大气中水滴降速的计算

A CALCULATION FORMULA OF THE TERMINAL VELOCITY OF WATER DROPS IN THE ATMOSPHERE

本文从理论上推导了流体介质中球体降速 v 随其半径 r 的变化形式 v=α(b/a)(1/r){(1+β(a/b^2)r^3)^(1/2)-1}。其中,a、b 为简化运动方程时引进的二个待定常数,由大气中水滴降速的实测资料确定,其值为 a=0.53563、b=1.37358。由此式计算的最大相对误差为24%。比较了这一半理论公式与他人经验公式各自的特点。推荐了三组形如 v=A(α/α_0)(β/β_0)^((B+1)/3)r^B 之新的统计公式,它们分别将 r=0～2900μm 分为三、四、五段,对应的计算最大相对误差分别为11%、7%、4%。

In this paper,for the terminal velocity v of a spheric water drop(with a radius r)falling inthe fluid medium,an analytical solution v=α(b/a)(1/r){(1+β(a/b^2)r^3)^(1/2)-1} is theoreticallyderived.The constants a and b in the formula are determined by the experimental velocity data ofwater drops in the atmosphere:a=0.53563,b=1.37358 with a maximum relative calculatingerror of 24%.This semi-theoretical formula is compared with the other empirical formulas.Threenew statistical formulas in the form of v=A(α/α_0)(β/β_0)^((B+1)/3)r^B are recommended.They divid-ed r (0～2900μm)into 3,4 and 5 ranges with a maximum relative error of 11%,7% and 4%,respectively.