A fluid supply system for providing a turbomachine fluid to a component of a gas turbine engine is disclosed. The fluid supply system includes a fluid container, a moveable barrier, and an airbag. The moveable barrier fluidly divides the fluid container into a first portion and a second portion. The moveable barrier is moveable between a flow-permitting position and a flow-restricting position. The turbomachine fluid experiences a circulating flow between the component and the second portion of fluid container when the moveable barrier is in the flow-permitting position. The circulating flow is at least partially impeded by the moveable barrier when the moveable barrier is in the flow-restricting position. The airbag is positioned within the first portion of the fluid container. The airbag is selectively operable to move the moveable barrier from the flow-permitting position to the flow-restricting position.