Abstract

A pressure reducing valve (PRV) regulates the outlet pressure regardless of the fluctuating flow and varying inlet pressure, thereby reducing leakage and mitigating the stress on the downstream water distribution network (WDN). Notwithstanding the crucial importance of PRVs, few experimental data are available in the literature. The aim of this paper is to overcome this gap by means of the results of a large number of tests carried out at the Water Engineering Laboratory of the University of Perugia, Italy. These tests have been executed on a standard type of PRV in steady-state conditions, to characterize it, and in unsteady-state conditions, to check its transient response. A broad range of laboratory conditions simulating possible events in WDNs has been examined and both short and long duration monitoring have been carried out. The analysis of the tests demonstrates the versatility of PRVs as a powerful tool for pressure management, and also when the flow condition changes according to the users' demand pattern. In fact, their transient response is appropriate with small pressure oscillations generated by the PRV self-adjustment. Moreover, proper PRV modelling has to include both its mechanical behaviour and the characteristics of the pressure pipe system in which it is installed.

INTRODUCTION

Complex topology and quite unpredictable users' demand of water distribution networks (WDNs) make it difficult to fulfil the requested functioning conditions. Particularly, within ordinary strategies to reduce leakage, there is the need for keeping the pressure at a given value downstream of some selected nodes. In fact, it often happens that, because of a reduction of the demand, the pressure exceeds the value in line with the discharge to be supplied downstream. As a consequence, an undesired increase of water losses takes place in the downstream part of the WDN. Instead of repairing pipe breaks – often time consuming and costly to detect and locate – leakage is managed by controlling the pressure regime by means of pressure reducing valves (PRVs). Such devices are hydraulically controlled and allow setting of the downstream pressure at a desired value (hereafter referred to as nominal set-point, HNSP, with H = piezometric head). When the upstream pressure exceeds HNSP, a partial closure of the PRV automatically happens and the local head loss through it increases.

Since PRVs control pressure by fully-automatic self-adjusting of their opening degree, and they do not require any type of external power source, they are installed throughout the world. Notwithstanding their crucial importance in the management of WDNs, a very narrow body of literature with an exhaustive experimental check of their actual behaviour is available. In fact, the literature is rich in contributions about the optimal location of PRVs in WDNs, as an example within the design of District Metered Areas (e.g., Vairavamoorthy & Lumbers 1998; Araujo et al. 2006; Liberatore & Sechi 2009; Nicolini & Zovatto 2009; Ali 2015; Creaco & Pezzinga 2015a, 2015b; Sivakumar & Prasad 2015; Covelli et al. 2016). Moreover, most of the scarce literature on the actual behaviour of PRVs is focused on their dynamic modelling and possible instability (e.g., Simpson 1999; Prescott & Ulanicki 2003, 2008; AbdelMeguid et al. 2011; Ulanicki & Skworcow 2014; Ulanicki et al. 2015), transients generated by their action (e.g., Meniconi et al. 2015a), and the related negative effects in terms of water quality (Brunone & Morelli 1999; Karney & Brunone 1999). As a result, there is a need for analysing the performance of PRVs with regard to some very important features from the management point of view: (i) fulfilment of HNSP for different values of the upstream pressure, (ii) response to fast/slow demand changes, and (iii) role of the pipe system configuration.

The purpose of this paper is to verify how well a PRV – in particular the one manufactured by Donald G. Griswold, the inventor of this kind of device in 1936 – maintains a fixed and specified downstream pressure under a range of rapidly and slowly changing flow conditions in a pipe system. Specifically, the aim is to fill some of the gaps in the PRV characterization with regard to both steady- and unsteady-state behaviour by means of the experiments executed at the Water Engineering Laboratory (WEL) of the University of Perugia, Italy. In such tests, the PRV is installed in a high-density polyethylene (HDPE) pipe, where different system configurations and demand patterns are simulated to check its performance; demand changes are carried out by manoeuvring an automatically controlled valve or by pump trip and start up.

This paper is an extension of the one presented at the 2nd edition of the International Conference on ‘Efficient & Sustainable Water Systems Management toward Worth Living Development – EWaS2016’ (Meniconi et al. 2016).

