Solenoid valves - Bürkert Fluid Control Systems

3.4.
Opening and closing
operations in pipes
with fluids
p R
Pressure waves
a
a
Valve upstream pressure
p R bei w = 0
p F bei w 1
3.4.1. Origination and propagation
of pressure waves
If the velocity of a fluid stream in a pipe
changes as the result of opening or
closing a valve, it results in a conversion
of the kinetic energy of the fluid
into a pressure wave which is propagated
from the valve at the propagation
speed “a” of the flow medium against
the flow direction (Figure 11), until
reaching the tank or vessel outlet
(deflection point) where it is reflected
again, etc. This results in pressure undershoots
and overshoots which are
referred to as suction surges and
pressure surges or “water hammer
phenomena”.
In the case of compressible fluids, the
propagation speed “a” of pressure
and velocity changes is equal to the
speed of sound a in the medium in
question.
Speed of sound “a” for fluids in thickwalled,
rigid pipes:
Where:
E: Modulus of elasticity of the
medium in N/m 2
: Density of the medium.
w 0
w 1
L
Figure 11:
Basic mechanical construction of a simple pipe run system
a =
E
[m/s]
Speed of sound “a” for fluids in thinwalled,
flexible pipes:
E F 1
a = · [m/s]
1+ D·E F
S·E R
w 0
w 1
Unobstracted outlet
The following approximate values can
be assumed for the speed of propagation
or speed of sound in water:
Thick-walled metal pipes: a ≈ 1300 m/s
Thin-walled pipes: a ≈ 1000 m/s.
Equation 10
Where:
D: Pipe diameter
S: Wall thickness
E F : Modulus of elasticity of the
fluid
E R : Modulus of elasticity of the
pipe material.
32/33