K S B K n o w - h o w , V o l u m e 1

Water Hammer

Table of Contents Page

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

2 General - The Problem of Hammer . . . . . . . . . . . . . . . . . . .4

2.1 Steady and Unsteady Flow in a Pipeline . . . . . . . . . . . . . . . .4

3 Water Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

3.1 Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

3.2 Elasticity of Fluid and Pipe Wall . . . . . . . . . . . . . . . . . . . . . .7

3.3 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 10

4 The Joukowsky Equation . . . . . . . . . . . . . . . . . . . . . . . . . .11

4.1 Scope of the Joukowsky Equation . . . . . . . . . . . . . . . . . . .12

5 Numerical Simulation of Water Hammer . . . . . . . . . . . . . .15

5.1 Accuracy of Numerical Surge Analysis . . . . . . . . . . . . . . . .15

5.2 Forces Acting on Pipelines as a Result of Water Hammer . .16

6 Computerised Surge Analysis . . . . . . . . . . . . . . . . . . . . . . 17

6.1 Technical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

6.2 Interaction between Ordering Party and Surge Analyst . . .17

7 Advantages of Rules of Thumb and Manual Calculations .18

8 Main Types of Surge Control . . . . . . . . . . . . . . . . . . . . . . .20

8.1 Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

8.1.1 Air Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

8.1.2 Standpipes, One-Way Surge Tanks . . . . . . . . . . . . . . . . . . .21

8.1.3 Flywheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

8.2 Air Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

8.3 Actuated Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

8.4 Swing Check Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

9 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25

9.1 Case Study: Long-Distance Water Supply System . . . . . . . .25

9.2 Case Study: Stormwater Conveyance Pipeline . . . . . . . . . .26

Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

Calculation of Actual Duty Data, First Results . . . . . . . . .27

Surge Control Measures . . . . . . . . . . . . . . . . . . . . . . . . . . .28

10 Additional Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

1

Contents

1 Introduction

Most engineers involved in theplanning of pumping systemsare familiar with the terms “hy-draulic transient”, “surge pres-sure” or, in water applications,“water hammer”. The questionas to whether a transient flow orsurge analysis is necessary dur-ing the planning phase or not isless readily answered. Under un-favourable circumstances, dam-age due to water hammer mayoccur in pipelines measuringmore than one hundred metresand conveying only severaltenths of a litre per second. Buteven very short, unsupportedpipelines in pumping stationscan be damaged by resonantvibrations if they are notproperly anchored. By contrast,the phenomenon is not verycommon in building servicessystems, e.g. in heating anddrinking water supply pipelines,which typically are short inlength and have a small cross-section.

The owners or operators of sys-tems affected by water hammerare usually reluctant to pass oninformation about any surgedamage suffered. But studyingthe photos taken of some “acci-dents” (Figs. 1-a, 1-b, 1-c) one

thing is clear: the damage causedby water hammer by far exceedsthe cost of preventive analysisand surge control measures.

The ability to provide reliablydesigned surge control equip-ment, such as an air vessel oraccumulator1, flywheel and airvalve, has long been state of theart. The technical instructionleaflet W 303 “Dynamic Pressu-re Changes in Water Supply Sys-tems” published by the GermanAssociation of the Gas andWater Sector clearly states thatpressure transients have to beconsidered when designing andoperating water supply systems,because they can cause extensivedamage. This means that a surgeanalysis to industry standardshas to be performed for everyhydraulic piping system at riskfrom water hammer. Dedicatedsoftware is available for thispurpose – an important tool forthe specialist surge analyst touse. Consultants and systemdesigners are faced with thefollowing questions, which wehope to answer in this brochure:

• How can we know whetherthere is a risk of water ham-mer or not?

• How significant are approxi-mation formulas for calculat-ing water hammer?

• Can the surge analysis of onepiping system be used as abasis for drawing conclusionsfor similar systems?

• Which parameters are requiredfor a surge analysis?

• What does a surge analysiscost?

• How reliable is the surge con-trol equipment available andhow much does it cost to ope-rate it?

• How reliable is a computerisedanalysis?

System designer and surgeanalyst have to work togetherclosely to save time and money.Water hammer is a complexphenomenon; the purpose ofthis brochure is to impart abasic knowledge of its manyaspects without oversimplifyingthem.

3

1Introduction

1 Air vessels, sometimes also called “accumulators”, store potential energy by accumulating a quantity of pressurised hydraulic fluid in a suitableenclosed vessel.

Fig. 1-c: DN 800 check valvefollowing a pressure surge in thedischarge pipe

Fig. 1-b: Destroyed support(double T profile 200 mm, per-manently deformed)

Fig. 1-a: Completely destroyedDN 600 discharge pipe (wallthickness 12 mm)

2 General – The problem ofwater hammer

2.1 Steady and unsteady flowin a pipeline

When discussing the pressure ofa fluid, a distinction has to bemade between pressure aboveatmospheric [p bar], absolutepressure [p bar(a)] and pressurehead h [m]. Pressure head h de-notes the height of a homogene-ous liquid column which gener-ates a certain pressure p. Valuesfor “h” are always referred to adatum, (e.g. mean sea level, axi-al centreline of pipe and pipecrown etc.).

As a rule, system designers startby determining the steady-stateoperating pressures and volumerates of flow. In this context, theterm steady2 means that volumerates of flow, pressures andpump speeds do not change withtime. Fig. 2.1-a shows a typicalsteady flow profile:

With a constant pipe diameterand a constant surface rough-ness of the pipe’s inner walls, thepressure head curve will be astraight line. In simple cases, apump’s steady-state operatingpoint can be determined graphi-cally. This is done by determin-ing the point where the pumpcurve intersects the piping cha-racteristic.

A pumping system can never beoperated in steady-state conditionall the time, since starting up andstopping the pump alone willchange the duty conditions.Generally speaking, every changein operating conditions and everydisturbance cause pressure andflow variations or, put differently,cause the flow conditions tochange with time. Flow condi-tions of this kind are commonlyreferred to as unsteady ortransient. Referring specifically topressures, they are sometimescalled dynamic pressure changes

or pressure transients. The maincauses of transient flowconditions are:

• Pump trip as a result ofswitching off the power supplyor a power failure.

• Starting or stopping up one ormore pumps whilst otherpumps are in operation.

• Closing or opening of shut-offvalves in the piping system.

• Excitation of resonant vibra-tions by pumps with an un-stable H/Q curve.

• Variations of the inlet waterlevel.

Fig. 2.1-b may serve as a repre-sentative example showing thepressure envelope3 with andwithout an air vessel followingpump trip.

4

2 General – The Problem of Water Hammer

2 Not to be confused with the term “static”. 3 The term “pressure envelope” refers to the area defined by the minimum and maximum head curves along the fixed datum line resulting from all

dynamic pressures occurring within the time period under review.

