The shorter limb of a curved tube is covered with a very thin, soft and impermeable membrane. The tube is filled with hydrogen and set with its open end downwards (Fig.). What position will the membrane adopt?
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Sol. The pressure on the membrane from inside equals the pressure of air at the open end of the tube, less the weight of a column of hydrogen, whose base area equals that of the tube's cross section, and whose height is h (Fig.). The pressure on the membrane from out-side equals the pressure of air at the open end less the weight of a column air of the same cross section and height h. Since air is heavier than hydrogen, the pressure from out-side is reduced by a greater amount than that inside, i.e. the external pressure is less than the internal pressure. Therefore, the membrane will bulge outwards.
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