transients. need for comprehensive transient analysis · transients. need for comprehensive...

2007 © American Water Works Association

112 JANUARY 2007 | JOURNAL AWWA • 99:1 | PEER-REVIEWED | JUNG ET AL

The need for comprehensive transient analysis

of distribution systems

Many surge analysis and design rules have evolved over time to help utilities cope with the

complexity of transient phenomena. These rules have been widely applied to simplify analysis

by restricting both the number and difficulty of the transient cases that need to be evaluated.

On further reflection, however, the implicit assumption that elementary and conservative

rules are a valid basis for design has often been shown to be questionable and sometimes

dangerous. Indeed, many published guidelines are so misleading and so frequently false

that they should only be used with extreme caution, if at all. This article specifically reviews

a number of guidelines or suggestions found in various AWWA publications for water hammer

analysis and provides a set of warnings about the misunderstandings and dangers that can

arise from such simplifications. The authors conclude that only systematic and informed

water hammer analysis can be expected to resolve complex transient characterizations

and adequately protect distribution systems from the vagaries and challenges of rapid

transients.

BY BONG SEOG JUNG,

BRYAN W. KARNEY,

PAUL F. BOULOS,

AND DON J. WOOD

distribution system is not a single entity but rather comprises a com-plex network of pipes, pumps, valves, reservoirs, and storage tanks thattransports water from its source or sources to various consumers. It isdesigned and operated to consistently and economically deliver water insufficient quantity, of acceptable quality, and at appropriate pressure.

Huge amounts of capital will continue to be spent on the design of new distrib-ution systems and the rehabilitation of existing systems in both developing anddeveloped countries. The magnitude of the needs is a challenge even to visualize:in the United States alone, some 880,000 mi of unlined cast-iron and steel pipesare estimated to be in poor condition, representing an approximate replacementvalue of $348 billion (Clark & Grayman, 1998).

BACKGROUNDTransients. Of the many challenges that face water utilities, one critical but

too-often-forgotten issue is protecting the system from excessive transient orwater hammer conditions. Surge analysis is essential to estimate the worst-case scenarios in the distribution system (Boulos et al, 2005). In essence, tran-sients occur whenever flow conditions are altered, for they are the physics ofchange, bringing “news” of any adjustment throughout the network. How-ever, transients are most severe when rapid changes occur, such as those result-ing from power failure, emergency valve operations, or firefighting. These

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JUNG ET AL | 99 :1 • JOURNAL AWWA | PEER-REVIEWED | JANUARY 2007 113

changes are generally character-ized by fluctuating pressures andvelocities and are critical preciselybecause pressure variations can beof high magnitude, possibly largeenough to break or damage pipesor other equipment or to greatlydisrupt delivery conditions.

Transient regimes in a distribu-tion system are inevitable and willnormally occur as a result of actionat pump stations and control valves.Regions that are particularly sus-ceptible to transients are high ele-vation areas, locations with eitherlow or high static pressures, andregions far removed from overheadstorage (Friedman, 2003).

Firefighting demands. Distribu-tion systems sometimes are calledon to deliver large flow demandsat adequate pressures for firefight-ing. Although these fire demandsoccur infrequently, they may con-stitute a highly constraining factorin pipeline design. Design proce-dures therefore should evaluate theability of the system to meet fire-fighting demands at all relevanthydrant locations. Even though theoccurrence of simultaneous fires atall possible locations is not realistic,a variety of firefighting demandpatterns must still be considered.Under transient conditions, the de-signer must anticipate both theestablishment of firefighting flowsand their ultimate curtailment, aprocess that often unfolds rapidly intime and can create significant tran-sient pressures, particularly if firecrews receive little specific trainingor instruction.

Water quality considerations. Amore recently highlighted motiva-tion for conducting a surge analy-sis arises from water quality con-siderations. One of the challenges in managing distributionsystem water quality is that contaminants can intrudeinto pipes through leaks from reduced- or negative-pres-sure transients. In reality, all pipeline systems leak, andhydraulic transients occur more or less continuously in dis-tribution systems, so it is not surprising that low-pres-sure transients introduce a considerable risk of drawinguntreated and possibly hazardous water into a pipelinesystem (Fernandes & Karney, 2004; McInnis, 2004; Kar-

ney, 2003). In fact, soil and water samples were recentlycollected adjacent to drinking water pipelines and thentested for occurrence of total and fecal coliforms, Clostrid-ium perfringens, Bacillus subtilis, coliphage, and entericviruses (Karim et al, 2003). The study found that indicatormicroorganisms and enteric viruses were detected in morethan 50% of the samples examined.

These and other results suggest that during negative-or low-pressure situations, microorganisms can enter the

Elevation = 500 m (1,640) Elevation = 480 m (1,574)

L1 D1 a1 L2 D2 a2

L3 D3 a3

FIGURE 1 Case study of single-pipeline system

a—wave speed, D—diameter, L—length

Three systems are considered: a pipeline with uniform properties, a pipeline with reflection points created by changes in properties, and a pipeline with an attached dead-end pipe segment.

1,600 m (5,250 ft)

Steady headMaximum head/minimum headMaximum head/minimum head (aV/g)

900 (2,950)

700 (2,296)

500 (1,640)

300 (984)

100 (328)

Distance—m (ft)

Pre

sure

Hea

d—

m (

ft)

FIGURE 2 Transient response for upstream valve closure

0 400 (1,312)

800 (2,624)

1,200 (3,937)

1,600 (5,249)

a—wave speed in m/s, aV/g—Joukowski surge head, D—diameter in in.