EXPERIMENTAL SETUP

The HDPE laboratory pipe at WEL has an internal diameter of D = 93.3 mm, a nominal diameter DN110, and a wall thickness equal to 8.1 mm (Figure 1). The pipe is supplied by a pressurized tank (T) in which the head is assured by means of two pumps whose shutoff heads are HT,Q=0 = 22 m and HT,Q=0 = 55 m (Q = discharge), respectively. In the downstream end section of the pipe, an automatically controlled motorized butterfly valve (MV), with DN80, is placed.

Figure 1

Sketch of the experimental setup (T = supply tank; PRV = pressure reducing valve; MV = manoeuvre valve; pressure measurement sections: U = upstream of the PRV; D = downstream of the PRV; V upstream of the MV).

Figure 1

Sketch of the experimental setup (T = supply tank; PRV = pressure reducing valve; MV = manoeuvre valve; pressure measurement sections: U = upstream of the PRV; D = downstream of the PRV; V upstream of the MV).

A PRV (Figure 2) with DN80 is installed at a distance L1 = 129.6 m downstream of T; to check the role played by the system configuration, during tests, two values of the length of the pipe downstream of the PRV, L2, have been considered (=69.7 m and 181.8 m, with L=L1 + L2 being the total length).

Figure 2

The experimental pipe and the PRV (in the insert) at the Water Engineering Laboratory (WEL) of the University of Perugia, Italy.

Figure 2

The experimental pipe and the PRV (in the insert) at the Water Engineering Laboratory (WEL) of the University of Perugia, Italy.

In Figure 3, a schematic of the PRV, with the main valve and the pilot control system, is reported. The main valve is hydraulically operated and diaphragm-actuated. It is controlled by the pilot (CP), in which HNSP is set by adjusting the compression of a spring placed above the CP diaphragm. When the pressure at section O exceeds HNSP, CP closes, and the flow from section I towards the cover chamber actuates the diaphragm of the main valve which closes. Otherwise, when pressure at the outlet section O is smaller than HNSP, CP opens, allowing the flow from the inlet section I to section O, through the strainer-orifice assembly (SOA). Such a pressure reduction downstream of the SOA lets a flow from the cover chamber to the SOA take place. This flow actuates the diaphragm of the main valve, which opens. The opening/closing speed of the main valve is set by means of the control valves CV.

Figure 3

Schematic of the PRV (modified from http://www.cla-val.com/waterworks-pressure-reducing-valves): I = inlet section, O = outlet section, CV = check valve, SOA = strainer-orifice assembly, CP = control pilot.

Figure 3

Schematic of the PRV (modified from http://www.cla-val.com/waterworks-pressure-reducing-valves): I = inlet section, O = outlet section, CV = check valve, SOA = strainer-orifice assembly, CP = control pilot.

During the tests, HNSP is fixed at 5, 10 and 26 m. Pressure signals, H, are acquired by piezoresistive transducers with a frequency acquisition of 1,000 Hz at: section V, placed immediately upstream of MV, section D, at a distance of 0.78 m downstream of the PRV, section U, at a distance of 0.79 m upstream of the PRV, and at the supply tank (Figure 1). The discharge, Q, and the minor head loss across the PRV, ζ, is measured by means of a magnetic flow meter (at a distance of 23.78 m from the tank), and a variable reluctance differential pressure transducer, respectively. Finally, the PRV relative opening degree, δ, is measured by means of an electronic valve position indicator.

PRV HYDRAULIC CHARACTERIZATION (STEADY-STATE TESTS)

Steady-state tests have been carried out to characterize the PRV: the minor head loss, ζ, has been measured for different values of δ (δ = 0% means fully closed valve, whereas 100% means fully open valve), and Q. Experiments have concerned turbulent flow – the usual flow regime in WDNs – and for each relative opening degree, the minor head loss coefficient, χ, has been determined through the following equation (Idel'cik 1986):  
formula
(1)
where g= gravity acceleration and A= pipe area. In Figure 4, the values of χ vs. δ, exhibit a typical power law behaviour (Idel'cik 1986), with the coefficient of determination, R2, equal to 0.985. The main differences between the interpolated curve and the experimental data happen at the small relative openings because of the unavoidable errors occurring for small values of Q, according to the findings of Brunone & Morelli (1999).
Figure 4

PRV steady-state characterization: experimental values of χ vs. δ and the interpolating curve.

