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Evaporation (in Conical flask)

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 By definition of the evaporation, the rate of volume change shall be directly proportional to that of the surface area exposed: In this case assume that the water is evaporating in a conical flask. The evaporation is done by the upper surface exposed to the air (the surface will always be a circle).  The volume of water at any time t would be enclosed in the shape of a frustum as shown. The volume is hence: Subject to the needs of the differential equation, we rearrange it in the form of Area as a function of Volume, By substitution, In which 

Fourier Expansion

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Important Series in solving PDEs