Page 53 - Valve Selection Handbook

40 Valve Selection Handbook

The speed at which the compression zone extends towards the inlet
end of the pipeline is uniform and equals the velocity of sound in the liq-
uid within the pipe. When the compression zone has reached the inlet
pipe end, all liquid is at rest, but at a pressure above the normal static
pressure. The unbalanced pressure now creates a flow in the opposite
direction and relieves the rise in the static pressure and the expansion of
the pipe wall. When this pressure drop has reached the valve, the whole
liquid column is again under normal static pressure, but continues to dis-
charge towards the inlet pipe end so that a wave of subnormal pressure is
created, starting at the valve. When this pressure wave has made the
round trip, the normal pressure and the original direction of flow are
restored. Now the cycle starts again and repeats itself until the kinetic
energy of the liquid column is dissipated in friction and other losses.
Joukowsky has shown that instantaneous valve closure raises the static
pressure in the pipeline by:

where
AP = rise in pressure above normal
v = velocity of a rested flow
a = velocity of pressure wave propagation
-il/2

=
Pfi+^1
_E{ Ee J_

p = density of the liquid
K = bulk modulus of the liquid
E = Young's modulus of elasticity of the pipe wall material
D = inside diameter of pipe
e = thickness of pipe wall
c = pipe restriction factor (c = 1.0 for unrestricted piping)
B (SI units) = 1.0
2
B (imperial units, fps) = g = 32.174ft/s

In the case of steel piping with a D/e ratio of 35 and water flow, the
pressure wave travels at a velocity of approximately 1200 m/s (about