Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)

Vibration and Noise in Pumps 437
upon the pump speed (frequency) and pipe length (distance traveled) and
the physical properties of the fluid.
The acoustic velocity, a function of the fluid density and bulk modulus,
is an important factor in determining the resonant frequency of a pipe
length. The API has published a comprehensive handbook for the physical
properties of hydrocarbon gasses and liquids [16]. Calculation procedures
for the acoustic velocity of water and other common liquids are
presented in the Appendix at the end of this chapter.
A resonant condition [17] exists when the standing wave amplitude is
reinforced so that the actual maximum dynamic pressure (pulsation) amplitude
is substantially greater than the induced pulsation. Thus at frequencies
(pump speeds) corresponding to resonance, there would be considerably
higher amplitude levels generated from the same amount of
energy than for frequencies off resonance.
If the wave frequencies are such that the incident and reflected waves
are additive, the pulsations are amplified. If no damping is present, the
pressure amplitudes at the anti-nodes would, theoretically, go to infinity.
Actual piping systems have acoustic damping as a result of:
• Viscous fluid action (intermolecular shearing).
• Transmission, i.e., lack of total reflection, at a line termination,
• Piping resistance, i.e., pipe roughness, restrictions, orifices.
Therefore, damping of acoustic modes may be accomplished by placement
of resistance elements, such as an orifice, that will work most effectively
at velocity maxima.
Length Resonances in Distributed Acoustic Systems. The concepts of
acoustic waves, reflections, and resonance can be applied to describe
some of the classical length resonances [13].
The length resonances of certain piping elements are described in
terms of a foil-wave length. The acoustic wave length is the distance required
for a complete cycle of dynamic pressure reversal. The wave
length is related to the driving frequency and the acoustic velocity or
speed of sound:
where X = wave length, ft/cycle
c = acoustic velocity, ft/sec
f = driving frequency, Hz