Properties are a/D (1,200/24 in.).



distribution system directly through pipeline leaks. Forthese reasons, the designer should not overlook the effectsof water hammer or pressure surges in the design andoperation of the distribution system or the evaluation ofeither system performance or ultimate system cost.

Design obstacles. In spite of the importance of waterhammer, the remaining and obviously troublesome prob-lem is the relative complexity of the required computermodeling and engineering analysis. The governing equa-tions describing the transient flow represent a set of non-linear partial differential equations with sometimes sophis-

ticated boundary conditions. Inaddition, the hydraulic devices arecomplex, performance data are dif-ficult to obtain and sometimespoorly understood, and pipelinesystems themselves are subject toa variety of operating conditionsand requirements. To make mat-ters worse, the physical character-istic of the pulse wave propagationis frequently hard to visualize orinterpret, even for the analyst ac-customed to transient phenomena(Karney & McInnis, 1990).

This complexity of both tran-sient phenomena and analysis hasat times induced engineers to usesimplified design procedures. Manysimplified guidelines have beenpublished in the past and can befound in various AWWA literature,e.g., Manual M11, Steel WaterPipe—A Guide for Design andInstallation (AWWA, 2004); Man-ual M23, PVC [polyvinyl chloride]Pipe—Design and Installation(AWWA, 2002); and C403-00,Selection of Asbestos–CementTransmission Pipe, Sizes 18 in.Through 42 in. (450 mm Through1,050 mm; AWWA, 2000). How-ever, any limited approach shouldcarefully consider a fundamentalquestion: “Are the simplificationsboth conservative and reasonable?”Unfortunately, the a priori assump-tion of design that some rudimen-tary and conservative system canbe found is questionable. This arti-cle identifies several of these mis-conceptions or limitations of sim-plified rules and describes thegeneral weakness and danger ofthe simplified designs for waterhammer. Case studies illustrate the

potential for erroneous application by comparing a com-prehensive analysis with a simplified one.

REVIEW OF RULESGuideline examples. To set the stage for more detailed

discussion, it is useful to briefly summarize a few spe-cific guidelines found in the AWWA literature. The AWWAliterature has not been singled out for its particularly ex-treme views; rather, it is readily at hand and is typical ofa large body of relatively accessible and widely dispersedliterature. Seven examples from the guidelines are given,

1,000 (3,281)

900 (2,953)

800 (2,625)

700 (2,296)

600 (1,968)

500 (1,640)

Max

imu

m H

ead

—m

(ft

)

1,200/24 (3,940/0.61)

1,200/30 (3,940/0.76)

1,200/36 (3,940/0.91)

300/24 (984/0.61)

300/30 (984/0.76)

300/36 (984/0.91)

Wave Speed—m/s (fps)/Diameter—in. (m)

aV/gUpstream closureDownstream closure

FIGURE 3 Maximum head of uniform pipeline

aV/g—Joukowski surge head


100 (328)

200 (656)

300 (984)

500 (1,640)

400 (1,312)

1,200/24 (3,940/0.61)

1,200/30 (3,940/0.76)

1,200/36 (3,940/0.91)

300/24 (984/0.61)

300/30 (984/0.76)

300/36 (984/0.91)

Wave Speed—m/s (fps) /Diameter—in. (m)

0

Max

imu

m H

ead

—m

(ft

)

FIGURE 4 Minimum head of uniform pipeline




followed by a discussion of the basis—and sometimesthe danger—of each articulated position.

Surge pressure. The pressure rise for instantaneousclosure is directly proportional to the fluid velocity atcutoff and to the velocity of the predicted surge wave butis independent of the length of the conduit (AWWA, 2004;2000). Thus, the relation used for analysis is simply thewell-known Joukowski expression for sudden closuresin frictionless pipes:

h = �a

g

V� (1)

in which h is the surge pressure, V is the velocity of waterin the pipeline, a is the wave speed, and g is the gravita-tional acceleration.

Wave speed. Pressure waves are established that movethrough the pipeline system at rates of 2,500–4,500 fps(760–1,370 m/s), with the exact rate depending primar-ily on the pipe wall material. The velocity of the wave isthe same as the velocity of sound in water, modified byphysical characteristics of the pipeline and is estimated bythe following equation (AWWA, 2000):

a =(2)

in which k is the modulus of compression of water, d isthe internal pipe diameter, E is the modulus of elasticityof the pipe, e is the pipe wall thick-ness, and Vs is the velocity ofsound in water.

Assumption of uniform prop-erties. When the flow rate ischanged in a time greater thanzero but less than or equal to 2L/a s in which L is the pipelinelength, a is the wave speed, and sis the time in seconds, the magni-tude of the pressure rise is thesame as with instantaneous clo-sure, but the duration of the max-imum value decreases as the timeof closure approaches 2 L/a s(AWWA, 2004). The thinking hereis that the time it takes for a waterhammer wave to travel the lengthof the system and back (i.e., 2 L/a)is the minimum time needed forthe possibly mitigating effect ofboundary conditions at the far endof the system to be experienced.

