关键词: 球形雨滴, 静止空气, 收尾速率, Wallis公式, 斯托克斯公式

Abstract: 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.

Key words:  spherical raindrop, still air, terminal velocity, Wallis formula, Stokes formula