A vertically directed dryer unit for compressed air, comprising a dryer cartridge which, together with a housing, defines an inlet head area and an outlet head area. A plurality of hollow membrane fibers extend inside the cartridge between the two head areas, the wall material thereof being more permeable with respect to water vapor than air. An outlet valve is provided between the outlet head area and an outlet of the drier unit. Said valve only opens when the pressure in the outlet head area produces sufficient pressure for the provision of purging air. The purging air is fed to the outer surface of the membrane fibers via a throttle element.