Maximum pressure. The max-imum pressure at the control valveexists along the full length of the

line with instantaneous closure and for slower rates movesup the pipe a distance equal to L – (Ta/2) in which T is theclosing time and then decreases uniformly (AWWA, 2004).

Assumption of surge pressure independence frompipeline profile. The surge pressure distribution alongthe conduit is independent of the profile or ground con-tour of the line as long as the total pressure remains abovethe vapor pressure of the fluid (AWWA, 2004).

Valve closing and maximum pressure rise. For valveclosing times greater than 2 L/a s, the maximum pres-sure rise is a function of the maximum rate of change inflow with respect to time, dV/dt (AWWA, 2004).

Pipe design and selection for pressure surges. To designor select a pipe for occasional pressure surges, the fol-lowing approach is sometimes recommended:

WPR = STR – (V × P�s) (3)

in which WPR is the working pressure rating in psi, STRis the short-term rating of the pipe in psi, V is the actual sys-tem velocity in fps, and P�

s is 1-fps surge pressure in psi. TheSTR is calculated by applying a factor of safety (SF�= 2.5)to the short-term strength (STS) of PVC pipe as in Eq 4:

STR = STS/SF� (4)

These levels should be considered to be the design surgecapacity limits for PVC pressure pipe manufactured toAWWA standards for a transmission main application(AWWA, 2002).

Vs�

�1�+��k

E�d

e��

900 (2,950)

700 (2,296)

500 (1,640)

300 (984)

100 (328)

Distance—m (ft)

FIGURE 5 Transient response for upstream valve closure

Pre

ssu

re H

ead

—m

(ft

)


a—wave speed in m/s, aV/g—Joukowski surge head, D—diameter in in.

Properties are a1/D1 (1,200/30) and a2/D2 (300/30).

400 (1,312)

800 (2,624)

1,200 (3,937)

1,600 (5,249)

0



Where simple rules can break down. Of course, theseexamples from AWWA transient guidelines do have con-siderable basis in fact. For example, the origin of the firstrule is the famous fundamental equation of water ham-mer, which is also called the Joukowski relation. The ori-gins of this relationship are somewhat complex, as Tijs-seling and Anderson (2004) have pointed out. Thisrelation equates the changein head in a pipe to the asso-ciated change in fluid veloc-ity. However, such a relationis applicable only underrestricted circumstances.When the required condi-tions are met, the simplerelationships are often aspowerful and accurate asthey are easy to determine.However, most publishedguidelines, such as those found in various AWWA litera-ture, are primarily applicable to simple changes such asa sudden flow stoppage in a single pipeline. Althoughthe initiating trigger is often assumed to be conservativein that sudden stoppage is a severe event, the degree orlack of conservatism is never evaluated. Thus the overalleffect of the approach may not be conservative.

To demonstrate some of the difficulties for many of theAWWA rules summarized in the previous sections, thefollowing discussion is intended to raise a number ofwarnings about where these guidelines might be mis-leading and thus lead to a poor basis of design. Afterthese general concepts, specific systems are described todemonstrate some of these warnings more precisely.

Surge pressure: how the rule breaks down. The guide-lines suggest that the pressure rise for instantaneous clo-sure is directly proportional to the fluid velocity and isindependent of conduit length; the associated initial up-surge (aV/g) is often referred to as the potential surge. Ingeneral, it might be reasonable to use this potential surgeconcept in a short pipeline fed from a reservoir and con-trolled by a valve. However, in a long pipeline, the total

drop in hydraulic grade line over the pipe length for theinitial flow may be greater than the potential surge (Wylie& Streeter, 1993). Because only part of the flow is stoppedby the first compression wave and then the flow is stoppedtotally at the valve, an increase in stored mass contin-ues—a phenomenon known as line packing. Thus, thepressure continues to rise, the pipe wall expands, and the

liquid continues to be compressed after the initial flowstoppage. More generally, the guideline relation attrib-utes no significant role either to friction loss (which caneither dissipate or accentuate the surge pressure) or the sys-tem’s profile. In fact, it is often important to rememberthat most pumping systems move water uphill, so that the“natural” flow direction is negative; thus, after a powerfailure, the flow tends to reverse if a check valve is notinstalled to prevent this, and the potential change in veloc-ity is often much greater than the initial velocity. Thisand many other circumstances can create an actual surgemuch larger than the so-called potential surge.

Wave speed: how the rule breaks down. Wave speedis a function of many fluid and pipe properties (e.g., pipediameter, thickness, and material; pipe restraint condi-tions; water density, elasticity, temperature, air, and solidscontent). Some of these conditions can be accuratelyassessed, but others can be difficult or uncertain anddepend on a complex set of interacting operating condi-tions. For this reason, an analysis sensitive to uncertaintyin the value of the wave speed is an essential componentof surge analysis and design work, and variations in the

wave speed should be expected andaccounted for. The largest estimate ofwave speed may not correspond tothe greatest actual surge conditions,even though it is clearly associatedwith the largest potential surge.

