I'm not certain if you are interested in hte noise generated at the discharge vent to atmosphere or the noise WITHIN a piping system. For a vent discharge to atmosphere I provide the following:
Formulas for noise level calculations are available from any major relief valve vendor such as Farris, Consolidated or Crosby. Crosby's, for exaample, may be found in hteir Engineering Handbook in Chapter 7, page 7-10. I'm providing it for you below:
L100 = L + LOG10 (0.29354*W*k*T/M)
where:
LOG10 means to take the LOG to the base 10
L100 = sound level at 100 feet from the point of discharge
in decibels.
L = noise int3ensity measured as the sound pressure level at 100 feet from the discharge (from figure 7 in hte handbook) If you don't have the handbook, calculate the pressure ratio = absolute relieving pressure/absolute back pressure. If the pressure ratio calculated is 3 or greater , L as about equal to 55. If the ratio is from 1.5 to 3, L varies in a linear way from 30 (at 1.5) to 55 (at 3). If below 1.5, it is beyoind the chart limits, but assume it varies from 0 (for ratio = 0) to 30 ( at ratio = 1.5).
W = maximum relieving capacity in pph
k = ratio of specific heats
T = absolute temperature in Degrees Rankine
M = molecular weight
Also, when the noise level is required at a distance of other than 100 feet, use the following equation:
Lp = L100 - 20 LOG10 (r/100)
where:
Lp = sound level at a disctance, r, from the point of discharge in decibels
r = disctance from the point of discharge in feet
NOise from the discharge of a vent will of course occur only if the discharge flow is sonic; which means that the pressure at the vent tip is greater than atmospheric pressure. If not sonic tip pressure is equal to atmospheric or containment vesel pressure.
The more you learn, the less you are certain of.