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

Vibration and Noise in Pumps 487
Figure 18-42, High speed pump vibrations after bearing modification.
At low pressure, water can be considered to be incompressible and the
acoustic velocity is primarily dependent upon the change of density with
respect to temperature. The acoustic velocity of water at low pressures
[48] is given for various temperatures from 32° to 212°F in Figure 18-
43. For elevated pressures, the acoustic velocity must be adjusted for
pressure effects and the function using the bulk modulus is convenient.
The bulk modulus of water [49] can be calculated with the following
equation for pressures up to 45,000 psig and various temperatures.
where K 0 = constant from Table 18-6
K s = isentropic tangent bulk modulus, psi
P = pressure psia
The calculation accuracy is ± 0.5 % for the isentropic bulk modulus of
water at 68°F and lower pressures. The error should not exceed ± 3% at
elevated pressures (greater than 44,000 psi) and temperatures (greater
than 212°F).
The bulk modulus for petroleum oils [50] (hydraulic fluids) can be determined
for various temperatures and pressures by using Figures 18-44
and 18-45 which were developed by the API. The isothermal secant bulk
modulus for petroleum oils at 20,000 psig is related to density and tern-