In: Advanced Math
In very dry regions, the phenomenon called Virga is very
important because it can
endanger aeroplanes. Virga is rain in air that is so dry that the
raindrops evaporate before they can reach the ground.
Suppose that
the volume of a raindrop is proportional to the 3=2 power of its
surface area; and
the rate of reduction of the volume of a raindrop is proportional
to its surface
area.
(a) Are these suppositions reasonable? Note that raindrops are not
spherical, but
let's assume that they always have the same shape, no matter what
their size may
be.
(b) Find a formula for the amount of time it takes for a virga
raindrop to evaporate
completely, expressed in terms of the constants you introduced and
the initial
surface area of a raindrop. Check that the units of your formula
are correct.
(c) Suppose somebody suggests that the rate of reduction of the
volume of a raindrop
is proportional to the square of the surface area. Argue that this
cannot be correct.