Allwright, D.J.

English

Mathematics in Industry Information Service Eprints Archive

Noise Generation by Water Pipe Leaks
Problem presented by
Matin Thompson
Mecon Ltd
Problem statement
Leaks from water supply pipes generate noise, which can be used to locate
the position of the leak. The Study Group was asked to clarify the processes
generating the noise, so that the noise characteristics might provide other
information about the leak, in particular the size of a leak if possible.
Study Group contributors
D. J.Allwright (Smith Institute)
C. J. Chapman (Keele University)
S.D.Howison (University of Oxford)
J.R.Ockendon (University of Oxford)
Report prepared by
D. J.Allwright
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1 Introduction
Leaks from water supply pipes generate noise, which can be used to locate the position
of the leak. Mecon would like to understand the processes generating the noise, in order
to use the noise characteristics to provide other information about the leak, in particular
the size of a leak if possible.
Experiments carried out by Mecon have used the experimental setup indicated in
Figure 1.








Tap
Pressure gauge
From mains supply
Steel wool to absorb sound
Vertical tube over leak
Figure 1: Diagram of Mecon experiment
Water supply was taken from the mains, via a length of hose, through a garden tap
which was used to control the pressure, then to a pressure gauge, then into a 5m long
ductile iron (DI) pipe of diameter 100mm. The pipe was supported on bags of grit at
0.5m intervals to provide some mechanical damping, and coarse steel wool was inserted
in the ends for the same reason. A leak hole was drilled half way along the pipe, and
noise was measured with a microphone attached to the outside of the pipe at different
positions. The noise was analysed over 0–40 kHz. Water leaking into air was found to be
very quiet. Therefore a plastic tube, of diameter 30mm, was attached to the pipe over
the leak with a silicone sealant, and provided a head of 200mm of water for the leak to
drive into. An increase in this height to 1m made little difference to the noise. However,
with 200mm, there were significant differences depending whether the tube was vertical
or at 20◦ to vertical, apparently due to swirl and induced air entrainment in the tube.
The main set of experiments was therefore conducted with a vertical 200mm tube
over the leak. The leak noise spectrum was measured for circular holes of diameter
d = 1mm, 2mm, 4mm, 6mm, 8mm, at pressure levels p = 1, 2, . . .Bar up to the
maximum pressure that occurred with the tap fully open. (This maximum pressure was
p = 5.6Bar for d = 1, 2mm; p = 4.6Bar for d = 4mm; p = 2.7Bar for d = 6mm; and
p = 1.4Bar for d = 8mm. These pressures are relative to atmospheric.) The detailed
noise spectra are included in the Mecon report [1], along with some discussion of them.
An independent comment on the problem was provided by S.V. Sorokin of
St. Petersburg on 30-Mar-2001, and this is included as an Appendix. However, the
Study Group participants did not have the chance to meet Prof Sorokin and therefore
did not really discuss his comments.
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2 Comments on the experimental results
It seemed to those working on this problem at the Study Group that the differences
between leaking into air, leaking into water in a vertical tube, and leaking into water
in an inclined tube were probably the most significant observations: they show that
the environment the water leaks into probably has much more influence on the noise
generated than the size of the leak itself.
A further observation about the spectra, in addition to those noted in [1] is most
noticeable in the results for d = 1mm. Whereas in general there is a trend that as
the pressure increases the noise level increases, a distinct exception to that is noticeable
in Graph 2 of [1]. Below about 4 kHz, the noise level for p = 1Bar exceeds that for
p = 2Bar, perhaps by 20 dB. The only explanation that the Study Group could offer for
this is to suggest that it may be an effect of noise generated at the tap that is used to
reduce the hydrostatic pressure in the pipe. It may be that with d = 1mm, and with the
tap closed off enough to reduce the pressure to 1Bar, the noise generated by the tap is
in fact greater than that generated by the leak. Thus when the tap is opened up slightly
to increase the pressure to 2Bar, although the leak noise as such increases, the drop in
tap noise is actually the main change, and results in a lower overall recorded noise level.
Checking with Mecon, it was confirmed that this was possible, and that no particular
care had been exercised to prevent tap noise from leaking into the experiment, other
than the steel wool already referred to.
This observation led the Study Group to treat the experimental data with some
caution, since we clearly cannot always be sure how much of what is recorded is genuinely
leak noise and how much is tap noise — which of course will have a generally similar
character.
3 Noise generation mechanisms in the experiment
3.1 Turbulent flow in the vertical tube
Following Mecon’s observation that the presence of the vertical tube is a significant
element in the noise generation, we discuss the general nature of the flow in the tube.
The velocity at exit from the leak will be U =
√
2p/ρ if all the pressure drop p is across
the leak. This gives U = 14m/s for p = 1Bar, 16m/s for 1.4Bar, and 32m/s for 5.6Bar.
The Reynolds number Re = Ud/ν for d = 1mm and U = 16m/s is Re = 1.6× 104. So
there will be a turbulent jet in the tube, and we also note that the boundary layers on
the edges of a drilled hole will be thin. (Of course, real leak holes present considerably
more variety than the drilled hole in the experiment.)
In general the turbulent jet in the exit tube will have a half angle of about 10◦, which
