Transonic liquid bells

The shape of a liquid bell resulting from the overflow of a viscous liquid out of a circular dish is investigated experimentally and theoretically. The main property of this bell is its ability to sustain the presence of a "transonic point," where the liquid velocity equals the speed of antisymmetric-or sinuous-surface waves. Their shape and properties are thus rather different from usual "hypersonic" water bells. We first show that the bell shape can be calculated very accurately, starting from the sonic point. We then demonstrate the extreme sensitivity of the shape of these bells to the difference of pressure across the interface, making them a perfect barometer. Finally, we discuss the oscillations of the bell which occur close to the bursting limit.