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.
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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.