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中国物理学会期刊

泥沙在动水中的沉淀运动(二)——泥沙在层流中的沉淀运动

CSTR: 32037.14.aps.13.399

SEDIMENTATION MOTION OF SAND PARTICLES IN MOVING WATER (Ⅱ)——SEDIMENTATION OF SAND PARTICLES IN LAMINAR FLOW

CSTR: 32037.14.aps.13.399
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  • 在前文中我们已经给出小球在不均匀流场中运动时所受到的阻力。本文中我们假定泥沙和水为两种不同的介质,同时假定泥沙的浓度很小。利用前文所得到的阻力公式,我们建立了在层流状态时泥沙和水各自的运动方程组。然后利用这一组方程来讨论明渠中水流流态为层流时泥沙沉淀的情况。最后我们得到泥沙和水的相对速度在主流方向的分量并不等于零。同时我们求得根据简单假定来计算时所引起的沉积位置的误差。这个误差和水深成正比而和泥沙颗粒的大小无关。一般说来,这个误差并不是一个可以忽略的数值。

     

    In dealing 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 examined. In the previous paper, we gave the resistance acting on a sphere moving in a non-uniform flow field. In this paper, we assume the concentration of sand particles to be very small, and using the previously obtained formula for the resistance, we establish the general equations of motion of laminar flow of sand particles and water. Then, we discuss the sedimentation motion of sand particles for laminar flow in an open channel.Finally, we find that the component of relative velocity parallel to the main stream is not equal to zero. Thereby, we obtain the error in the position of sedimentation as calculated by means of the usual simplified assumption. This error in position is proportional to the depth of water, and is independent of the size of sand particles. In general, it is not a negligible quantity.

     

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