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In: Advanced Math

In very dry regions, the phenomenon called Virga is very important because it can endanger aeroplanes....

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.

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Expert Solution

Colby Messinger answered 7 months ago
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