Problem 2 in chapter 1 for Friday 23 January

Clouds consist of moist air and particles of condensed water, either in the liquid or solid state. Here, consider an idealized, but nevertheless "typical" cloud that contains only liquid water droplets of uniform radius r_d=15 micrometers. The droplet number concentration is n_d=100 cm^-3, the temperature T=0C, and the pressure p=600 hPa. Calculate the following cloud properties:

a) The approximate distance between the centers of the droplets. How many droplet radii does this spacing represent? (It is sufficient to assume that the drops are uniformly spaced for this problem.)

b) What is the "volume fraction" of liquid water in the cloudy air? (i.e., What fraction of any given volume of the cloudy air, say 1 m³, is occupied by the liquid drops?). What is the dominant phase of the cloud (by volume)?

c) The "liquid water concentration" w_L of the cloud, in units of g m^-3.