will mean that it hits the wall of the tube at a height of about 85mm. In general terms,
the jet will “run out of momentum” in a distance of order l = d
√
Re, and for the figures
above, this jet length l = 120mm. For larger diameter holes or larger pressures, the
jet length is larger than this. Hence when the jet hits the walls of the tube it will still
be carrying significant turbulent pressure fluctuations which will be transmitted to the
tube, and hence to the pipe.
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We should point out that we have not estimated the fluid-solid coupling at all, merely
shown that the turbulent jet in the tube will reach the walls.
The aeroacoustics of the sound generated by a fluctuating flow in the vicinity of a
small stationary object show that the total power radiated is proportional to
ρ0U
6
c L
2/c30 (1)
where ρ0 and c0 are the fluid density and sound speed, Uc is an appropriate characteristic
flow velocity and L the size of the object. (See [5] p.125). This is expected to give the
scaling of the dipole sound generated by this interaction of the turbulent flow with the
rigid boundary.
3.2 Pressure fluctuations in shear layers
These are internal to the fluid, and would be expected to be only weak sources of noise.
3.3 Vortex shedding
One possible source of instability in the flow through the hole is vortex shedding. The
frequency of this is of order U/d which is of order 104–105 Hz, larger than shown in the
experiments, and with a definite d-dependence, whereas the experiments showed that the
spectrum of the noise had a fairly standard form, with features occurring at frequencies
that did not depend on d.
3.4 Bubbles
No bubbles were seen in the tube in the Mecon experiments. This makes it difficult to
see how they can be involved in the noise production, even though of course bubbles are
much the most common means of converting pressure fluctuations in a flow into noise.
The possibility that there might be small bubbles that escaped observation was raised,
but as pointed out in [2] the resonant frequency of an air bubble in water is 340/DHz
where D is the diameter in cm. Hence bubbles too small to be seen would produce
frequencies higher than we are considering here.
The only way in which bubbles might be playing a role would be if they were entrained
in a way that prevents them from rising up the tube.
4 Noise generation mechanisms in practice
If we consider what might happen for a real pipe leak, then of course there are
considerable differences from the experiment above. The jet will gradually excavate
a cavity, which will either be full of water or have some air in it, depending on the
nature of the surrounding material. In a cavity with air, there is the possibility of air
entrainment at the free surface, which will be noisy. Whether or not air is present, there
is the possibility of solid particles being carried round in swirling flow, generating noise
by their impacts on the pipe. The spectrum of this would be expected to have a peak
at frequencies of order L/U (the reciprocal of the residence time), so for a cavity of
diameter L ≈ 1 cm, this would be 1.6 kHz.
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5 Suggestions for further experiments
The observation made earlier suggests that tap noise should be carefully controlled in
any future experiments.
Also, there is perhaps value in looking at the noise generated by water leaking into a
cavity, and the dependence of this on cavity size, and on whether the cavity is water-filled
or contains some air.
A Appendix: comments of S.V. Sorokin
The mechanism of noise generation most likely is:
At low frequencies — unsteady flow separation at the hole
At high frequencies — cavitation.
Both mechanisms provide a uniform excitation in broad frequency bands. This is why no
particular frequency is specified for plastic pipes and measurements may be performed at
any frequency up to 200Hz, i.e. at the range of low frequencies. This statement for high
frequencies is supported by experimental results reported for DI pipe: there is a broad
maximum around 16 kHz. The presence of resonant frequencies at 3.3 kHz and 4.175 kHz
in DI pipe may be explained by an influence of some inhomogeneities (e.g. joints) which
add a discrete frequency spectrum on top of a continuous spectrum of an infinitely long
tube. This aspect should be clarified by some additional experimental data. Does a pipe
have joints? How is the pipe mounted in the experimental rig? What is the influence of
the pipe’s thickness and radius on these resonant frequencies?
In the case when noise generation is related to a flow separation (low frequencies),
its intensity should depend on the area of the hole, because this area controls the water
discharge. In the high-frequency case, the intensity of cavitation-generated leak noise
does not depend on the leak size.
The mechanism of transportation of the noise is related to duct (axisymmetric)
modes in fluid loaded elastic cylindrical shells; it has been analysed by Fuller and Fahy,
see [3] and [4]. The mechanism of generation of the noise is (most likely) of a purely
hydrodynamic nature. It is related to an unsteady flow at the hole and is not coupled
with the deformation of the pipe.
References
[1] Leak noise tests at AES. Mecon Ltd. Supplied at Study Group.
[2] Waves in fluids. James Lighthill. CUP, 1978.
[3] Characteristics of wave propagation and energy distributions in cylindrical elastic
shells filled with fluid. C.R. Fuller and F. J. Fahy. Journal of Sound and Vibration 81
501–518, 1982.
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[4] The input mobility of an infinite circular cylindrical elastic shell filled with fluid.
C.R. Fuller. Journal of Sound and Vibration 87 409–427, 1983.
[5] Aeroacoustics. M.E.Goldstein. McGraw-Hill, 1976.
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Noise Generation by Water Pipe Leaks

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