Leakages and pressure relation : an experimental research

Leaks in water systems are presently a frequent and increasing event that involves cost increase and poor service, not compliant to quality standards and modern management criteria. The most recent data available in Italy, resumed into the report issued by Control Committee for Water Resources Use (CONVIRI), shows leakages with an average value of 37 %. It is therefore important, for maintenance perspective, to investigate occurrence and evolution of water leaks and the analytical link between leaks Qp and network pressure P, for a reliable calibration of water networks quali-quantitative simulation models. The present work reports the first results of an experimental campaign started at Laboratory of Hydraulics of Department of Hydraulics, Geotechnical and Environmental Engineering of University of Naples Federico II in order to analyze the features ofQp(P) relation, which are compared with other results issued in literature.


Introduction
Leaks in water systems are presently a frequent and increasing event causing cost increase and poor service levels not compliant to quality standards and modern management criteria.The most recent data available in Italy are resumed into the report issued by Control Committee for Water Resources Use (CONVIRI, 2010) which shows leakages between 21 % and 61 %, with an average value around 37 %.The recovery of part of these lost water volumes would allow to acquire "new" resources and also economical benefits due to adduction, treatment and distribution cost savings.Losses reduction could obviously be achieved by well planned maintenance campaigns, both ordinary and extraordinary: they are, however, expensive actions from a financial perspective and are often not rewarded by the economical value of the recovered resource.
A different approach is to control network operation pressure by installing PRVs (Pressure Reducing Valves) or realizing District Meter Areas (DMAs).For this purpose it is important to analyze the forming and evolution mechanisms of water leaks and the analytical link between the leaks Q p and the network pressure P.An experimental research on these topics has been started at the Hydraulics Laboratory of Department of Hydraulics, Geotechnical and Environmental Engineering of University of Naples Federico II (De Paola et al., 2010;De Paola and Giugni, 2010), in order to investigate the parameters affecting the leakage/pressure relationship for different pipe materials.The present work gives a global summary of all the experimental tests conducted so far.In particular, results of the dynamic tests performed on steel and ductile iron pipes are presented, and compared to the other ones present in literature (Sendil and Al Dhowalia, 1992;Lambert, 2000;Thornton and Lambert, 2005;Greyvenstein and Van Zyl, 2006;Milano, 2006;Coetzer et al., 2006;Ferrante et al., 2010;Massari et al., 2012).(Fig. 1).This latter in the first tests was a steel pipe 100 mm nominal diameter (DN 100) and thickness s = 4 mm, 6.70 m long and flat; in the second tests was a last generation ductile iron pipe (BLUTOP -PAM Saint Gobain) nominal diameter (DN 125) and thickness s = 3 mm.The choice of the pipe materials at this early stage of the research is due to the the large use of steel and ductile iron pipes in Italian water distribution networks.
At the downstream end of the experimental duct was fitted a rubber wedge sluice valve (Fig. 1), connected to a PVC ∅110 pipe which collects discharge to a recirculation tank.At 3.35 m downstream of the experimental pipe was installed a junction with an interception spherical valve at the end of which there is a nozzle used to simulate the occurrence of a leak (detail of Fig. 1).
This layout is assumed to reliably reproduce private connections in water distribution networks, where leakages due to metal pipe damages are more likely to occur.Furthermore the flow that is established in the pipe branch is surely a function of the geometry and the roughness of the main pipe.The boundary conditions must be taken into account and they are established only by the pressurized pipeline.
During the tests the water discharge flowing out of the nozzle is collected into a tank suitably calibrated, measuring filling time or, as alternative (for the ductile iron pipe), is measured by a small size electromagnetic flow meter (DN 25) (Fig. 1).Pressure measure is run by a WIKA transducer with a 0-10 bar range and sample frequency equals to 10 Hz.
In the tests the following parameters were varied: 1. feeding pressure, between 2 and 7 bars; 2. water discharge between 3 and 45 l s −1 ; 3. nozzle geometry: the presence of leaks with different shape and size was simulated by using suitable nozzles: round, rectangular, square, irregular (Fig. 2); aiming to achieve, by tests analysis, the water discharge and feeding pressure relationship.

