Impedance methods of pipeline analysis

Abstract

It is possible for resonance to occur in pipe networks. Organ pipes and other musical wind instruments operate by generating such a resonance. Small pressure or flow fluctuations applied at one end of a pipeline can superimpose upon one another if their frequency matches a simple multiple of the pipeline’ s period leading to the development of a standing wave of considerable magnitude. This phenomenon has caused some major catastrophes: pipelines have ruptured when the forcing vibration has been of trivial magnitude. One of the circumstances which will generate small fluctuations of pressure or flow is the oscillating valve. A very common example of this is the vibrating ball valve in a domestic water supply. As the level in the cistern rises it raises the ball which progressively closes the valve. If the valve is very nearly closed, a small further closing movement shuts off all flow causing a pressure wave to travel down the supply pipe. The pressure rise tends to force the valve off its seat and to let flow recommence so initiating a negative pressure wave which starts off down the pipe following the initial positive wave.