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

Vibration and Noise in Pumps 439
Figure 18-8. Erroneous pressure measurement caused by stub resonance.
For example, an installation where the speed of sound was 4500 ft/sec
and the transducer was mounted one foot from the inside surface, the stub
(quarter-wave) frequency would be 1125 Hz. A fictitious pressure pulsation
component will be measured at this frequency and also at 3X, 5X,
7X, etc. The pulsation exists in the stub; however, it may not be present
in the main pipe. If this stub frequency is close to the vane or blade passing
frequency, the measured amplitude at the stub frequency will not be
valid because it would be amplified by the acoustical resonance. The
acoustical amplification factor can be as high as 200. To measure highfrequency
pulsations, the transducer should be mounted flush to the inside
surface of the pipe.
Measurements of peak-to-peak pulsations on an oscilloscope are often
suspect. If the transducer signal frequency spectrum is analyzed and the
quarter-wave resonance identified, then credible results can be obtained.
An electronic filter may be used to eliminate the undesired frequency.
Coincidence of Driving Acoustic Frequencies and Length Resonances.
The existence of quarter or half-wave natural frequencies alone
does not constitute resonances. For resonance to occur, a dynamic pulse
must be generated at a frequency equal to an acoustical natural frequency.
The build-up in amplitude occurs because a reflected wave arrives
at the proper time to reinforce the wave generated at the pump. The
arrival of the reflected wave is dependent upon the path length of the piping
elements. Therefore, the standing wave pattern amplitude is reinforced
so that the actual maximum pulsating wave amplitude is substan-