雨滴下落的形状和收尾速度  

THE SHAPE AND TERMINAL VELOCITY OF THE FALLING RAINDROPS

作　　者：高德文[1] 赵昶[1] GAO Dewen;ZHAO Chang(Department of Mathematics and Physics, Beijing Institute of Petro-Chemical Technology, Beijing 102617)

机构地区：[1]北京石油化工学院数理系

出　　处：《物理与工程》2019年第6期65-70,共6页Physics and Engineering

基　　金：北京市自然科学基金(No.1132010);北京市教委科技计划项目(KM201710017007)资助

摘　　要：雨滴收尾速度的计算是大学物理教学中的典型案例。一些文献给出了在空气阻力系数视为常数的情况下,球型雨滴下落时的收尾速度,但由此得出的结果与实验结果有较大差别。笔者认为,问题出现的原因包括两个方面:一是空气阻力系数选取问题,二是雨滴模型问题。本文采用空气阻力系数Park公式、Wallis公式,利用Matlab软件计算雨滴以球模型、近似椭球模型(以下简称PP模型)以及汉堡模型(即半球模型)下落时的收尾速度,并利用Origin Pro8.0进行绘图对比。结果表明本办法给出的雨滴模型和收尾速度计算值更接近实验结果。The calculation of the terminal speed of raindrops is a classic case in college physics teaching.Some literatures have given the terminal velocity of a spherical raindrop when the air resistance coefficient is regarded as a constant,but the results are quite different from the experimental results.In our opinion,there are two reasons for this problem.One is the selection of air resistance coefficient,the other is the problem of the raindrop model.In this paper,the Park formula and Wallis formula of air resistance coefficient are used to calculate the terminal velocity of raindrops falling with spherical model,approximate ellipsoid model(PP model)and Hamburg model(hemispheric model)by using MATLAB software,and the Origin Pro 8.0 is used for drawing comparison.The results show that the raindrop model and the calculated value of the terminal velocity given by our method are much closer to the experimental results.

关 键 词：雨滴 空气阻力系数 雷诺数 收尾速度 

分 类 号：G62[文化科学—教育学]