On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium

Abstract

Falling motion of a sphere in the stationary medium is an important basic research and has a wide range of engineering application prospects. This paper studies the free fall motion of spheres in a stationary medium considering air drag. This paper calculates the acceleration, velocity and displacement of the falling process of the sphere by Excel, and discusses the influence of the density, diameter and Re on the motion. Some analysis and fitting of displacement over time are performed. The results show that the varied-acceleration motion of the falling spheres is similar for different sphere materials, namely, the falling acceleration, the velocity and falling displacement all can be divided into three segmentations and fitted with polynomial functions. The relationship between displacement<i> h</i> and time <i>t </i>during falling with varied- acceleration is also greatly affected by the density of the sphere, the greater the density of the sphere, the closer the relationship between <i>h</i> and<i> t </i>during the fall process is closer to no drag free fall, the smaller the density of the sphere is, the closer the relationship between <i>h</i> and<i> t </i>is nearer to linear relationship. The displacement data of different solid material sphere is located between the fall of water and the free drop without drag, but does not meet power function or the multi-relationship function. Some results are compared with the literature experiments, and are consistent with the experiments.