An exemplary fluid supply system for use on a turbomachine includes a turbomachine fluid container having a moveable barrier. A pressurized fluid is delivered to one side of the moveable barrier, and an opposing side of the flexible barrier communicates with a source of lubricant. Pressurized fluid is selectively delivered to the one side to move the moveable barrier between a flow-permitting position that permits flow from the source of lubricant to the turbomachine fluid container and a flow-restricting position that restricts flow from the source of lubricant to the turbomachine fluid container.