Kote m

stationäre Druckhöhenlinie

Länge

hNN+m hm

Fig. 2.1-a: Steady-state pressure head curve of a pumping system

Steady-state pressure head curve

Metres above sea level

Length

hsteady in Fig. 2.1-b is the steady-state pressure head curve. Pres-sure head envelopes hminWK andhmaxWK were obtained from aninstallation with, hmin and hmax

from an installation without airvessel. Whereas hminWK andhmaxWK are within the permissiblepressure range, hmin gives eviden-ce of vapour pressure (macro-ca-vitation) over a pipe distancefrom 0 m to approximately 800m. Almost across the entirelength of the pipe, the value ofhmax exceeds the maximum per-missible nominal pressure of thepipe PN 16 (curve marked “PN

pipe“) and is, therefore, inad-missibly high. As a rule, vapourpressure is a most undesirablephenomenon. It can have thefollowing harmful effects:

• Dents in or buckling of thin-walled steel pipes and plastictubes.

• Disintegration of the pipe’s ce-ment lining.

• Dirty water being drawn intodrinking water pipelinesthrough leaking connectingsockets.

We will come back to the sub-

ject of macro-cavitation, i.e.liquid column separation, insection 3.1.

5

2General – The Problem of Water Hammer

700

600

500

400

300

200

Co

te [m

]

500 1000 1500 2000 2500Longueur de tuyauterie [m]

0

Cote de tuyauterie

hmax

Tuyauterie PN

hmax WK

hmin WK

hsteady

hmin

Fig. 2.1-b: Pressure head envelope of pressure transients following pump trip

Pipe length L: 2624 mInside diameter of pipe Di: 605.2 mmSteady-state flow rate: 500 l/s Hpump sump: 287.5 mHoutlet: 400 mAir vessel inlet pipe with a bypass and a non-return valve: Vair = 3.8 m3, Vwater = 6.2 m3

3 Water hammer

Pressure transients are also refer-red to as surge pressure or, if -referring to water systems, waterhammer. The latter term suitablyreflects the harmful effects thatthe hammer-like blows accompa-nying the pressure surges canhave on pipes and system com-ponents. Water hammer causespiping, valves, pipe fixtures, sup-ports, system components, etc. tosuffer the added strain of dynamicloads. The term “water hammer”is used to describe the phenome-non occurring in a closed conduitwhen there is either an accelera-tion or retardation of the flow. Incontrast to a force, pressure isnon-directional; i.e. it does nothave a vector. Not until a hydro-static pressure starts acting on alimiting area, is a force exerted inthe direction of the area normal.

As it is not possible to altogetheravoid pressure transients whenoperating a piping system, theart lies in keeping the pressuretransients within controllablelimits. What makes matters evenmore complex, is the fact thatthe damage caused by impermis-sibly high surge pressures is notalways visible. Often the conse-quences do not become apparentuntil long after the event, forexample a pipe rupture, loose ordisconnected flanges. The rootcause of damage then tends toremain in the dark. Some repre-sentative incidents caused bywater hammer are listed below:

Pressure rise:

• Pipe rupture

• Damaged pipe fixtures

• Damage to pumps, founda-tions, pipe internals and valves

Pressure fall:

• Buckling of plastic and thin-walled steel pipes

• Disintegration of the cementlining of pipes

• Dirty water or air being drawninto pipelines through flangedor socket connections, glandpacking or leaks

• Water column separationfollowed by high increases inpressure when the separateliquid columns recombine(macro-cavitation)

3.1 Inertia

The sudden closure of a valve ina pipeline causes the mass iner-tia of the liquid column to exerta force on the valve’s shut-offelement. This causes the pres-sure on the upstream side of thevalve to increase; on the down-stream side of the valve the pres-sure decreases. Let us consideran example: for a DN 200 pipe,L = 900 m, v = 3 m/s, the vol-ume of water in the pipeline iscalculated by

This is more or less the same asthe weight of a truck; v = 3 m/scorresponds to 11 km/h. Inother words, if the flow is sud-denly stopped, our truck – toput it in less abstract terms –runs into a wall (closed valve) at11 km/h (water mass inside thepipe). In terms of our pipeline,this means that the sequence ofevents taking place inside the pi-pe will result in high pressuresand in high forces acting on theshut-off valve.

As a further example of inertia,Fig. 3.1-a shows a pump dis-charge pipe. At a very smallmoment of inertia of pump andmotor, the failing pump comesto a sudden standstill, which hasthe same effect as a suddenlyclosing gate valve, only this timeon the downstream side of thegate valve. If mass inertia causesthe fluid flow on the down-stream side of the pump tocollapse into separate columns,a cavity containing a mixture ofwater vapour and air comingout of solution will be formed.As the separate liquid columnssubsequently move backwardand recombine with a hammer-like impact, high pressures deve-lop. The phenomenon is referredto as liquid column separationor macro-cavitation4.

6

3 Water Hammer · Inertia

4 Macro-cavitation in pipelines is not to be confused with microscopic cavitation causing pitting corrosion on pump and turbine blades. The latter al-ways strikes in the same place and is characterised by local high pressures of up to 1000 bar or more that develop when the microscopically smallvapour bubbles collapse. With macro-cavitation, repetitive strain of this kind, or the bombarding of a sharply contoured area of the material sur-face, does not occur since the pressure rises are considerably lower.

(1)mwater = –––– · 900 · 1000 = 28274 kg0.22�4

3.2 Elasticity of fluid and pipe wall

The attempt at visualising waterhammer resulting from the iner-tia of a body of water made insection 3.1 is only partly correct,because no allowance was madefor the elasticity of fluid and pipewall. As long as safety belts areworn and the barrier impactspeed is not too high, even ahead-on collision will not putdrivers in too much dangertoday, because the vehicle’smomentum is converted to harm-less deformation heat5. Contraryto the body of a car, however,water and pipe walls are elastic,even though they are so hardthat this property is not noticea-ble in every day use.

What actually goes on inside thepipe will, therefore, be describedusing the following example of aheavy steel spring slidingthrough a pipe. This spring suf-fers elastic deformation when itis suddenly stopped (Fig. 3.2-a):

The front end deformation trav-els in the opposite direction tothe original direction of move-ment at the speed typical for thesteel spring, i.e. wave propaga-tion velocity a in m/s. In thecompression zone, the velocityof the steel spring is v = 0everywhere.

Following these, admittedlypoor but hopefully helpful,examples chosen to illustrate thesubject, we will now go back tothe real situation inside the pipe,

which is shown in Fig. 3.2-b,with friction being neglected.The shut-off valve installed atthe downstream end of a hori-zontal pipeline with a constantinside diameter, which is fedfrom a reservoir at constantpressure, is suddenly closed:

7

3Elasticity of Fluid and Pipe Wall

5 To withstand the regular pushing and shoving over rare parking spaces, cars have to be elastic. To minimise the damage of a collision at high speed,however, carmakers spend vast amounts of time and money to make their products as inelastic as possible!