Figure 4

PRV steady-state characterization: experimental values of χ vs. δ and the interpolating curve.

Since the PRV is not a partially closed in-line valve with a fixed opening degree (Meniconi et al. 2011a, 2011b), but a self-adjusting opening valve, HNSP and the inlet pressure, HU, play a crucial role.

To better understand the experimental behaviour of the PRV for a given Q but different HU and HNSP, the hydraulic grade line for the tests of Table 1 is reported in Figure 5. Figure 5(a) shows two tests with the same Q (=2.64 l/s) and inlet condition (HU = 46.0 m) but a different nominal set-point, which constrains the PRV to be more closed for test no. 1 (δ1 = 23.2% and χ1 = 4,425) with respect to test no. 2 (δ2 = 26.6% and χ2 = 2,786). Figure 5(b) concerns two tests with the same Q (=1.90 l/s) and nominal set-point but a different inlet condition (HU = 21.6 m for test no. 3 and HU = 48.4 m for test no. 4). In essence, the PRV has been automatically settled to a larger opening degree for test no. 3 (δ3 = 25.6% and χ3 = 3,156) with respect to test no. 4 (δ4 = 19.0%, and χ4 = 8,726).

Table 1

Steady-state tests for evaluating the role of the inlet and outlet pressures

Test (no.) Q (l/s) HU (m) HNSP (m) χ (–) δ (%) 
2.64 46 10 4,425 23.2 
2.64 46 26 2,786 26.6 
1.90 21.6 10 3,156 25.6 
1.90 48.4 10 8,726 19.0 
Test (no.) Q (l/s) HU (m) HNSP (m) χ (–) δ (%) 
2.64 46 10 4,425 23.2 
2.64 46 26 2,786 26.6 
1.90 21.6 10 3,156 25.6 
1.90 48.4 10 8,726 19.0 
Figure 5

Steady-state hydraulic grade line, with the sketch of the experimental setup for: (a) tests no. 1 and no. 2; (b) tests no. 3 and no. 4 of Table 1.

Figure 5

Steady-state hydraulic grade line, with the sketch of the experimental setup for: (a) tests no. 1 and no. 2; (b) tests no. 3 and no. 4 of Table 1.

In order to make the experimental results more general and clear, the following dimensionless quantities are considered: h=H/HNSP, Re = VD/ν, θ = t/Θ, where Re is the Reynolds number (V = mean flow velocity and ν = fluid kinematic viscosity), and Θ is the pipe characteristics time (=2L/a), with the pressure wave speed, a, assumed as equal to 368 m/s, according to Pezzinga et al. (2016).

Further steady-state tests have been executed to check the PRV behaviour for different values of Re. Figure 6 plots show that the difference occurring between the nominal set-point and the measured value of downstream pressure does not depend on Re.

Figure 6

Dimensionless PRV outlet pressure, hD, vs. the Reynolds number, Re.

Figure 6

Dimensionless PRV outlet pressure, hD, vs. the Reynolds number, Re.

PRV TRANSIENT RESPONSE (UNSTEADY-STATE TESTS)

This section shows the results of the tests (Table 2) executed to check the performance of the PRV during transients simulating changes specified by the user. In the laboratory tests, the discharge is changed by (i) manoeuvring the MV valve and (ii) varying the functioning conditions of the pumps feeding the tank. To cover the broadest range of the possible events taking place in WDNs, both short (i.e., with a duration of few seconds), and long (i.e., with a duration of some hours) tests have been considered. Moreover, to check the effect of the characteristics of the experimental setup, two different lengths of the pipe downstream of the PRV, L2, have been analysed. For the sake of clarity, transient tests are examined separately below on the basis of their duration; in Table 2 Rei (Ref) indicates the steady-state Reynolds number before (after) the manoeuvre.