Assumption of uniform properties:how the rule breaks down. Simplerelationships are available or applica-ble only for a single uniform pipelineexperiencing simple events. Simplerelationships do not consider wavereflections from different pipe prop-erties, nor do they allow for the influ-ence of friction. Thus another problem

a D V aV/gm/s (fps) in. (m) m/s (fps) m (ft)

1,200 (3,940) 24 (0.61) 2.82 (9.25) 344.7 (1,131)

1,200 (3,940) 30 (0.762) 3.01 (9.88) 368.0 (1,207)

1,200 (3,940) 36 (0.914) 2.94 (9.65) 359.4 (1,179)

300 (984) 24 (0.61) 2.82 (9.25) 86.2 (283)

300 (984) 30 (0.762) 3.01 (9.88) 92.0 (302)

300 (984) 36 (0.914) 2.94 (9.65) 89.9 (295)

a—wave speed, aV/g—Joukowski surge head, D—diameter, V—velocity

TABLE 1 System information for a uniform pipeline

Huge amounts of capital will continueto be spent on the design of newdistribution systems and the rehabilitationof existing systems in both developingand developed countries.



is the implicit assumption of uni-form pipeline properties. If a sin-gle pipeline has different physicalproperties (i.e., diameter, pipe mate-rial, and wall thickness), a reflectedwave will originate from each dis-continuity point, producing a dif-ferent, and sometimes more severe,transient response (Wylie &Streeter, 1993). If the system inquestion is a network of pipes, thepressure rise is strongly influencedby system topology. The pipes in asystem can thus be a source of tran-sient waves or a receiver–transmit-ter, and these different roles influ-ence the nature of the assessment.

Maximum pressure: how therule breaks down. For slower ratesof change in simple systems, therelationships indicate the maximumpressure travels up the pipe a dis-tance equal to L – (Ta/2) and thendecreases uniformly. Only at theextreme end of the pipe are simplerules applicable. Granted, consid-ering relatively sudden changes isan attempt to be conservative, butas is shown later, the rules are notconservative in many cases, nor aresudden changes particularly rare.Modern pumps typically have suchsmall rotational inertia that powerfailures often generate essentiallyinstantaneous changes; however,the overall system dynamics cancreate maximum pressures that aresignificantly greater than those pre-dicted through the potential surgeconcept.

Assumption of surge pressureindependence from pipeline pro-file: how the rule breaks down.The independence of the profileor ground contour of the line, aswell as the characteristic of thehydraulic grade line, can directlyinfluence the pressure heads that occur under surgeconditions. Clearly, if the surge pressure is expressedas pressure head (as is appropriate to the stress condi-tions in the pipe wall), the surge pressure depends on theprofile along the pipeline.

Valve closing and maximum pressure rise: how therule breaks down. For more complex transients, simplerules cannot be applied even for a single uniform pipelinebecause the reflected waves modify the overall response.

Therefore, the calculation of the nature and influence ofreflected waves should be included in the analysis anddecision process.

Pipe design and selection for pressure surges: how therule breaks down. Like many other simplified rules, thedesign for water hammer considers the rapid transientwithin a single uniform pipeline only. If the surge-inducedoperation time can be modified (i.e., to more than 2 L/a),the diminished surge pressure may reduce the pipe cost.


800 (2,625)

600 (1,968)

400 (1,312)

200 (656) 0 400

(1,312) 800

(2,624) 1,200

(3,937) 1,600

(5,249)

Distance—m (ft)

Pre

ssu

re H

ead

—m

(ft

)

FIGURE 6 Transient response for downstream valve closure

a—wave speed in m/s, aV/g—Joukowski surge head, D—diameter in in. Properties are a1/D1 (1,200/36) and a2/D2 (300/24).

1,000 (3,281)

900 (2,953)

800 (2,625)

700 (2,296)

600 (1,968)

500 (1,640)

Max

imu

m H

ead

—m

(ft

)

1,200/30 +(3,940/0.76)

300/30 (984/0.76)

1,200/24 + (3,940/0.61)

300/36 (984/0.91)

1,200/36 +(3,940/0.91)

300/24 (984/0.61)



FIGURE 7 Maximum head of nonuniform pipeline




Because of the dangers of an imprecise water hammeranalysis, a large safety factor, often set at 2.5 or higher, issometimes used in an attempt to cover these contingen-cies. With the safety factor largely arbitrary, however, ahigh safety factor can create a twofold problem: (1) thestrength might be unreasonably large, creating an unnec-essarily expensive system or (2) should the factors ofsafety be insufficient, the pipe strength might be inade-quate, leaving the system vulnerable to water hammer.

To summarize, simple rules such as those found in sev-eral AWWA publications ignore the complications ofinteraction of the different pipe properties in a distribu-tion system. Actual pipes in distribution systems are nec-essarily connected, and water hammer waves are signif-icantly affected by these connections. At pipe junctionsand dead ends, wave reflections and refractions occur,which often magnify or attenuate the surge waves. More-over, simplified rules cannot simulate a variety of loadingsin the quest for the worst-case scenarios in a distribution

network. Any reflective practitionermust ask, “What’s at stake?” In fact,both overdesign and underdesigncan put the system at risk. This riskcan take the form of a risk to thepipeline and its associated hydraulicdevices, a risk of water contamina-tion, and even a risk to human life.The next section explores and illus-trates these claims in more detail.

CASE STUDIESThe purpose of these case studies

was to apply and compare compre-hensive surge analyses and simpli-fied analyses suggested by the rulespublished in the AWWA literature.In particular, the studies providecounter-examples to show how andwhen the simplified rules can breakdown. Comprehensive water ham-mer analysis is defined here as thetransient analysis that can simulate

a head loss resulting from friction and wave reflectionfrom any hydraulic devices or boundary conditions inthe system. It can be produced numerically using either themethod of characteristics (Wylie & Streeter, 1993) or thewave characteristic method (Boulos et al, 2006; Woodet al, 2005a; 2005b). Indeed, any of these results arereproducible using any number of commercial or in-housewater hammer codes.

