Dynamics of Falling Raindrops

A standard undergraduate mechanics problem involves a raindrop which grows in size as it falls through a mist of suspended water droplets. Ignoring air drag, the asymptotic drop acceleration is g/7, independent of the mist density and the drop radius. Here we show that air drag overwhelms mist drag, producing drop accelerations of order 10-3g. Analytical solutions are facilitated by a new empirical form of the air drag coefficient C = 12R-1/2, which agrees with experimental data on liquid drops in the Reynolds-number range 10\u3cR\u3c1000 relevant to precipitating spherical drops. Solutions including air drag are within reach of students of intermediate mechanics and nonlinear\u3edynamics