1. Steady-state condition prior

to pump trip

2. Formation of a vapour pocket

(cavitation cavity) following pump trip

3. High-impact reunion of separate

liquid columns accompanied

by surge pressures

Fig. 3.1-a: Macro-cavitation following pump trip

s1� t1

s2 � t2

s3 � t3

Fig. 3.2-a: Sudden closure of gate valve, visualised by a heavy steelspring

1 For t = 0, the pressure profileis steady, which is shown bythe pressure head curve run-ning horizontally because ofthe assumed lack of friction.Under steady-state condi-tions, the flow velocity is v0.

2 The sudden closure of thegate valve at the downstreamend of the pipeline causes apulse of high pressure �h;and the pipe wall is stretched.The pressure wave generatedruns in the opposite directionto the steady-state directionof the flow at the speed ofsound and is accompanied bya reduction of the flow veloc-ity to v = 0 in the high pres-sure zone. The process takesplace in a period of time 0 < t < 1/2 Tr, where Tr is theamount of time needed by thepressure wave to travel upand down the entire length ofthe pipeline. The importantparameter Tr is the reflectiontime of the pipe. It has avalue of 2L/a.

3 At t = 1/2Tr the pressure wavehas arrived at the reservoir.As the reservoir pressure p =constant, there is an unbal-anced condition at this point.With a change of sign, thepressure wave is reflected inthe opposite direction. Theflow velocity changes signand is now headed in thedirection of the reservoir.

4 A relief wave with a head of -�h travels downstreamtowards the gate valve andreaches it at a time t = Tr. It isaccompanied by a change ofvelocity to the value -v0.

5 Upon arrival at the closedgate valve, the velocitychanges from -v0 to v = 0.This causes a sudden negativechange in pressure of -�h.

6 The low pressure wave -�htravels upstream to the reser-voir in a time Tr < t < 3/2Tr,and at the same time, vadopts the value v = 0.

7 The reservoir is reached in atime t = 3/2Tr, and the pres-sure resumes the reservoir’spressure head.

8 In a period of time 3/2Tr < t <2Tr , the wave of increasedpressure originating from thereservoir runs back to thegate valve and v once againadopts the value v0.

9 At t = 2Tr , conditions areexactly the same as at theinstant of closure t = 0, andthe whole process starts overagain.

8

3 Elasticity of Fluid and Pipe Wall

t = 0

0 < t < 1/2Tr

t = 1/2Tr

1/2Tr < t < Tr

Tr < t < 3/2Tr

t = 3/2Tr

3/2Tr < t < 2Tr

t = 2Tr

t = Tr

∆h

v = 0

v = v0

v = v0

L

-

∆h

-

-

∆h

v = 0

∆h

v = 0v = -v0

v = -v0

∆h

v = -v0 v = 0

v = 0

-∆h

v = v0 v = 0

v = v0

Fig. 3.2-b: Pressure and velocitywaves in a single-conduit, fric-tionless pipeline following itssudden closure. The areas ofsteady-state pressure head areshaded medium dark, those ofincreased pressure dark, those ofreduced pressure light. The ex-pansion and contraction of thepipeline as a result of rising andfalling pressure levels, respec-tively, are shown. To give anidea of the relationship involved:With a 100 bar pressure rise, thevolume of water will decrease byabout 0.5%.

1

2

3

4

5

6

7

8

9

So, one might ask, what hap-pened to the original steady-statekinetic energy of the fluid follow-ing the sudden closure of the gatevalve? A closer look at Fig. 3.2-bwill reveal the answer. Accordingto the law of the conservation ofenergy, it cannot simply disap-pear. First it is converted into ela-stic energy of the fluid and thepipe wall, then changes into ki-netic energy again as a result ofreflection, then becomes elasticenergy again, and so forth. Let’slook at Fig. 3.2-b up to the pointwhere t = 1/2Tr. The conversioninto elastic energy takes placewithin this period of time. Im-mediately preceding the reflec-tion of the wave at the reservoir,the velocity of the liquid columnis v = 0 everywhere, and it istotally devoid of kinetic energy.Instead, the kinetic energy hasbeen changed into elastic energy,comparable to the situation of acompressed steel spring. The en-ergy conversion in reverse alsobecomes apparent from Fig. 3.2-b – specifically from the

condition prevailing at t = 2Tr. Ifthe gate valve were to be sudden-ly opened at this point, we wouldhave the old steady-state condi-tion at t = 0 again without chan-ge, and there would be no elasticenergy left.

Without friction, the pressurefluctuations would not diminish.In actual fact, no system is everentirely without friction, but thereduction in pressure fluctuationis relatively small in reality, be-cause the energy conversion intofrictional heat as a result of thefluid rubbing against the pipewalls, the inherent fluid frictionand, finally, the deformation ofpipe walls and fixtures is rela-tively small.

To show the process in a lessabstract manner, Fig. 3.2-c pro-vides the results of a computer-ised simulation of the examplegiven in Fig. 3.2-b for a realpipeline with the following para-meters:

L = 100 m, DN 100, k = 0.1 mm,hinlet = 200 m, linear throttling ofQ = 10 l/s at the outlet of the pi-pe to Q = 0, starting at t = 0.1 sin a period of time �t = 0.01 s.

Based on Fig. 3.2-b, the reflec-tion of pressure waves at the up-stream and downstream ends ofthe pipeline can be explained ina general manner as follows:

• If a pressure wave �p reachesthe closed end of a pipe, �pbecomes twice the amountwith the same sign, i.e. p = p ± 2·�p. The velocity at thepipe ends is always v = 0.

• At the open end of a pipe witha constant total head (e.g. res-ervoir with a constant waterlevel), the pressure change al-ways equals zero.

• At valves, throttling sections,pumps and turbines, pressureand velocity are always foundon the resistance or machinecharacteristic curve.

9

3Elasticity of Fluid and Pipe Wall

1.000.800.600.400.200

360

300

240

180

120

Pre

ssur

e he

ad a

bov

e p

ipe

cent

relin

e at

pip

e ou

tlet

[m l.

c.]

Time [s]

60

Fig. 3.2-c: Pressure head up-stream of gate valve. Comparedwith the situation shown in Fig.3.2-b, small differences are ap-parent. For example, the pressu-re flanks are not perfectly per-pendicular, because of the finiteclosing time of �t = 0.01 s. As aresult of friction, the pressureplanes are not perfectly horizon-tal – this phenomenon will bediscussed in greater detail in sec-tion 4.1.

Surge pressures travel at a veryhigh wave propagation velocity,for example a = 1000 m/s inductile or steel piping (see 4.1).They dampen out only graduallyand, therefore, remain danger-ous for a long time. The timeneeded to subside depends onthe length of the pipeline. In anurban water supply installation,they only last several seconds. Inlong pipelines, it can take a fewminutes until a pressure surgehas dampened out.

