An apparatus includes a valveless cartridge assembly that has a housing with an opening at a proximal end and an outlet port for dispensing the liquid at a distal end, with the opening being configured to accept a cartridge of the liquid therethrough and communicating with an interior space of the housing. A metered dispensing device is coupled to the valveless cartridge assembly and includes a positive displacement pump in fluid communication with the interior space and the outlet port for selectively dispensing the liquid through the outlet port. The apparatus may be such that at least a portion of the metered dispensing device is disposed within the housing or it may alternatively be coupled to an exterior of the housing. The positive displacement pump may be a gear pump.