Abstract
This paper deals with the velocity of propagation of waves in flexible liquid-filled tubes lying on a flat horizontal surface. The tubes considered are of sufficiently small rigidity that their cross-sectional shape is determined by the internal hydrostatic pressure, lying quite flat when empty.
It is shown that at low internal pressures very long waves propagate essentially as gravity waves in a canal. The wave velocity increases with the internal pressure and, at the same time, is increasingly affected by the extensibility of the tube wall. At very high pressures, long waves propagate essentially as axisymmetric waves in distensible circular cylinders. The calculated and measured velocities of propagation of very long waves are in substantial agreement.
The system is frequency dispersive and the wave velocity rapidly increases with the wave number. An approximate analysis is presented, applying only when the tube contains little liquid, establishing the mechanism underlying this behaviour. This is qualitatively supported by experimental observations.
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