Knowing these facts, the basicworking principles of all surgecontrol equipment, such as airvessel or accumulator, flywheel,standpipe and air valves can bededuced. They prevent the dan-gerous conversion of steady-state kinetic energy into elasticdeformation energy. Air vesselsare ideally suited to explain theunderlying principle. The pres-surised air cushion in the airvessel stores potential energy. Ifthere were no air vessel, the dre-aded conversion of kinetic ener-gy into elastic deformation ener-gy following a pump trip wouldtake place at the pump outlet,which could cause the liquid col-umn to separate (Fig. 3.1-a).However, this does not happen,because the energy stored in theair cushion in the vessel takes

over the work of the pump. Im-mediately following pump trip,the air cushion starts expandingand takes over the pump’s job ofdischarging the water into thepipeline. Provided that the vesselis properly designed, it will pre-vent rapid changes in the flowvelocity in the pipeline. Instead,the water level in the vessel andthe undreformed liquid columnin the pipeline will continue torise and fall over a longer periodof time. The process is kept inmotion by the energy dischargedby the air cushion each time flu-id flows out of the vessel and bythe energy absorbed again bythe air cushion on the fluid’sreturn. The energy stored in theair cushion is only graduallydissipated. That is why it takesmany minutes for air vesseloscillations to die away, inlonger pipelines in particular.

3.3 Resonance

Resonant vibrations are anexception. These occur when ex-citer frequencies of whateverorigin, generated, for example,by the pump drive or by flowseparation phenomena in valvesand pipe bends, happen tocoincide with a natural frequen-cy of the pipeline. Improperly

anchored, unsupported pipelinesections in pumping installationsare particularly prone to reso-nant vibrations transmitted bythe fluid pumped and by thepiping structure. By contrast,resonance is all but negligiblefor buried piping. In order todesign adequately dimensionedanchoring, all pipe anchors inpumping installations should beexamined using structuraldynamics analysis, with thepump speed serving as theexciter frequency.

10

3 Elasticity of Fluid and Pipe Wall • Resonance

6 The adjective “rapid” is to be seen in relation to the system’s operating conditions. For example, the pressure transients caused by the closure of avalve in a 2 km long pipeline may well stay within the permissible range, whereas the same closing process could generate unacceptably high pres-sures in a 20 km long pipeline.

Water hammer occurs when the kinetic energy of a fluid is converted into elastic energy. But onlyrapid6 changes of the flow velocity will produce this effect, for example the sudden closure of agate valve or the sudden failure or tripping of a pump. Due to the inertia of the fluid, the flowvelocity of the liquid column as a whole is no longer capable of adjusting to the new situation.The fluid is deformed, with pressure transients accompanying the deformation process. The rea-son why surge pressure is so dangerous is that it travels at the almost undiminished speed ofsound (roughly 1000 m/s for a large number of pipe materials) and causes destruction in everypart of the piping system it reaches.

4 The Joukowsky equation

The pressure change DpJou in afluid caused by an instantaneouschange in flow velocity Dv is cal-culated by:

Dv:Flow velocity change in m/s

r: Density of the fluid in kg/m3

a: Wave propagation velocitythrough the fluid in thepipeline in m/s

DpJou: pressure change in N/m2

The DpJou formula is referred toas the Joukowsky equation. Aswell as Dv, equation (4.1) con-tains the density r and wavepropagation velocity a. The rela-tionship only applies to the pe-riod of time in which the veloci-ty change Dv is taking place. IfDv runs in opposite direction tothe flow, the pressure will rise,otherwise it will fall. If theliquid pumped is water7, i.e. r = 1000 kg/m3, equation (4.1)will look like this:

g: Acceleration due to gravity9.81 m/s2

DhJou: Pressure head change in m

In 1897, Joukowsky conducteda series of experiments on Mos-cow drinking water supply pipesof the following lengths / dia-meters: 7620 m / 50 mm, 305 m / 101.5 mm and 305 m /152.5 mm. He published the

results of his various experi-ments and theoretical studies in1898.

It may seem inconsistent thatDpJou in the Joukowsky equation(4.1) seems to have nothing todo with the mass of the flow in-side the pipeline. For example, ifthe water hammer described inthe first example in section 3.1had been based on a pipe dia-meter twice that of the diameterused, A = D2p/4 would havecaused the fluid mass and itskinetic energy to turn out fourtimes as large. What seems to bea paradox is instantly resolved ifone considers the force exertedon the shut-off valve, i.e. force F = Dp · A, the defining para-meter for the surge load. Becauseof A, it is now in actual fact fourtimes as large as before.

This shows that one must alsoconsider the fluid mass to judgethe risk of water hammer, al-though that does not seemnecessary after a superficialglance at Joukowsky’s equation.At the same time, this explainswhy the pressure surges occur-ring in domestic piping systems

with their small diameters andlengths are usually negligible. Inthese systems, the kinetic energylevels and fluid masses are verysmall. In addition, it is practical-ly impossible to close a valvewithin the very short reflectiontime of a domestic water system.

The Joukowsky equation can beused to calculate simple esti-mates. Let’s consider threeexamples:

Example 1:

In a DN 500 pipeline, L = 8000 m,a = 1000 m/s and v = 2 m/s, agate valve is closed in 5 seconds.Calculate the pressure surge.Calculate the force exerted onthe gate.

Answer:

5 s < Tr = 16 s, i.e. Joukowsky’sequation may be applied. If theflow velocity is reduced from 2 m/s to zero as the valve isclosed, Dv = 2 m/s. This gives us apressure increase Dh = 100 · 2 =200 m or approximately Dp = 20 · 105 N/m2, which is 20 bar.The valve cross-section measuresA = D2 · 0.25 · p Ä 0.2 m2. Theforce acting on the gate is p·A =0.2 · 20 · 105 = 4·105 N= 400 kN.

11

4The Joukowsky Equation

7 Despite the high flow velocities common in gas pipes, these do not experience surge problems, because p · a is several thousand times smaller thanfor water.

(4.1)

(4.2)

Nikolai Egorovich Joukowsky

Example 2:

A pump delivers water at Q =300 l/s and a head Dh = 40 mthrough a DN 400 dischargepipe measuring L = 5000 m intoan overhead tank; a = 1000 m/s.The inertia moments of pumpand motor are negligible. Isthere a risk of liquid columnseparation, i.e. macro-cavi-tation, following pump trip? Ifso, what is the anticipated pres-sure increase?

Answer:

Q = 300 l/s in a DN 400 pipe-line roughly corresponds to aflow velocity v = 2.4 m/s. As aresult of pump trip and the lossof mass inertia moment, thepump comes to a sudden stand-still, i.e. Dv = 2.4 m/s. Accordingto the Joukowsky equation, thiscauses a head drop of Dh = -100 · 2.4 m = -240 m. Since thesteady-state head is just 40 m,vacuum is reached, the liquidcolumn collapses and macro-cavitation sets in. Following theliquid column separation nearthe pump outlet, the two liquidcolumns will recombine withgreat impact after some time.For reasons of energy conserva-tion, the highest velocity of thebackward flow cannot exceedthe original velocity of the stea-dy-state flow of 2.4 m/s. Underthe most unfavourable condi-tions, the cavitation-inducedpressure rise will, therefore, beDh = 100 · 2.4 = 240 m, whichis the equivalent to 24 bar.