The case study shown in Figure 1 represents a singlepipeline system. The system comprises a pipe connectedto two reservoirs with a head difference of 20 m (65.6 ft).The length and Hazen-Williams roughness coefficient forthe pipe are 1,600 m (5,250 ft) and 120, respectively.Three pipeline systems are considered: one with uniformproperties, one with reflection points created by changesin properties, and one with an attached dead-end pipesegment. The terminal reservoirs, each having a valvewith a discharge coefficient (e.g., the valve’s Cv or Esvalue) of unity, which means that a head loss of 1 m (3.28

500 (1,640)

400 (1,312)

300 (984)

200 (656)

100 (328)

0

Max

imu

m H

ead

—m

(ft

)

1,200/30+ (3,940/0.76)

300/30 (984/0.76)

1,200/24 +(3,940/0.61)

300/36 (984/0.91)

1,200/36 +(3,940/0.91)

300/24 (984/0.61)



FIGURE 8 Minimum head of nonuniform pipeline


Pipe 1 Pipe 2

a D V aV/g a D V aV/gm/s (fps) in. (m) m/s (fps) m (ft) m/s (fps) in. (m) m/s (fps) m (ft)

1,200 (3,940) 30 (0.762) 3.01 (9.88) 368.0 (1,207) 300 (984) 30 (0.762) 3.01 (9.88) 92.0 (302)

1,200 (3,940) 24 (0.61) 3.71 (12.2) 453.3 (1,487) 300 (984) 36 (0.914) 1.65 (5.41) 50.5 (166)

1,200 (3,940) 36 (0.914) 1.65 (5.41) 201.9 (662.4) 300 (984) 24 (0.61) 3.71 (12.2) 113.3 (371.7)

a—wave speed, aV/g—Joukowski surge head, D—diameter, V—velocity

TABLE 2 System information for nonuniform pipelines



ft) occurs when the valve discharges 1 m3/s (35 cu ft/s;Karney & McInnis, 1992). To introduce transient con-ditions into this case study, a rapid valve closure (1 s)was chosen.

Uniform pipeline. A uniform single pipeline is first con-sidered. Table 1 shows the wave speed (a), diameter (D),corresponding velocity (V), and Joukowski surge head(aV/g). Two values of wave speed—1,200 m/s (3,940 fps)and 300 m/s (984 fps)—were usedto represent a rigid pipe (e.g.,steel) and an elastic pipe (e.g.,PVC). In addition, different pipediameters—24 in. (0.61 m), 30in. (0.762 m), and 36 in. (0.914m)—were used and compared toset the stage for subsequent studyinto nonuniform pipeline systems.

Figure 2 shows the case of anupstream valve closure. The firstdownsurge initiated at theupstream valve is similar to theJoukowski downsurge exceptthat the friction loss along thepipeline causes a slightly differ-ent slope along the pipe. How-ever, the reflected upsurge fromthe downstream reservoir resultsin a significant head differencefrom the Joukowski upsurge eventhough the valve closure time (1s) is fast enough to be classified asa rapid closure (i.e., the valveoperation time is less than 2 L/a).The reason for this difference isthe dissipation of downsurge andupsurge in the downstream reser-voir for 1 s. The downsurge froman upstream valve propagates tothe downstream reservoir andthen is converted into the corre-sponding upsurge. At the sametime, the upsurge interacts withthe remaining downsurge, caus-ing some pressure dissipation,which is added to the frictionaldissipation in the pipe.

Figures 3 and 4 depict themaximum and minimum pressurehead for the uniform pipelinemodel shown in Table 1 for thedifferent locations (upstream ordownstream) of the valve closure.Not surprisingly, the higher wavespeed systems have greater ups-urge and downsurge pressuresthan those with lower wave

speeds. The two figures also show that the downsurgepressures attributable to the closure of the upstream valve,as already indicated in Figure 2, are similar to theJoukowski surge pressure (aV/g); however, the upsurgepressures consistently give a head difference of ~40 m(131 ft) regardless of wave speed and diameter. For thecase of the downstream valve closure, the observed trendsare exactly opposite those associated with the upstream

800 (2,625)

600 (1,968)

400 (1,312)

200 (656) 0 400

(1,312) 800

(2,624) 1,200

(3,937) 1,600

(5,249)

Max

imu

m H

ead

—m

(ft

)

Distance—m (ft)


FIGURE 9 Transient response for downstream valve closure

a—wave speed in m/s, aV/g—Joukowski surge head, D—diameter in in. Properties are a1/D1 (1,200/36), a2/D2 (300/24), and a3/D3 (300/30).

1,000 (3,281)

900 (2,953)

800 (2,625)

700 (2,296)

600 (1,968)

0

Max

imu

m H

ead

—m

(ft

)

Wave Speed—m/s/Diameter—in.


L1: 1,200/24 1,200/36 1,200/30 1,200/24 1,200/36 L2: 300/36 300/24 300/30 300/36 300/24 L3: 1,200/30 1,200/30 300/30 300/30 300/30

FIGURE 10 Maximum head considering dead end


1,200/30

1,200/30 300/30



closure. The upsurge attributable to the downstream valveclosure is almost the same as the Joukowski surge pres-sure, but the minimum pressures are consistently ~40 mless. However, in this case overall agreement with theJoukowski relation is good. For a single pipeline sub-jected to a simple incident, the actual surge is well approx-imated by the potential surge.

