Page 55 - Valve Selection Handbook

42 Valve Selection Handbook

with the liquid or separated from the liquid by a flexible wall or a pres-
sure relief valve.
The effects of waterhammer may also be altered by deliberately
changing the acoustic properties of the fluid. This can be done, for exam-
ple, by introducing bubbles of a non-dissolvable gas directly into the
fluid stream. The effect of this is to reduce the effective density and bulk
modulus of the fluid. A similar effect can be achieved if the gas is
enclosed in a flexible walled conduit, or hose, which runs the length of
the pipe.
If even a small amount of gas is present, the effect of pipe wall elastic-
ity in Equation 2-26 becomes insignificant, and the modified acoustic
velocity may be expressed by:

where
K = modified fluid bulk modulus

", ri)V'l
j
UJK
+

p = modified fluid density

V v
g i
= P + (
*f H
B = 1.0 (coherant SI units)
2
B = 32.174 ft/s , (imperial units, fps)
K g = bulk modulus of gas
K! = bulk modulus of liquid
= volume of gas
V g
Vj = volume of liquid
= total volume
V t
= density of gas
p g
p! = density of liquid