Table 2

Unsteady-state tests for evaluating the PRV transient response (HNSP = 26 m)

Type of transient Test (no.) Type of manoeuvre Main characteristics 
Short duration MV complete fast closure Rei = 3.43*104, L2 = 69.7 m 
MV complete slow closure 
MV complete fast opening Ref =3.29*104, L2 = 69.7 m 
MV complete slow opening 
Pump trip Rei = 3.43*104, L2 = 69.7 m 
10 Rei = 2.47*104, L2 = 69.7 m 
11 Pump start up Ref = 3.43*104, L2 = 69.7 m 
12 Ref =2.47*104, L2 = 69.7 m 
Long duration 13 Daily demand pattern L2 = 69.7 m 
14 L2 = 181.8 m 
Type of transient Test (no.) Type of manoeuvre Main characteristics 
Short duration MV complete fast closure Rei = 3.43*104, L2 = 69.7 m 
MV complete slow closure 
MV complete fast opening Ref =3.29*104, L2 = 69.7 m 
MV complete slow opening 
Pump trip Rei = 3.43*104, L2 = 69.7 m 
10 Rei = 2.47*104, L2 = 69.7 m 
11 Pump start up Ref = 3.43*104, L2 = 69.7 m 
12 Ref =2.47*104, L2 = 69.7 m 
Long duration 13 Daily demand pattern L2 = 69.7 m 
14 L2 = 181.8 m 

Short duration transients

The effect of the complete closure of the manoeuvre valve (MV) placed at the pipe end section can clearly be inferred by signals reported in Figure 7: for a given Rei, the plots in the left (Figure 7(a)7(c)) and right (Figure 7(d)7(f)) part of the graph refer to a fast and slow closure of MV, respectively. With regard to the fast closure manoeuvre (Figure 7(a)7(c)), it can be observed that the fast increase of hD causes the simultaneous increase of hU, which oscillates because of the effect of the upstream boundary condition at the tank (Figure 7(a)). After the first phase of the transient, i.e., when the oscillations end, the value of hD (larger than 1) coincides with the one of hU since the PRV does not close fully. The same behaviour happens for the slow closure manoeuvre (Figure 7(d)7(f)): the much smoother trend of the signals – with the pressure oscillations suppressed both upstream and downstream of the PRV – is clearly due to its larger duration.

Figure 7

Short duration transients due to the fast (test no. 5) and slow (test no. 6) complete closure of MV.

Figure 7

Short duration transients due to the fast (test no. 5) and slow (test no. 6) complete closure of MV.

To check the performance of the PRV during transient causing an increase of Re, opening manoeuvres of MV with a different duration have been carried out (Figure 8). The fast opening manoeuvre (Figure 8(a)) generates a sudden decrease of hD, quite remarkable oscillations of hU (20% of HNSP at most), and an increase of Re (Figure 8(b)) and δ (Figure 8(c)). As for the closure manoeuvre, the effect of a longer duration of the opening manoeuvre is a much smoother behaviour of all signals: particularly, in Figure 8(d), hU exhibits much smaller oscillations (3% of HNSP at most). It is worth noting that for both transients of Figure 8 the final value of hD coincides approximately with 1 (Figure 8(a) and 8(d)).

Figure 8

Short duration transients due to the fast (test no. 7) and slow (test no. 8) complete opening of MV.

Figure 8

Short duration transients due to the fast (test no. 7) and slow (test no. 8) complete opening of MV.

To simulate an increase in user demand, the pressure upstream of the PRV has been reduced by abruptly stopping the electricity supply of the pump. Transients due to the pump trip are reported in Figure 9, where the plots in the left (Figure 9(a)9(c)) and right (Figure 9(d)9(f)) part of the graph differ for the value of Rei. These signals exhibit clearly that hU decreases quite fast, whereas in the first phase of the transient, hD (Figure 9(a) and 9(d)) and Re (Figure 9(b) and 9(e)) are almost constant since the PRV opens (Figure 9(c) and 9(f)), and the local head loss through it decreases. Thus, it can be stated that in such a phase the opening of the PRV offsets the decrease of hU. For hD smaller than 1 the action of the PRV is no longer necessary for pressure management (i.e., the small value of Re makes the PRV unreliable). Such a behaviour is more evident for the smaller value of Rei: in fact, at the end of test no. 9, δ is almost constant, whereas for test no. 10 there is not a clear automatic control of the opening degree and δ decreases (Figure 9(f)).

Figure 9

Short duration transients due to the supply pump trip.

Figure 9

Short duration transients due to the supply pump trip.