Example 3:

A pump delivers water at Q =300 l/s and a head Dh = 40 minto a 2000 m long pipeline DN400; a = 1000 m/s. The massmoment of inertia8 of all rota-ting components (pump, motor,etc.) is J = 20 kgm2, the speed ofrotation n0 = 24 s-1 and the totalefficiency = 0.9, i.e. 90%. Isthere a risk of liquid columnseparation, i.e. macro-cavitation,following pump trip?

Answer:

For the instant of pump failure,the change in speed n. may be de-rived from the inertia equationas follows:

Mp = 2·�·J·n.

Assuming as an (extremelyrough) approximation a linearspeed reduction , then, if

Mp = �p·Q__________2�·n0·�

,

we obtain a time Dt in which thespeed has dropped to zero, and,if Dp = 1000 · 9.81 · Dh,

The reflection time of the pipe-line is Tr = 4 s (for a = 1000m/s), which means that the re-flected pressure relief wave willnot reach the pump until afterthe speed has dropped to zeroand it is too late for the relievingeffect to take place. It is, there-fore, probably safe to say thatmacro-cavitation will develop.

4.1 Scope of the Joukowskyequation

The Joukowsky equation onlyapplies to:

• Periods of time which areequal to or shorter than thereflection time of the piping Tr

• The period of time which fallswithin the velocity change Dv

• Pipes characterised by frictionlosses within the limits typicalof water transport systems

Reflection time Tr:

In Fig. 3.2-b the wave of re-duced pressure reflected by thetank has arrived at the gatevalve after Tr has lapsed, andevens out some of the pressureincrease Dp. If the change inflow takes place in a period oftime Dt longer than Tr, the risein pressure DpJou will only occurat the wave’s source, whereas itwill have diminished to thevalue given by the boundarycondition by the time it reachesthe opposite end of the pipeline.

Fig. 4.1-a shows the pressure en-velope, which applies to a caseof this kind:

12

4 The Joukowsky Equation

8 Mass moment of inertia J: J expressed in kgm3 is the correct physical quantity. Flywheel moment GD2, which was used in the past, should no longerbe used, because it can easily be confused with J!

�t =(2� · n0)2 · J · ��p · 0.001 · Q

Ä 4 · n02 · J · �

�h · Q= 3.4 s

n. = no

Dt

Friction

If the liquid pumped is highlyviscous or if the pipeline is ex-tremely long (say, 10 km andmore), the work done by thepump only serves to overcome thefriction produced by the pipeline.Changes of geodetic head due tothe pipe profile, by comparison,are of little or no importance. TheJoukowsky equation no longer

applies, not even within the reflec-tion time of the pipeline. In a caselike this, the actual pressure risefollowing the sudden closure of agate valve can be several timesthat of DpJou as calculated by theJoukowsky equation! The pheno-menon caused by the pipe frictionis commonly called line packing.The following flow simulationcalculation gives an example ofthis:

The gate valve in the exampleshown in Fig. 4.1-b closes 20 safter the start of the calculation.The first steep increase by ap-prox. 20 bar to approx. 55 baris DpJou according to the Jou-kowsky equation; the continuedincrease to almost 110 bar iscaused by line packing. Linepacking is only of significancefor long pipelines or highlyviscous media. It is unlikely tooccur in urban water supply andwaste water disposal plants.

13

4The Joukowsky Equation · Wave Propagation Velocity

∆hJou

∆hJou

hmax

hmin

Fig. 4.1-a: Pressure head envelope for closing times > reflection time Tr .

400320240160800

120

100

80

60

40

20

Initi

al p

ress

ure,

abs

olut

e, in

bar

(ap

prox

.)

Time [s]

Fig. 4.1-b: Pressure curve at the outlet of a 20 km long crude oilpipeline following a sudden gate valve closure. Calculation para-meters: DN 300, k = 0.02 mm, inlet pressure 88 bar constant, Q = 250 l/s, fluid pumped: crude oil, � = 900 kg/m3

Wave propagation velocity

The wave propagation velocityis one of the elements of the Jou-kowsky equation and, therefore,a vital parameter for definingthe intensity of a surge. It is cal-culated by solving equation(4.1).

�: Density of the fluid in kg/m3

EF: Modulus of elasticity of thefluid in N/m2

ER: Modulus of elasticity of thepipe wall in N/m2

di: Inside pipe diameter in mm s: Pipe wall thickness in mm�: Transverse contraction num-

berEquation (4.1) produces a rangeof values from approximately1400 m/s for steel pipes toaround 300 m/s for ductile plas-tic pipes. Wave propagationvelocity “a” in an unconfinedbody of water is approximately1440 m/s. To all intents andpurposes, the validity of equa-tion (4.1) should not be over-estimated; surge analyses areoften performed without it, inwhich case the value of “a” isestimated. The volume of air

contained by the fluid, whichequation (4.1) does not take intoaccount, can have a strong im-pact on “a”, as is shown by so-me examples in Table 4-1: Indrinking water supply pipelinesthe gas content is negligible; inwaste water installations it nor-mally is not. Further elements ofuncertainty with regard to “a”mainly concern pipes made ofsynthetic material. An unknownand varying modulus of elastici-ty, manufacturing tolerances, theage of the pipeline and, in parti-cular, the question whether thepipeline is laid in the ground ornot, all play a part. A buriedpipeline has considerably highervalues of “a” than a pipe laidabove ground.

14

4 The Joukowsky Equation · Wave Propagation Velocity

(4.1)m/s

Gas content a m/s% by volume

0 12500,2 4500,4 3000,8 2501 240

Table 4-1: “a” as a function ofthe gas content at a static waterpressure of approximately 3 bar

5 Numerical simulationof water hammer

In current theory, the dependentmodel variables are the pressurep and the flow velocity v in thetwo partial differential equa-tions (5.1) for every single pipeof a piping system; the time tand an unrolled reach of pipe xare independent variables.

Equations (5.1) are generally validand cover the effects of bothinertia and elasticity. Mathema-tically, the pipe ends serve as theboundary conditions of equations(5.1); different types of boundaryconditions are introduced to in-clude internal components such aspipe branches, vessels, pumps andvalves in the model. For example,the creation of a complete pipingsystem by connecting a number ofindividual pipes is done by takinga pipe node to be the boundarycondition. The starting conditionof equation (5.1) is the steady-state flow inside the pipe concer-ned before the onset of the dis-turbance. Equations (5.1) aresolved by means of the character-istics method, which provides thebasis for almost all surge analysissoftware available today.

