静止空气中球形雨滴收尾速率及斯托克斯黏性阻力使用条件

The terminal velocities of spherical raindrops in still air and the usage conditions of Stokes viscous resistance

文章利用光滑球体空气阻力系数较为准确的Wallis公式,逐步地分析计算出20℃的静止空气中不同半径球形雨滴的收尾速率,并与部分实际测量值进行比较,指出差距的原因.文章又以Wallis公式为标准,估计出在精度要求不是太高的情况下,光滑球体的斯托克斯一次方黏性阻力公式大致适用于R e<0.1的雷诺数区间,其间的相对误差<3.0%.这对20℃的静止空气中雨滴下落时斯托克斯公式始终能够成立的半径要求便是r<1.9×10^(-5)m,可见斯托克斯公式完全不能适用于通常大小的雨滴.文章指出,撰文的目的在于对球形模型下雨滴的收尾速率进行较为精确的计算,以弥补其他某些文献的不足,而所使用的Wallis拟合公式相对最值得信耐.

The article uses the Wallis formula,which is more accurate for the air resistance coefficient of smooth spheres,to gradually analyze and calculate the terminal velocities of spherical raindrops with different radii in still air at 20℃,and compares them with some actual measurement values,pointing out the reasons for the differences.The article also takes Wallis formula as the standard,and estimates that under the condition of not too high precision requirements,the Stokes first power viscous resistance formula of a smooth sphere can roughly be applied to the Reynolds number interval with Re<0.1,and the relative error is less than 3.0%,which requires the radius of raindrops in 20℃still air to be r<1.9×10^(-5) m for the Stokes formula to always hold true.It can be seen that the Stokes formula is completely unsuitable for raindrops of ordinary size.The article points out that the purpose of the article is to accurately calculate the terminal velocities of spherical model raindrops to make up for the shortcomings of some other literature,and the Wallis fitting formula used is relatively the most reliable.