A quite different behaviour can be observed for the transients due to the pump start up (Figure 10), which simulates a decrease of the users' demand in WDNs. In comparison to the pump trip, for both values of Ref, there is a much closer link between hU and hD (Figure 10(a) and 10(d)) as well as a larger rate of change of Re (Figure 10(b) and 10(e)). The reason why in the first phase of the transient hD increases accordingly with hU is that, in that period of time, hD is smaller than 1. On the contrary, for both tests an abrupt reduction of the PRV opening degree (Figure 10(c) and 10(f)) and Re (Figure 10(b) and 10(e)) happens at about t = 340 s for test no. 11, and t = 260 s for test no. 12, when hD becomes larger than 1 (Figure 10(a) and 10(d)).

Figure 10

Short duration transients due to supply pump start up.

Figure 10

Short duration transients due to supply pump start up.

Long duration transients

Long duration (i.e., 12 hours) tests no. 13 and 14 of Table 2 have been executed to check the PRV performance when a typical demand pattern of WDNs with specified changes at designated times happens. In test no. 13, two peaks of the demands are imposed by regulating MV: about at the 4th (θ = 1.33) and 9th hour (θ = 3.13), respectively (Figure 11(b)). As expected, the PRV opening (Figure 11(c)) is directly proportional to the variation of Re (Figure 11(b)). In the time period far away from the demand variations, while hU changes accordingly with the pump characteristic curve – it diminishes with increasing RehD is about constant around 1 (Figure 11(a)). As pointed out in the previous section, the manoeuvre of MV modifies the pressure values with a maximum oscillation equal to 13% for hU, and 38% for hD.

Figure 11

Long duration transient due to the flow variation modulated by MV (test no. 13, with L2 = 69.7 m).

Figure 11

Long duration transient due to the flow variation modulated by MV (test no. 13, with L2 = 69.7 m).

To look at these variations in more detail, Figure 12 reports two magnified visions of Figure 11 in the time interval when the largest demand decrease (Figure 12(a)12(c)) and increase (Figure 12(d)12(f)) take place. In both cases, the larger pressure variations happen downstream of the PRV, whereas smaller pressure changes occur upstream, because of the combined actions of the supply tank and the PRV that almost isolates the upstream branch of the pipe.

Figure 12

Long duration transient (test no. 13): magnified vision of Figure 11 in the time interval when the largest demand decrease (a)–(c) and increase (d)–(f) take place, respectively.

Figure 12

Long duration transient (test no. 13): magnified vision of Figure 11 in the time interval when the largest demand decrease (a)–(c) and increase (d)–(f) take place, respectively.

The effect of the characteristics of the experimental setup has been checked in test no. 14. Particularly, the same demand pattern of test no. 13 (Figure 11) has been used but in a quite different system. In fact, the length, L2, of the pipe downstream of the PRV has been significantly increased (181.1 m compared to 69.7 m). Figure 13 demonstrates that the value of L2 does not affect significantly the PRV transient response since all the signals do not change appreciably.

Figure 13

Long duration transient due to the flow variation modulated by MV (test no. 14, with L2 = 181.8 m).

Figure 13

Long duration transient due to the flow variation modulated by MV (test no. 14, with L2 = 181.8 m).

PRV RESPONSE TO A LONG DURATION UNSTRESSED CONDITION

A continuous series of transients typifies what the actual functioning conditions of a WDN are: in fact, the variability of the users' demand signifies a repeated series of discharge variations, which give rise to as many pressure changes. The entity of such pressure variations depends on not only the value of the discharge change but also the topology of the system and in which part it happens. Moreover, the characteristics of the boundary conditions play a crucial role. As an example, a given incoming pressure wave splits into a number of smaller pressure waves at a cross-junction whereas it doubles at a dead end. As a consequence, in a WDN the pressure regime is the result of the overlapping of pressure waves coming from different parts of the system (e.g., Meniconi et al. 2015b) and the flow regime can be assimilated to a sort of ‘permanent’ unsteady condition. This implies that during the day – as for the above long duration transients – each part of the system is continuously more or less stressed.