Nonuniform pipeline. Another application encounteredfrequently in practice is a nonuniform series pipeline. Inthis study, the single pipeline consists of two pipes withthe same length but with a stepwise change in diameterand/or wave speed. Table 2 shows wave speed, diame-ter, corresponding velocity, and Joukowski surge pres-sure in the two pipe sections. The first pipe has greaterwave speeds, causing greaterJoukowski surge pressurethan anticipated in the sec-ond pipe; the smaller-diam-eter pipe also has the highervelocity, inducing a higherpotential surge.

Figure 5 shows the tran-sient response through aprofile plot of the system fortwo pipes with the same diameter but different wavespeeds; the first pipe has a wave speed of 1,200 m/s (3,940fps), and the second pipe has a wave speed of 300 m/s(984 fps). The transient is initiated by closing the upstreamvalve. The first downsurge from the upstream valve isnearly the same as that predicted by the Joukowski rela-tion. Yet when the wave arrives at the junction, a portionof the downsurge is transmitted downstream and some is

reflected upstream. The figureclearly shows that the minimumhead in the second pipe is nowmuch lower than its Joukowskivalue because of the transmittedpressure but higher than theJoukowski downsurge of the firstpipe. Similarly, Figure 5 shows thatthe reflected positive pressure inthe first pipe is much lower thanthe Joukowski upsurge, becauseof the reflection at the junction,the friction along the pipeline, andthe energy dissipation at the down-stream reservoir.

Figure 6 depicts the maximumand minimum pressures caused bythe downstream valve closure; thewave speeds are the same as in theFigure 5 case, but the diameters ofthe two pipes are now 36 in. (0.91m) and 24 in. (0.61 m), respec-tively. The pressure envelope foreach pipe section is again signifi-

cantly different from the Joukowski analysis. The initialupsurge from the downstream valve is the same as in theJoukowski analysis, but the reflected wave from the junc-tion increases the maximum pressure. When the initialupsurge is transmitted through the junction, the wavespeed increases from 300 m/s (984 fps) to 1,200 m/s(3,940 fps), causing the increase in pressure head. How-ever, if the pipe diameter increases from 24 in. (0.61 m)to 36 in. (0.91 m), there is a resulting decrease in head.Overall, the wave reflections complicate a Joukowski-based analysis.

Figures 7 and 8 summarize the maximum and mini-mum pressures for a sequence of runs in the two-pipemodel characterized in Table 2 with the different location

for the valve closure. Clearly the differences are muchhigher than those of Figures 3 and 4 because of the reflec-tion at the junction. Another distinctly visible feature isthat the location of valve closure affects the maximum andminimum pressure significantly, whereas the Joukowskianalysis does not make this distinction. In the worst case,a head difference of ~400 m (1,310 ft) is shown in theminimum head (Figure 8). The overall conclusion drawn

500 (1,640)

400 (1,312)

300 (984)

200 (656)

100 (328)

0

Max

imu

m H

ead

—m

(ft

)

Wave Speed—m/s/Diameter—in.


L1: 1,200/24 1,200/36 1,200/30 1,200/24 1,200/36 L2: 300/36 300/24 300/30 300/36 300/24 L3: 1,200/30 1,200/30 300/30 300/30 300/30

FIGURE 11 Minimum head considering dead end


1,200/30 300/30

1,200/30

A more recently highlighted motivationfor conducting a surge analysis arisesfrom water quality considerations.



from this analysis is that the poten-tial surge in complex systems issometimes a conservative measureand at other times greatly underes-timates the surge pressures.

Dead-end considerations. An issueoften ignored but sometimes cru-cially important is the influence ofdead ends on surge pressure. Dodead ends make simple rules andpublished guidelines more conserv-ative or more dangerous? On thebasis of a potential surge analysis,the dead end itself would not evenbe expected to experience a waterhammer problem; moreover, deadends are routinely purged fromsteady-state simulations becausethey have no direct hydraulic effecton system behavior. Why thenshould they be of concern in a waterhammer analysis?

To test this case, the hypotheti-cal system is similar to the nonuni-form case described in the secondstudy but with a dead end attachedat the middle of the second pipe(1,200 m [3,940 ft]). The length,diameter, and Hazen-Williams fric-tion factor of the dead end are 200m (656 ft), 30 in. (0.762 m), and120, respectively. Two wavespeeds—1,200 m/s (3,940 fps) and300 m/s (984 fps)—are selected toconsider the influence of different pipe properties. Theproperties of pipe 1 and pipe 2 are the same as shownin Table 2, but the dead-end pipe (pipe 3) is analyzedusing different wave speeds.

Figure 9 shows the transient response of the case inFigure 6 including a dead end with a wave speed of 300m/s (984 fps). The dead end is located at 1,200 m (3,940ft), causing the wave reflection from that location andmaking the system response more complicated than thatshown in Figure 6.