The time frame covered byequations (5.1) is less appro-priate for computing resonantvibrations. These can be calcu-lated much more precisely usingthe impedance method, or, inother words, by looking at thefrequency range.

5.1. Accuracy of numericalsurge analysis

Computer programs based on thecharacteristics method producesolutions whose accuracy by farexceeds that which is called for inpractice. This is evidenced bynumerous comparisons withactual measurements. Significantdifferences were only found forcalculations aimed at predictingmacro-cavitation or dampening ofpressure waves inside a pipe.

For example, the pressures com-puted using the standard modelof vapour cavitation derivedfrom equations (5.1), i.e. theassumption of a simple cavity oflow pressure following liquidcolumn separation, are alwayshigher than what they are in real-ity. However, the advantage ofthe conservative outcome is thatone is always on the safe side.

The real energy losses due tofriction, and the degree of warp-ing of pipeline and pipe fixturesare somewhat larger than theforecast supplied by simulation.The first pressure peaks and val-leys, therefore, tend to be simu-lated very precisely, whereas thepressures further down the lineare on the whole depicted withan increasing lack of dampe-ning. But imperfections of thiskind are negligible comparedwith inaccuracies caused byentering wrong or insufficientinput data.

Some of the potential sources oferror are:

• Inaccurate valve and/or pumpcharacteristics.

• Lack of knowledge about theactual wave propagationvelocity inside the pipeline.

• Lack of information abouttapping points in a main pipe.

• Unawareness of the degree ofincrustation inside the pipes.

This shows that the quality ofthe surge analysis stands or fallswith the accuracy of the inputdata.

15

5Numerical Simulation of Water Hammer

Accuracy of Numerical Surge Analysis

(5.1)

A surge analysis can only be as accurate as the system data

entered as inputs. Only if the input is accurate, and the com-

putation model is a faithful reproduction of the real system

conditions, will the analysis yield a high degree of accuracy.

In practice, it is often impossibleto obtain exact data. If this isthe case, one has to estimate therequired inputs.

An example:

For a valve manufacturer, a smallindividual loss coefficient in theopen condition of a valve is apowerful sales argument. Bycontrast, for a surge analysis thevalues obtained immediatelypreceeding total closure of avalve are of the essence, andmeasuring these is a time-consu-ming and complex affair. As aresult of this, many individualloss characteristics available forvalves do not extend far enoughinto the closing range. For costreasons, the individual losscurves provided by most manu-facturers are extrapolations,rather than curves plotted on thebasis of original measurements.

When designing a plant with theaid of surge analyses, inaccura-cies of this kind should be ac-counted for by designing thesurge control equipment slightlyon the conservative side.

5.2 Forces acting on pipelinesas a result of waterhammer

After computing the time-depen-dent pressure gradients, it takesa further separate step to calcu-late the forces acting on the el-bows and connections of un-supported pipes. The interactionbetween fluid and pipe wall doesnot enter into the computation(separate calculation). Apartfrom the odd exception, whichis of no relevance in the field ofwater supply and waste waterdisposal anyhow, this methodtends to produce forces whichare somewhat higher than whatthey are in reality, so that theconclusions drawn from the cal-culation results will definitely beon the safe side.

16

5 Accuracy of Numerical Surge Analysis ·Forces Acting on Pipelines as a Result of Water Hammer

6 Computerised surge analysis

6.1 Technical procedure

A surge analysis will not providedirect solutions for the requiredparameters, such as, for exam-ple, the optimum air vessel size,compressor settings, valve clos-ure characteristics, flywheel di-mensions, etc. Instead, the surgeanalyst must specify the type ofsurge control to be employedand provide estimates of therelevant parameters. Afterchecking the outcome of thesurge analysis, the original para-meters are suitably adjusted anda complete re-run of the surgeanalysis is made for the system.After several runs, the valuessupplied will come very close tothe technical and economicaloptimum. As surge analysesnecessarily need to be performedby surge specialists, they remaintime and labour intensive despi-te the use of modern computertechnology.

Considering that powerful surgeanalysis software is now com-mercially available, users maywonder whether they cannot dotheir own analysis just as well.As reliable9 surge analysis soft-ware is far from a mass product,the low sales volume makes itexpensive. Add to this the highcost of training and hands-onpractice. Also if the software isnot used for some time, opera-tors usually have to brush uptheir skills. So, if users requirefewer than, say, ten analyses peryear, the cost involved in doingtheir own will probably not beworthwhile.

6.2 Interaction betweenordering party and surgeanalyst

First of all, a distinction has tobe made between the quotationphase and the calculation itself.During the quotation phase, thesurge analyst requires thefollowing information from theplant-engineering contractor tocompute the cost involved:

1. A rough flow diagram of theinstallation indicating all im-portant equipment, such aspumps, valves, additional in-let and outlet points, as wellas any existing safety devices,such as aerators, air vessels,etc. The flow diagram can byall means be in the form of aquick sketch, which does nottake more than a couple ofminutes to draw.

2. A rough list of all main para-meters, i.e. principal pipelengths, diameters and flowrates.

3. A list of all major operationand downtime periods.

4. A list of all known incidentsthat could have been causedby water hammer.

5. Irregularities observed duringoperation.

If a surge analysis is to be per-formed, additional data to bespecified by the surge analystwill have to be obtained. Someexamples of additionally re-quired data are:

- Piping elevation profile

- Lengths

- Diameters

- Wall thickness

- Materials of construction, liningmaterial, pipe connections

- Pressure class, design pressurehead curve

- Permissible internal pipe pres-sures (pmin, pmax)

- Method used to lay the pipes:buried or placed on supports

- Modulus of elasticity of pipematerials

- Surface roughness coefficient

- Provision of air valves at thehighest points of the piping

- Branch connections

- Zeta or flow factors as well asvalve closing characteristices

- Characteristic curves or perfor-mance charts and characteristicdata of all hydraulic equipment

- Mass moments of inertia of allhydroelectric generating sets

- Characteristic curves and dataon surge control equipment al-ready installed in the system

- Characteristic values of all ae-ration and deaeration equip-ment

- Settings of control equipment

- Water levels in tanks and reser-voirs

- Rates of flow in the individualpiping branches

- Degrees of opening of all shut-off and throttling valves

– Operating pressures

17

6Computerised Surge Analysis

9 Users are in the uncomfortable position of not being able to verify the workings of surge analysis software. It is, therefore, important that a reput-able manufacturer vouch for the quality of the product. Surge analysis software, as a rule, is developed by specialist university institutes. There aresome examples of programs that were bought by commercial enterprises and provided with a sophisticated user interface, which makes them easierto handle for the user.

7 Advantages of rules ofthumb and manual calcula-tions

A rough estimate can be a veryuseful tool to quickly assess therisk of water hammer. This leadsus to the validity of rules ofthumb and to the questionwhether the surge characteristicsof one system can be applied toanother, similar installation (scal-ability). To answer that question,we should start by pointing outthat there is a great variety ofwater supply and waste waterdisposal plants, and that these areso different from each other thatapproximation formulas cannotbe applied. Even if the characteri-stic values of different systems arevery similar, i.e. same rates offlow, same pipe lengths, theycannot normally be scaled.

