I'm a former physics student and I've been thinking about an interesting problem that eventually led me to the following thought experiment that I'm having trouble resolving. Imagine a two-compartment system, where one compartment is filled with He gas, and the other is filled with standard atmospheric gas. Both compartments have the same volume, both are cubes, and the heights of both compartments are small enough so that changes in g are negligible between the top and bottom. The second compartment with the atmospheric gas has (1) a tiny valve that can be opened and closed located on the face (recall the compartment is cubic) farthest away from the other compartment containing the He gas Also, (2) the walls of the second compartment can be fully folded in and collapsed (and attached to the first compartment containing the He gas) so that the total volume of the system in its collapsed/folded state is only non-negligibly greater than the volume of just the first compartment filled with the He gas. Initially, the (1) valve is closed, and (2) the walls are not collapsed/folded in, and the relative ratio of He to atmospheric gas is such that the system begins to rise because the buoyant force exceeds the weight of the system. Let's consider two scenarios. In scenario #1, only the valve is opened. Recalling that the valve is extremely small, with itswidth <<<< size of the container, does the buoyant force get halved (the two compartments are of equal volume, as stated in the beginning) even though the valve's size is <<< size of container? I would think no, since the hole is too small for the second compartment to suddenly "not count" toward the total volume of the air displaced by the overall structure. But on the flip side, I tend to think yes, since if you made the hole incrementally larger until it became as large as the entire side of the face it's situated on, the second compartment with the now giant hole couldn't really be said to be displacing the surrounding air anymore. In scenario #2, the walls of the second compartment are collapsed and folded in, and then attached to the second compartment so that the total volume is basically halved. This would in turn halve the mass and hence weight of the air displaced by the structure, thus halving the buoyant force. Making the hole larger and larger, as in scenario #1, seems to make scenario #1 effectively indistinguishable from scenario #2. In scenario #2, the buoyant force is clearly (I think?) halved. How large does the hole have to be to eliminate that compartment from contributing to the buoyant force? Is this reduction of buoyancy discontinuous or continuous? What errors have I made in this thought experiment given the assumptions stated?