Pure liquid benzene (C₆H₆) at 290 K flows as a thin film down the outside of a vertical, 0.08-m-diameter cylinder at a flow rate of 4.0 kg/hr. Dry air at 290 K and 1.0 atm flows perpendicular to the cylinder at a velocity of 4.0 m/s. The liquid benzene exerts a vapor pressure of 8100 Pa. Determine the length of the cylinder if the entire outer surface of the cylinder is used for the evaporating process, and all of the benzene flowing down the cylinder evaporates. Assume that the surrounding air serves as an infinite sink for mass transfer.