A simple example shows why:The only difference between twootherwise completely identicalwater supply systems are theelevation profiles of the mainpipes; one system has a highpoint, the other does not. Thesystem without the high pointcan be safely protected by an airvessel. A vessel of the same sizewill not adequately protect thesecond system, however, becausethe falling water level in the airvessel would cause the minimumdynamic pressure head to inter-sect the pipeline’s high point.The low pressures thus createdwould pose a risk of dirty waterbeing drawn into the system.

It takes lots of experience to beable to judge whether approxi-mation formulas can be used toreliably calculate transient flowconditions. For every day en-gineering purposes, approxima-tion formulas should be used ex-clusively to roughly estimate thepotential risk in a system (exam-ples, see section 4). Using themas a basis for a serious surgeanalysis or, even worse, for de-signing the surge control equip-ment, would have to be regard-ed as highly irresponsible. Abrief description of all knownprocesses of approximation andestimation formulas are detailedbelow:

18

7 Rules of Thumb and Manual Calculations

Fig. 7-1: Graphical method developed by Schnyder-Bergeron

• Before the days of moderncomputer software, the graphi-cal Schnyder-Bergeron methodwas often employed and pro-duced relatively reliable surgeanalysis. For practical reasons,use of this method is limited tosystems comprising a singlepipeline. Friction can only betaken into account by complexprocedures. Besides, it takes aspecialist to apply this methodand obtain the desired results.Fig. 7.1 is an example of atypical Schnyder-Bergeron dia-gram, which shows how thepressure wave propagationdue to the closure of a valve isdetermined by graphicalmeans.

• Application of the Joukowskyequation for rapid changes inflow velocity v (examples un-der 4).

• Graphical method to deter-mine the required air vesselsizes.*)

• Graphical method used toestimate the condition of linepacking.*)

• The largely ideal valve closingcharacteristics for the ex-ceptional case of a single-con-duit pipeline can be calculatedby approximation.*)

These are the only manual cal-culation methods. This apparentlack is more easily understood ifwe take another look at the airvessel, our representative exam-ple of before. Reading the totalvolume of the vessel from adesign curve is not all that is re-quired. The way the air vesselworks depends to a large extenton the ratio of water volume toair volume in the vessel, or, inother words, on the questionwhether pre-pressurisation ofthe vessel is “hard” or “soft”.The pre-pressurisation level hasan impact on the total vessel vo-lume required. The pipeline pro-file also plays a significant part.For example, if it has a high po-int which should not be intersec-ted by the minimum dynamicpressure head curve followingpump trip (area of low pres-sure), the basic conditions fordesigning the vessel will be dif-ferent, even if the plant para-meters are otherwise the same.The vessel will have to be consi-derably larger. In many cases,the swing check valve andthrottle installed in a bypass willkeep the reverse pressure wavefrom causing an impermissiblerise in pressure levels in the airvessel. It is impossible to de-termine these crucial variablesusing rules of thumb orgraphical design methods.

19

7Rules of Thumb and Manual Calculations

*) Expertise required.

8 Main types of surge control

The purpose of surge control isto stop kinetic energy frombeing converted into elasticdeformation energy. This can bedone by the following basicmethods:

– Energy storage

– One-way surge and ventingfacilities

– Optimization of valve closingcharacteristics10

– Optimisation of the strategydesigned to control the pipingsystem

8.1 Energy storage

With air vessels and standpipes,energy is stored as pressure en-ergy; when a flywheel is instal-led, the energy stored takes theform of rotational energy. Thereis a sufficient amount of energystored to maintain the steady-state flow for a relatively longtime and to make sure the decre-ase in flow velocity due to dis-sipation will be slow to take fulleffect. A rapid pressure drop isthus prevented. If air vessels andstandpipes are installed upstreamof a pump in a long inlet pipe,they not only prevent a pressuretransient by means of energy dis-sipation, but also the other wayaround, by absorbing energy.

8.1.1 Air vessels

Air vessels come in the form ofcompressor vessels (Fig. 8.1.1-a), [bag-type] accumulators (Fig.8.1.1-b) and vessels with a ventpipe. Compressor- and accumu-lator-type air vessels basicallywork on the same operatingprinciple. The reason for choos-ing one or the other is based ontechnical or commercial conside-rations. Because of their design,accumulators are only suitablefor small volumes.

As explained earlier, the vesselvolume is not the only impor-tant factor. If the water-to-airvolume ratio is carefully chosen,a vessel with a substantiallylower total volume may be used.

20

8 Surge Control Systems

10 The valve closing charasteristics describe the closing angle of a valve as a function of time.

Hgeo

HWIN

WSH

D1

Va

Vw

D2

Z2

Z1

ZB

D0

100 mmCompressor on

Compressor off

Fig. 8.1-a: Schematic layout of a compressor-type air vessel. To avoid excessive pressures on return of thevessel water, the connecting pipe may have to be fitted with a swing check valve with a throttled bypass.

To make sure compressor vesselsare always filled to the correctlevels, they can be equippedwith sensors which will switchthe compressor on or off as re-quired. Bag-type accumulatorsare typically adjusted by pre-pressurising the gas inside thebag or membrane enclosure to acertain initial pressure prior toinstallation.

Air vessels are not just installedat the pump discharge end toguard against the consequencesof pump trips. They can also beinstalled in other suitable places

in a piping system. For examplein long inlet pipes, an additionalair vessel at the inlet end of thepump provides effective surgecontrol. If the pump fails ortrips, an upstream vessel will ab-sorb energy, while a down-stream vessel will dissipate ener-gy.

Air vessels or accumulators arenot suitable for waste water di-sposal systems11, because

• With waste water, it is notpossible to measure the waterlevel needed to set the com-pressor.

• The bag-like enclosure in anaccumulator would be punc-tured by the sharp objectscontained in the wastewater,such as razor blades, nails, etc.

• There is a major risk of in-crustations, deposits andblockages.

Provided they are adequatelymonitored, the operating relia-bility of air vessels is high. Dur-ing their operation, attentionhas to be paid to the following:

• Monitoring of the water levelin the vessel.

• For reasons of hygiene, thewater volume must be conti-nuously or regularly replaced.

• The compressed air must notcontain any oil.

• To be able to take the airvessel out of service for aninspection, spare vesselsshould be available.

• It must be possible to lock theshut-off valves in the connec-ting pipeline against unintent-ional closure; the open posi-tion has to be monitored.

• Maintenance of the compres-sor (compressor vessel).