Figures 10 and 11 show the maximum and minimumhead for the system with the different locations of valveclosure. As a comparison of Figures 10 and 11 with Fig-ures 7 and 8 shows, the dead end influences the waterhammer response in dramatic and important ways. Fur-thermore, its different wave speeds alter the systemresponse, especially for the case in which a1/D1 =1,200/36 and a2/D2 = 300/24. The reason the dead endcan affect the maximum and minimum head signifi-cantly is that the surge pressure increase attributable tothe wave speed increase conflicts with the surge pressuredecrease attributable to the pipe diameter increase.

Therefore the dead end located at pipe 2 affects themaximum and minimum head more significantly than dothe other system conditions. In addition, Figures 10 and11 indicate that the dead end causes surges consider-ably different from Joukowski predictions, dependingon the system characteristics. One of the significant con-clusions of these studies is that the rules of skeletoniza-tion and simplification that often remove dead ends insteady-state analysis or replace a multidiameter pipewith an “equivalent” one having similar head loss do notapply to transient applications.

Pipe network system. In most distribution systems,loops are formed to ensure system reliability and flexibility.The intention of this case study was to demonstrate howthe use of the simplified Joukowski analysis could lead toincorrect conclusions for the transient response in a com-paratively complicated network (looped) system.

The example pipe network is shown in Figure 12.The system comprises one reservoir at node 1, 45 pipes,and 29 nodes. This is a gravity-flow system that drawswater from the reservoir to supply the network. The ele-vation of the reservoir at node 1 is 50 m (164 ft), and all

1

4

9

15

22 23 24 25

27 26

28 29 45

43 44

42

41 40

31 32 33 34 35 36

39 38 37

26 27 28 29 30

25 24 23 22 21 20

9 10 11

15 16 17 18 19

13 12

5 6 7 8

14

2

3

1

4

8

13 14

20 21 19 18 17 16

12 11 10

5 6 7

2 3

0.05 m3/s

0.05 m3/s

Reservoir (at node 1)NodePipe

FIGURE 12 Pipe network

0.05 m3/s



other nodes have zero elevation. For simplicity, the length,diameter, wave speed, and Darcy-Weisbach friction fac-tor of all pipes are 500 m (1,640 ft), 0.3 m (0.984 ft),1,200 m/s (3,940 fps) and 0.015, respectively. At the endof the network, three 50-L/s (1.77-cu ft/s) demands atnodes 3, 21, and 29 are considered here. In order tointroduce transient conditions into the case study, thevalves at nodes 3, 21, and 29 are closed instantaneouslyto introduce a rapid transient into the system. Althoughclearly an arbitrary andsomewhat dramatic tran-sient load, the difficult ques-tion any analyst faces inpractice is this: “What load-ing cases are appropriateand suitably severe?” His-torically, little thought orreflection has been given tothis important question.

Figure 13 shows the dif-ference on the maximumheads between a detailed surge analysis and a simplifiedJoukowski one. Results clearly demonstrate that theJoukowski analysis results are not suitable to estimate thetransient response in most pipes. In the worst case, thedifference in surge pressure predictions for pipe 2 is morethan 200 m (656 ft). This is because its steady-state veloc-ity is higher than the other pipes, which causes the greaterJoukowski upsurge. Another interesting and importantfeature of the results is that the system responses deter-mined using the detailed surge analysis are worse than theJoukowski upsurge computed on the basis of initial pipevelocities for pipes in the middle of the network. TheJoukowski upsurge and downsurge may be more severe

(and thus conservative) thanresults from more-detailedsurge analysis in some sys-tems; however, the oppositeeffect unfortunately is not rarein looped networks. In addi-tion, the inability of theJoukowski rule to predict rea-sonable surge pressures isapparent if the wave speeds inpipes 1, 30, and 45 arechanged to 300 m/s (984 fps)instead of 1,200 m/s (3,940fps). These pipes are locatednext to the valves at nodes 3,21, and 29, so the decreasesof the wave speed eventuallyaffect the system response inall the pipes. However,Joukowski analysis decreasesthe surge pressure predictiononly in pipes 1, 30, and 45.

Another noticeable defect of the Joukowski rule is itsinability to simulate a variety of loadings in the quest forthe worst-case scenarios in a distribution network sys-tem. Logic using the Joukowski relation ignores wavereflections at the different pipe properties and the prob-ability of conjunctive events in a distribution system,which can significantly magnify or attenuate the waterhammer wave. Moreover, the Joukowski rule cannot con-sider liquid column separation in a pipeline. The pres-

sure below the vapor pressure of a liquid may producevapor cavities in the flow, and the collapse of the cavitiesresults in a large pressure rise, which may damage thepipeline system. Its occurrence may have a significanteffect on subsequent transients in the system. Therefore,the simplified surge analysis cannot provide a reliabletool for estimating the risk of water hammer.

CONCLUSIONSWater hammer analysis is important, but its com-

plexity (perhaps coupled with its mysterious nature andthe need for specialized analysis tools) has led to a num-ber of published guidelines promoting simplifications in

Of the many challenges that face waterutilities, one critical but too-often-forgottenissue is protecting the system fromexcessive transient or water hammerconditions.

100 (328)

50 (164)

0

–50 (–164)

–100 (–328)

–150 (–492)

–200 (–656)

Pipe Number

1 6 11 16 21 26 31 36 41

Dif

fere

nce

s o

f M

axim

um

Hea

d—

m (

ft)

FIGURE 13 Difference between the maximum heads and Joukowski upsurge



the analysis. AWWA literature in particular suggests sim-plified rules to estimate water hammer phenomena; thisstudy showed these rules to be inaccurate in certain casesand thus likely to lead to poor designs.

