根据流体力学的基本理论讨论了一个小球在不均匀流场中运动时候的情况。在讨论的时候,我们引进了两个基本假定:(1)圆球直径和流场的线性尺度比较起来小得很多;(2)水和圆球的相对速度很小。有了这两个假定以后,我们就可以把运动方程式线性化,然后再利用拉普拉斯转换找出线性化以后的方程式的解。最后得到小球在非均匀流场中运动时所受到的阻力。

SEDIMENTATION MOTION OF SAND PARTICLES IN MOVING WATER (Ⅰ)——THE RESISTANCE OK A SMALL SPHERE MOVING IN NON-UNIFORM FLOW

In hydraulics, when we deal with the problem of sand particles moving relative to the surrounding water, Stokes' formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be carefully considered. In this paper, we discuss the problem of a sphere moving in a non-uniform flow field, on the basis of the fundamental theory of hydrodynamics. We introduce two assumptions: i)the diameter of the sphere is much smaller than the linear dimension of the flow field, ii) the velocity of the sphere relative to surrounding water is very small. Usnig these two assumptions, we solve the linearized Navier-Stokes' equations and equations of continuity by the method of Laplace transform, and finally we obtain a formula for the resistance acting on a, sphere moving in a non-uniform flow field.