Experimental results
Experimental tests were run with both static and dynamic approach, in order to simulate various operating conditions of a water system.The static tests simulate the night operating conditions (suitable to verify more precisely leaks occurrence), while the dynamic tests simulate day running.During each test, pressure was detected at least for 60 s, in order to evaluate pressure variation features due to the leak.

Steel pipe -static tests
Generally a power law function is used to interpret the relation between water leaks (Q P ) and pressure (P) as follows: In static tests conducted on steel pipe the driving pressure P was varied in the range 2-7 bar, while the discharge Q between 1 and 30 lps.The tests results allowed to calculate for the considered nozzle shapes, with a very high correlation rate (R 2 always above 0.99), the values of coefficient a and exponent b in Eq. ( 1), as reported in Fig. 3.The coefficient a in both cases increases, as obvious, according to nozzle size.The exponent b, instead, is always little far from the theoretical value 0.50.

Steel pipe -dynamic tests
Dynamic tests allow to analyze, as already mentioned, the daily demand variation, by generating different discharge values (varying from about 3 to 45 lps) by the downstream valve.The tests duration was always about several minutes.In these tests, leaks increase, as expected, as pressure and nozzle size increase.The exponent b tends to a constant value, close but not equal to the theoretical value 0.50, also for dynamic test conditions (Fig. 4).
It can be also highlighted that coefficient a has an almost linear trend as surface ratio A n /A p (A n = nozzle area; A p = pipe cross sectional area) varies for nozzles having either square or rectangular section, while for round section it shows a linear trend according to d 2 /D 2 ratio and a parabolic trend according to d/D ratio (d = nozzle diameter; D = pipe diameter) (Fig. 4) as also shown for the static tests.

Ductile iron pipe
In the first phase of experimental tests (steel pipe) the discharge was detected by a volumetric tank of small volume (see Fig. 1) and the duration of dynamic tests was therefore limited to few minutes.An evolution in the laboratory equipment was brought by introducing an electromagnetic flow meter on the pipe branch which allowed a continuous record of leakage discharge.The electromagnetic flowmeter, provided by Automation Progetti s.r.l., measures discharge in the range 0.047-5.55lps with a precision of ± 0.5 % of the upper limit.
Experimental tests for ductile iron pipes were run in the already described way but with longer duration (almost 1 h), in order to analyze leaks variations as discharge and pressure vary in the feeding pipe.
Figure 5 shows the close correlation between outflow discharge and pipe pressure for a rectangular (10 × 2 mm) and a round (6 mm diameter) nozzle.In Fig. 6 is also shown the time progress of flow experimental values compared to the points given by Eq. ( 1) after calibrating a and b coefficients using a Genetic Algorithm (GANetXL software, CWS, 2010).The GA was run varying at each iteration the a and b values in order to minimize the sum of the square differences between measured discharge at time t and that obtained by Eq. ( 1) at the same time.
The model resulted very effective in the calculation of losses, and calibration leads to exponent b values slightly lower than the theoretical value 0.50.
The results of the dynamic tests performed on ductile iron pipe (Fig. 7) confirmed the findings of the tests carried out on steel pipe.For the b exponent, tests indicate a substantial invariance, with values almost always slightly below 0.50.

