A Gasometer Problem

Extract

Figure 1 shows a vertical cross-section of a bell floating freely in water in a circular vessel, both the gas pressure inside the bell and the atmospheric pressure above being p. The problem, which appeared in the Mechanical Sciences Tripos, Part I, 1957, is to find an expression for the distance δy the bell rises when the pressure in the bell is increased δp by the admission of gas through a small pipe.