A subsynchronous vibration problem with a large water injection pump was solved in 1974 by modifying the discharge piping transition to a long taper configuration. This paper describes a quantitative theory based upon the dynamic modeling of the pump rotor and piping system. The model successfully duplicates the experimental results of the pump instability and reproduces the subsynchronous vibration described in the original paper. The analysis results in a log decrement of the system that is dependent upon the time delay of the acoustic pulsation. It shows that the system can be driven unstable for acoustic path lengths that are much less than the quarter wavelength. The analysis also shows the log decrement is minimized when the time delay is equivalent to exactly that of one eighth wavelength of the resonant frequency of the pump.

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