Transients discussed in the previous section are examples of possible pressure surges where the PRV plays an important role but with its behaviour – i.e., its response – being a clear consequence of the WDN functioning conditions (as an example: if hU increases, the PRV closes and vice versa). On the contrary, in this section a ‘limit’ flow condition is examined to point out the PRV response to a long duration unstressed condition according to the intrinsic characteristics of the system (i.e., pipe material). The starting point of test no. 15 is the transient caused by the complete closure of the manoeuvre valve with Rei = 2.88*104 – i.e., a transient very close to the one in Figure 7 – with some pressure oscillations propagating upstream of the PRV (Figure 14(a)) and, as a final condition, Ref = 0 and hUhD. In fact, the PRV is not fully closed (Figure 14(c)), but its opening degree is quite close to zero. In other words, the system becomes a unique system and, since the PRV is inactive but partially open, static conditions take place. As time passes, it can be observed that hD moves towards 1, whereas hU does not change (Figure 14(d)) even if the measured Re is equal to zero (Figure 14(e)). Such an apparently unaccountable behaviour is justified, having in mind that a PRV only works if there is a flow through it or, in other words, it cannot reduce hD in a static system. This implies that a very small discharge takes place – undetectable by the installed magnetic flow meter – due to the elasticity of the pipe (a quite deformable polymeric one) system. In the meanwhile, since the value of the opening degree δ is close but not exactly equal to zero, when the effects of the initial closure manoeuvre vanish (Figure 14(f)), the PRV closes progressively until the flow stops completely. At this point the system is static, but with hD equal to 1, because the upstream and downstream sides of the pipe are not actually connected anymore. Ultimately, in such a behaviour of the PRV, which is due to a sort of ideal unstressed condition, the nominal set-point is slowly fulfilled and the PRV fully closes. The mechanism that generates a small flow, making the PRV active, depends on the characteristics of the pipe system: in the examined case, it is due to the remarkable deformation of the pipe and the steady pumping supply.

Figure 14

Transient due to the fast complete closure of MV: (a)–(c) short term monitoring, (d)–(f) long duration unstressed condition monitoring.

Figure 14

Transient due to the fast complete closure of MV: (a)–(c) short term monitoring, (d)–(f) long duration unstressed condition monitoring.

CONCLUSIONS

The target of the PRVs is to set the pressure downstream of a selected node at a given value (i.e., the nominal set-point) regardless of the upstream one. As a consequence, they play a crucial role in pipe system management since they allow reduction of leakage through pressure control.

Despite their great importance, in the literature there is a lack of knowledge about their actual performance. In this paper, laboratory tests have been executed on a standard PRV to characterize the steady-state behaviour and to examine the transient response.

Steady-state tests concerned the evaluation of the local head loss for different relative opening degrees in a turbulent regime. Moreover, since the PRV is not a partially closed in-line valve with a fixed value of the opening degree but a self-adjusting valve, the effect on its behaviour of both the inlet pressure and nominal set-point has been examined.

The aim of the unsteady-state tests is to check the response of the PRV to transients generated to simulate the variability of users' demand and supply conditions in WDNs. To explore a broad range of functioning conditions, different types of transients have been examined: (i) short duration events caused by discharge changes due to closing and opening manoeuvres of a controlled motorized valve or supply pump trip and start up; and (ii) long duration tests during which a typical daily demand pattern has been considered. Moreover, a long duration unstressed condition test has been monitored.

The executed tests demonstrate the versatility of PRVs as a powerful tool for pressure management in WDNs. Their transient response is appropriate with small pressure oscillations generated by the PRV self-adjustment. Proper PRV modelling must include both its mechanical behaviour and the characteristics of the pressure pipe system in which it is installed.

ACKNOWLEDGEMENTS

This research has been supported jointly by the University of Perugia, the Italian Ministry of Education, University and Research (MIUR) – under the Projects of Relevant National Interest ‘Advanced analysis tools for the management of water losses in urban aqueducts’ and ‘Tools and procedures for an advanced and sustainable management of water distribution systems’ – Fondazione Cassa Risparmio Perugia, under the project ‘Hydraulic and microbiological combined approach towards water quality control (no. 2015.0383.021)’, HK Research Grant Council (RGC)'s Theme-based Research Scheme and the Hong Kong University of Science and Technology (HKUST) under the Project ‘Smart Urban Water Supply System (Smart UWSS)’.

