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# Flow Induced Vibration of Power and Process Plant Components: A Practical Workbook

By
M. K. Au-Yang, Ph.D., P.E.
M. K. Au-Yang, Ph.D., P.E.
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ISBN-10:
0791801667
No. of Pages:
494
Publisher:
ASME Press
Publication date:
2001

Although not the most costly, acoustically induced vibration is probably one of the most common vibration problems in the power and process industries. Vessels, piping systems, valve cavities, heat exchanger internals, ducts and many other components are potential resonators in which standing waves can form, while fans, pumps, valves, elbows, obstruction and discontinuities in flow channels, or even the addition or removal of heat all have the potential to excite these standing waves. Once the resonant conditions are met, the resulting sound intensity in most cases will require remedial action. In some cases, acoustic excitation can cause rapid fatigue failure of piping welded points, valve internal parts and other components.

The first requirement in acoustically induced vibration analysis is to calculate the velocity of sound in the fluid media. The velocity of sound in air at 68 deg. F (20 deg. C) and one atmospheric pressure is 13,500 in/s or 343 m/s. The velocity of sound at other temperatures can be readily calculated from the equation,
$c=(∂p∂ρ)s=γpρ=γGT∝Tγ=Cp∕Cv$
where T is the absolute temperature in either deg. R or deg. K, depending on which unit system is used. At atmospheric pressure and 0 deg. C (32 deg. F) the velocity of sound in water is 55,288 in/s or 1,404 m/s. The velocity of sound in water, steam or water-steam mixture at any given temperature and pressure combination can be calculated from information given in the ASME Steam Table (1979), as outlined in Examples 12.2 and 12.3. A table of velocity of sound in water at selected values of temperatures and pressures are given in Chapter 2, Table 2.1.
In a heat exchanger, the velocity of sound in the direction transversal to the tube bundle axis is decreased by the presence of the tubes. If c0 is the velocity without the tubes and c is the velocity in the presence of tubes, then
$c=c01+σ$
where σ is the ratio of the heat exchanger internal volume occupied by the tubes to the total volume.
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