Most simple expressions, such as the Joukowski rela-tion, are applicable only under a set of highly restricted andoften unrealistic circumstances. When the required con-ditions are met, the simple relationships are both power-ful and accurate. In the case of the Joukowski relation, thetwo most important restrictions are that there should beonly a small head loss resulting from friction and no wavereflections from any hydraulic devices or boundary con-ditions in the system. If these conditions are not met, theJoukowski expression is no longer valid and the conclu-sions based on this rule also may not be applicable. More-over, the Joukowski relation does not consider liquid col-umn separation. If a negative surge is below the vaporpressure, all gas within the water is gradually released,and the collapse of the cavities will result in a large pres-sure surge spike. Of course, the question might be raisedas to whether system designers or water utilities can affordto complete a transient analysis. To this question, theauthors pose another: Given the importance of this analy-sis and the magnitude of the errors that overly simplifiedrules can lead to, can utilities afford not to be compre-hensive in their analyses of their distribution systems?

No simplified rules can provide a prediction of theworst-case performance under all transient conditions.The water hammer response in distribution systems isstrongly sensitive to system-specific characteristics, andany careless generalization and simplification could eas-

ily lead to incorrect results and inadequate surge protec-tion. Comprehensive water hammer analysis is not onlyneeded, but this approach is both justified by its impor-tance and practical, thanks to the rapid development offast computers and both powerful and efficient numeri-cal simulation models for water hammer analysis.

ABOUT THE AUTHORSBong Seog Jung is a professional engi-neer with MWH Soft in Pasadena,Calif. He has BS and MS degrees inenvironmental engineering from PusanNational University in Pusan, SouthKorea, and a PhD in civil engineeringfrom the University of Toronto inOntario. His research and consulting

experience has focused on hydraulic transients andoptimization of distribution systems. Bryan W. Karneyis a professor in the Department of Civil Engineering atthe University of Toronto. Paul F. Boulos (to whomcorrespondence should be addressed) is the presidentand chief operating officer of MWH Soft, 380 Inter-locken Crescent, Ste. 200, Broomfield, CO 80021; e-mail [email protected]. Don J. Wood is aprofessor in the Department of Civil Engineering at theUniversity of Kentucky in Lexington.

If you have a comment about this article,please contact us at [email protected].

REFERENCESAWWA, 2004 (4th ed.). Manual M11, Steel Water Pipe—A Guide for

Design and Installation. AWWA, Denver.

AWWA, 2002. Manual M23, PVC Pipe—Design and Installation.AWWA, Denver.

AWWA, 2000. C403-00, The Selection of Asbestos–Cement Transmis-sion Pipe, Sizes 18 in. Through 42 in. (450 mm Through 1,050mm). AWWA, Denver.

Boulos, P.F.; Lansey, K.E.; & Karney, B.W., 2006 (2nd ed.). Comprehen-sive Water Distribution Systems Analysis Handbook for Engi-neers and Planners. MWH Soft Inc. Publ., Pasadena, Calif.

Boulos, P.F. et al, 2005. Hydraulic Transient Guidelines for ProtectingWater Distribution Systems. Jour. AWWA, 97:5:111.

Clark, R.M. & Grayman, W.M., 1998. Modeling Water Quality in Drink-ing Water Distribution Systems. AWWA, Denver.

Fernandes, C. & Karney, B.W., 2004. Modeling the Advection EquationUnder Water Hammer Conditions. Urban Water Jour, 1:2:97.

Friedman, M.C., 2003. Verification and Control of Low Pressure Tran-sients in Distribution Systems. Proc. ASDWA Ann. Conf., Boston.

Karim, M.R.; Abbaszadegan, M.; & LeChevallier, M., 2003. Potentialfor Pathogen Intrusion During Pressure Transients. Jour.AWWA, 95:5:134.

Karney, B.W., 2003. Future Challenges in the Design and Modeling ofWater Distribution Systems. Pumps, Electromechanical Devicesand Systems (PEDS) Conf., Valencia, Spain.

Karney, B.W. & McInnis, D., 1992. Efficient Calculation of TransientFlow in Simple Pipe Networks. Jour. Hydraulic Engrg.—ASCE,118:7:1014.

Karney, B.W. & McInnis, D., 1990. Transient Analysis of Water Distrib-ution Systems. Jour. AWWA, 82:7:62.

McInnis, D., 2004. A Relative Risk Framework for Evaluating TransientPathogen Intrusion in Distribution Systems. Urban Water Jour.,1:2:113.

Tijsseling, A.S. & Anderson, A., 2004. A Precursor in WaterhammerAnalysis—Rediscovering Johannes von Kries. Intl. Conf. onPressure Surges, Chester, United Kingdom.

Wood, D.J. et al, 2005a. Numerical Methods for ModelingTransient Flow in Pipe Distribution Systems. Jour. AWWA,97:7:104.

Wood, D.J.; Lingireddy, S. & Boulos, P.F., 2005b. Pressure WaveAnalysis of Transient Flow in Pipe Distribution Systems. MWHSoft Inc. Publ., Pasadena, Calif.

Wylie, E.B. & Streeter, V.L., 1993. Fluid Transients in Systems. Pren-tice Hall, Englewood Cliffs, N.J.

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