A system for controlling fluid flow through multiple conduits for use in a fluid administration device. The system includes a housing, a cam, and a control element used to move the cam to selectively occlude the conduits. When used with a medical burette, the cam is located between the vent and supply conduits and rotates to alternately occlude one or the other conduits or to leave both conduits patent. A cam lobe occludes the conduits by pressing the conduit against a pressure surface until occlusion is obtained. Depending on the rotational position of the cam, the continuous flow mode, the intermittent flow mode, and the priming mode are all obtained with a single control lever. The housing secures the conduits in predetermined, fixed positions both above and below the contact location of the cam to the conduit. A positive locking device is included to assist in locating the cam in the desired position. A tactile sensation is also provided to the operator by the locking device to indicate that the cam has been placed in the desired location. Clear visual indicators are included on the housing so that the flow mode in which the burette is presently operating can be seen from a distance.