When working out the numerical problems, make sure you use a consistent set of units. 1. It has been empirically esablished that the growth rate of deposition nuclei can be expressed as:

Where S_i = the supersaturation percentage of air (i.e. 101) and b and a are constants. N_D is the number of ice nuclei per cubic meter. Experimentally b = 0.13 and a ranges from 3 to 8.

From this empirical relationshop, specify the combinations of S_i and a that are required to produce N_D = 100 and 10,000,000 respectively. Even better, please provide a graphical representation of your solutions

2. Calculate the times taken for water drops of radii 1, 10 and 100 microns to fall a distance of 1 km in air at terminal velocity. Take the air viscosity to be 2 x10^-5 kg m^-1 s^-1 In the case of the largest droplet (where you should find a fall time of 10 minutes) comment on why this calculation is incorrect.

3. A drop enters the base of a cloud with radius r_o and grows with constant collection efficiency. After going up into the cloud and returning to the base of the cloud, the drop has radius R. Assume a constant updraft velocity w . Show that R depends only on r_o and w . (Hint: since the drop returned to the cloud base, H = 0).

4. Suppose that Mt. St Helens blows and that ash particles are blown to a height in the stratosphere where the pressure = 50 mb. Assume the tropsphere starts at a pressure of 200 mb. The ash particles are spherical with a mean radius of 0.1 microns and a density of 2600 kg m^-3, Estimate the time it takes for these particles to reach the earth's surface.

5 HINT: