Saturated vapor from a chemical process condenses at a slow rate on the inner surface of a vertical, thinwalled cylindrical container of length L and diameter D. The container wall is maintained at a uniform temperature Ts by flowing cold water across its outer surface.
Derive an expression for the time, tf, required to fill the container with condensate, assuming that the condensate film is laminar. Express your result in terms of D, L, (Tsat - Ts), g, and appropriate fluid properties.