Resonance in Pressurized Piping Systems

A new approach, based on the transfer matrix method used in the theory of vibrations, is presented to study the steady-oscillatory flows, and to determine the resonating characteristics of pressure conduits. By linearizing the friction loss term, considering the system as distributed, and assuming the discharge and pressure head fluctuations as sinusoidal, field matrices for simple pipelines and for parallel systems are derived. Point matrices for orifices, and for oscillating valves having sinusoidal valve movement are obtained by linearizing the gate equation. Point transfer matrices for branch systems with the side branch having different boundary conditions are also developed. A procedure is outlined to determine the resonant frequencies of system types commonly used in waterpower development and water supply schemes. A number of examples are solved.