REFERENCES

REFERENCES
AbdelMeguid
,
H.
,
Skworcow
,
P.
&
Ulanicki
,
B.
2011
Mathematical modelling of a hydraulic controller for PRV flow modulation
.
J. Hydroinform.
13
(
3
),
374
389
.
Araujo
,
L. S.
,
Ramos
,
H.
&
Coelho
,
S. T.
2006
Pressure control for leakage minimisation in water distribution systems management
.
Water Resour. Manage.
20
(
1
),
133
149
.
Brunone
,
B.
&
Morelli
,
L.
1999
Automatic control valve induced transients in an operative pipe system
.
J. Hydraul. Eng.
125
(
5
),
534
542
.
Covelli
,
C.
,
Cozzolino
,
L.
,
Cimorelli
,
L.
,
Della Morte
,
R.
&
Pianese
,
D.
2016
Optimal location and setting of PRVs in WDS for leakage minimization
.
Water Resour. Manage.
30
,
1803
1817
.
Idel'cik
,
I. E.
1986
Handbook of Hydraulic Resistance
.
Hemisphere Publishing Corp
,
New York
.
Karney
,
B. W.
,
Brunone
,
B.
1999
Water hammer in pipe network: two case studies
. In:
Proc., Int. Conf. on Water Industry Systems: Modelling and Optimization Applications (CCWI1999)
(
Savic
,
D. A.
&
Walters
,
G. A.
, eds).
Research Studies Press Ltd
,
Baldock
,
UK
,
1
, pp.
363
376
.
Meniconi
,
S.
,
Brunone
,
B.
,
Ferrante
,
M.
&
Massari
,
C.
2011a
Potential of transient tests to diagnose real supply pipe systems: what can be done with a single extemporary test
.
J. Water Res. Plan. Manage.
137
(
2
),
238
241
.
Meniconi
,
S.
,
Brunone
,
B.
&
Ferrante
,
M.
2011b
In-line pipe device checking by short period analysis of transient tests
.
J. Hydraul. Eng.
137
(
7
),
713
722
.
Meniconi
,
S.
,
Brunone
,
B.
,
Ferrante
,
M.
,
Mazzetti
,
E.
,
Laucelli
,
D. B.
&
Borta
,
G.
2015a
Transient effects of self-adjustment of pressure reducing valves
.
Procedia Eng.
119
,
1030
1038
.
Meniconi
,
S.
,
Brunone
,
B.
,
Ferrante
,
M.
,
Capponi
,
C.
,
Carrettini
,
C. A.
,
Chiesa
,
C.
,
Segalini
,
D.
&
Lanfranchi
,
E. A.
2015b
Anomaly pre-localization in distribution–transmission mains by pump trip: preliminary field tests in the Milan pipe system
.
J. Hydroinform.
17
(
3
),
377
389
.
Meniconi
,
S.
,
Brunone
,
B.
,
Mazzetti
,
E.
,
Laucelli
,
D. B.
&
Borta
,
G.
2016
Pressure reducing valve characterization for pipe system management
.
Procedia Eng.
162
,
455
462
.
Nicolini
,
M.
&
Zovatto
,
L.
2009
Optimal location and control of pressure reducing valves in water networks
.
J. Water Res. Plan. Manage.
135
(
3
),
178
187
.
Pezzinga
,
G.
,
Brunone
,
B.
&
Meniconi
,
S.
2016
Relevance of pipe period on Kelvin-Voigt viscoelastic parameters: 1D and 2D inverse transient analysis
.
J. Hydraul. Eng.
142
(
12
),
04016063-1-12
.
Prescott
,
S. L.
&
Ulanicki
,
B.
2003
Dynamic modeling of pressure reducing valves
.
J. Hydraul. Eng.
129
,
804
812
.
Simpson
,
A. R.
1999
Modeling of pressure regulating devices – a major problem yet to be satisfactorily solved in hydraulic simulation
. In:
Proc. 29th Annual Water Resources Planning and Management Conference (WRPMD'99), June 6–9, 1999, Tempe, AZ, USA
.
Ulanicki
,
B.
&
Skworcow
,
P.
2014
Why PRVs tends to oscillate at low flows
.
Procedia Eng.
89
,
378
385
.
Vairavamoorthy
,
K.
&
Lumbers
,
J.
1998
Leakage reduction in water distribution systems: optimal valve control
.
J. Hydraul. Eng.
124
(
11
),
1146
1154
.