The size distribution of raindrops

TLDR

The study defines W as the amount of liquid water per unit volume of air and identifies A, C, p, r, and n as constants in the drop‑size distribution formula. The authors generate tables from the formulae to present W, drop counts, and total volumes across diameter ranges for various rainfall rates. Experimental data confirm that rain drop size distribution follows the proposed exponential formula with mean constants A = 1.30, C = 67, p = 0.232, r = 0.846, n = 2.25, though n may vary for showery or orographic precipitation.

Abstract

Abstract Experimental data relating to drop size distribution in rain are examined and it is shown that in many cases the size distribution is in accordance with the following formulae 1 ‐ F = exp [‐(x/a) n ] a = A I p W = C I r where F = fraction of liquid water in the air comprised by drops with diameter less than x. I = rate of precipitation. W = amount of liquid water per unit volume of air. A, C, p, r and n are constants. If × is measured in mm, I in mm/hr and W in mm 3 /m 3 the mean values of A, C, p, r and n are 1.30, 67, 0.232, 0.846 and 2.25 respectively. There may be appreciable variations from these mean values, particularly in the case of n, if the precipitation is essentially of a showery or orographic nature. Tables based on these formulae are given showing values of W and of the number and total volume of drops between certain diameter limits for various rates of rainfall.