Conclusive remarks
Starting from the first experiments run in UK (Goodwin, 1980), the relation between water leaks and pressure ratio was analyzed through the monomial Eq. ( 1).Some research works afterwards developed in Saudi Arabia (Sendil and Al Dhowalia, 1992), UK (Burnell and Race, 2000) and Iran (Ardakanian and Ghazali, 2003) by the analysis of field data on different kind of pipes and different discharge range, confirmed such equation: available data are summarized in Table 1, showing that exponent b resulted systematically higher than 0.50.
The experiments run so far in Naples for metal pipes, with pressure varying within a wide range not investigated in other experimental works, have shown as follows:    -the relation (1) allows a reliable forecast of leaks depending on pressures, if (a) and (b) coefficients are suitably defined; -a values show an increasing trend with the size of the outflow orifice.Since the combination of the pressure and the pipe stiffness for metal pipes produces negligible strains around the hole there is a linear dependence from A n /A p ratio, also for circular nozzles for which in Figs. 3, 4, 7 the influence of the only characteristic dimension (diameter d) was highlighted.
-b exponent resulted little far from the theoretical value 0.50 for both round and rectangular nozzles; -b values resulted slightly dependent from test characteristics (static or long-term dynamic).
Experimental data collected in Naples so far, therefore, confirm the results achieved by other tests for steel pipes (Fig. 7) with round nozzles (Coetzer et al., 2006), with reference to a range of pressures slightly smaller.The b values significantly higher than 0.50 reported in literature are related instead to steel pipes affected by corrosion and asbestos cement or plastic pipes with longitudinal cracks.Probably they are due to a reduced consistence of material around the holes (due to corrosion) (Greyvenstein and Van Zyl, 2006) or to the remarkable flexibility of plastic pipes (Farley and Trow, 2003;Walski et al., 2006;Ferrante et al., 2010;Bovolin and Picciotti, 2008).
For pipes characterized by high elasticity, then it would be appropriate to refer to an equation that takes into account the pressure/area link of the hole (such as FAVAD equation, Cassa et al., 2010).The analysis is, however, further complicated by the viscoelastic characteristics of materials such as HDPE.
Nevertheless, in the authors opinion these topics require more investigations to discern if they depend on the physics of the problem or maybe there is a distortion induced by the ThamesWater (Burnell and Race, 2000) 1.00 Supply-pipe leakage patterns in over 2000 accurately-logged domestic sites Iran (Ardakanian and Ghazali, 2003) 1.10-1.18Old cast iron with high leakage in Sanadaj (Kurdistan) Figure 8. Corroded steel pipes (Greyvenstein and Van Zyl, 2006).
analysis of experimental data.For example, for steel pipes with holes caused by corrosion, the coefficients b identified experimentally (Greyvenstein and van Zyl, 2006) for the pipes 4, 5 and 6 shown in Fig. 8 are, respectively, 0.67, 1.96 and 2.3; for an undamaged pipe, with the same mechanical properties, with an artificial hole diameter of 12 mm, the identified coefficient is equal to 0.518.Further experiments are still in progress in the Hydraulics Laboratory of Naples on pipes of different materials (HDPE, GRP), in order to acquire new elements about the influence of the characteristics of the pipe and the features of the hole simulating the leak on the outflow mechanisms and, therefore, on the leakage law.

Figure 2 .
Figure 2. Test nozzles with different shape and size.

Figure 3 .
Figure 3. Discharge coefficients according to: (a) surface ratio A n /A p (rectangular nozzles); (b) diameter ratio d/D (round nozzles).Static tests on steel pipe.

Figure 4 .
Figure 4. Discharge coefficients according to: (a) A n /A p ratio (rectangular nozzles); (b) d/D ratio (round nozzles).Dynamic tests on steel pipe.

Figure 5 .Figure 6 .
Figure 5. Trend of detected pressures and outflow discharge for a rectangular (a) and a round (b) nozzle.

Figure 7 .
Figure 7. Discharge coefficients according to: (a) A n /A p ratio (rectangular nozzles); (b) d/D ratio (round nozzles).Dynamic tests on ductile iron pipe.

Table 1 .
Exponent b values as reported in literature.Operating districts with little night metered consumptions SaudiArabia(Sendil and Al Dhowalia, 1992) 0.54-1.61Tenoperating districts in Riyadh