A liquid transport mechanism for use particularly in transporting and evenly distributing printing ink in a rotary printing machine is disclosed. A plurality of generally cone shaped ink transport rollers are placed about the periphery of one or more ink relief equalizing cylinders. The axes of rotation of the rollers are angled with respect to the axes of rotation of the ink relief equalizing cylinders. The covered surfaces of the rollers, which are disposed generally in pairs, contact the surface of the ink cylinders to form ink bridges which split the ink coating on the cylinders and cross transport it longitudinally along the length of each of the ink relief equalizing cylinders. The ink metering unit in accordance with the present invention uniformly and rapidly equalizes ink thickness without the need for ink zone adjusting screws and doctor blades.