8.1.2 Standpipes, one-waysurge tanks

Standpipes can only be installedat points of a piping systemcharacterised by low-pressureheads. As a rule, a standpipecannot replace a downstream airvessel. Fitted with a swing checkvalve in the direction of the flowand a filling mechanism (one-way surge tank), it is used tostop the pressure falling belowatmospheric at the high points

21

8Surge Control Systems

Gaz

Membrane

Liquide

Grille de limitation de

l'expansion de la vessie

Fig. 8.1.1-b: Schematic of an accumulator

11 An exception is a vessel fitted with a vent pipe; this arrangement, comprising an air vessel, a standpipe and a vent valve, is very rarely used in Ger-many.

Fig. 8.1.1-c: Accumulators

of long clean-water pipelines.Because of the possibility ofmalodorous fumes, standpipesare rarely found in wastewaterinstallations. Standpipes andone-way surge tanks are highlyreliable pieces of equipmentprovided the following pointsare observed:

• Continuous or regular changesof water (problem of hygiene).

• Filtering of air flow.

• Functional tests of the checkvalve on one-way surge tankarrangements.

• Monitoring of water level orfilling device on one-way surgetank arrangement.

8.1.3 Flywheels

Mounted on the driver, a flyw-heel prolongs the rundown timeof a pump to standstill by meansof the stored rotational energy:

J: Mass moment of inertia offlywheel in kgm2

�: Angular velocity s-1

For a homogeneous solid discwith a radius r and a mass m,for example, the mass momentof inertia is

Figs. 8.1.3-a and 8.1.3-b showseveral practical applications.However, with a type of fly-wheel that is economically andtechnically feasible, one can onlyachieve a prolongation of therunning down time of the kindwhich is suitable for a relatively

short pipeline, or, put different-ly, with a short reflection timeTr. The limits for employing aflywheel are in the region of 1 to2 km pipeline length. Example 3in section 4 includes a roughestimate performed to checkwhether a flywheel can be used.For reasons of design, the fly-wheel solution is not suitable forsubmersible motor pumps. Onother pump types, it must bechecked in advance that the

flywheel will not interfere withthe starting procedure of thepump driver. Flywheels areprobably the safest and mostelegant types of surge control.Their reliability beats that of allother surge control methods.With the exception of the bear-ings of larger-scale systems, theydo not require any in-operationmonitoring.

22

8 Surge Control Systems

Fig. 8.1.3-b: Vertically mounted flywheel (driven by means of cardanshaft, D = 790 mm)

Fig. 8.1.3-a: The V-belt pulleys in this arrangement are solid discs

Ekin = – · J · �212

J = ––––––m · r2

2

(8.1)

8.2 Air valves

Air valves should not be useduntil every other solution hasbeen ruled out. Their drawbacksare:

• They require regular mainte-nance.

• If arranged in the wrong placeor mounted incorrectly, theycan aggravate pressure varia-tions instead of alleviatingthem.

• Under certain circumstances,operation of the plant may belimited, because the air drawninto the system has to be re-moved again.

• The handling of wastewatercalls for special designs.

Air valves (Fig. 8.2-a) have to becarefully designed. On large dia-meter pipelines, one has to ar-range air outlet valves on top ofdomes, to make sure that the airdrawn into the system will col-lect there. As long as the fluidflow has not reached the steadystate, air drawn into pipes can,under unfavourable conditions,have a very negative effect. Aircushions normally have a damp-ening effect. However, the airdrawn into the pipeline can alsogive rise to dangerous dynamicpressure increases. It has to bepressed out of the piping slowly;a large air outlet cross-sectionwould lead to sudden pressurevariations towards the end ofthe air outlet operation. For thisreason, aerators and deaeratorshave different nominal dia-meters depending on which waythe air flows. Air normally flowsin through a large cross-section

and out through a small cross-section.

The reliability of aerators /deae-rators depends on their designand is the lowest of all surgecontrol equipment. They have tobe tested for proper functioningin regular intervals and it maybe necessary to filter the in-coming air.

8.3 Actuated valves

Suitable actuation schedules forthe opening and closing ofvalves are calculated and veri-fied by means of a surge analysison the basis of the valvecharacteristic.

The valves will give very reliableservice if, on valves with electricactuator, adequate protection isprovided for the actuating timesand the break points of the actu-ation schedules or if, on valveswith hydraulic actuators, ade-quate safety elements, such asorifice plates or flow controlvalves, are used. Proper valvefunctioning has to be checked atregular intervals with regard tothe actuating times and closingcharacteristics.

23

8Surge Control Systems

Fig. 8.2-a: Duojet*) two-way airvalve with a medium-operatedsingle-compartment valve.

Large vent cross-section fordrawing in and venting largeamounts of air during start-upand shutdown of pumpingsystems.

Small cross-section for removingsmall amounts of air during op-eration against full internal pres-sure.

*) With the friendly permission of VAG-Armaturen GmbH.

Fig. 8.3-a: Motorised shut-off butterfly valve

8.4 Swing check valves

The dynamics of swing checkvalves often have a major in-fluence on the development ofsurge, because the valve’s closu-re, after reversal of flow, gener-ates velocity changes which,according to Joukowsky’s equa-tion (4.1), produce pressurevariations.

Check valves generally have tomeet the following two contra-dictory requirements:

• bring the reverse flow to astandstill as quickly aspossible,

• keep the pressure surge gener-ated during the process assmall as possible.

Drinking water pumping instal-lations protected by air vesselsshould ideally be equipped withnozzle check valves. Free-swing-ing valve discs can have a very

unfavourable effect, becausethey take a long time to close,which means reverse flow sets inwhile they are still partly open,and the valve disc re-seats withconsiderable impact. The pheno-menon is known by the term“check valve slam” and is muchdreaded. Since the closing timeis the main criterion for checkvalve slam, limit position dam-pers will improve the situation,but not eliminate the risk alto-gether. In waste water systems,nozzle check valves cannot beused because they tend to clogup. This means that valves withfree-swinging discs and limit po-sition dampers are the only re-maining option, despite theirdrawbacks.

Pump check valves installed inthe cooling pipes of a powerstation are designed to throttlethe reverse flow in a controlled

manner after the pump trips.This feature is important onpumps operated in parallel,when one pump fails whilst theremaining pumps continue torun and deliver flow against thetripped pump. In a case like this,controlled closing is achieved byadjustable hydraulic actuatorswithout external supply butwith a lever and counterweight,with the free-swinging valve discopening in the direction of theflow and, upon actuation,closing in one or two stagesaccording to a set closingcharacteristic.

The operating reliability ofcheck valves is relatively high. Inoperation, they have to bechecked for proper functioningat regular intervals.

24

8 Surge Control Systems

Fig. 8.4-a: Swing check valve equipped with a hydraulic actuator and counterweight

9 Case studies

The case studies below weretaken from surge analysesperformed by KSB. Although wehave altered the system para-meters, so that the installationsconcerned remain anonymous,the problems involved and theway these were resolved havenot been altered.

9.1 Case study: long-distancewater supply system

The system parameters are indi-cated in Fig. 2.1-b. A steady-state flow Qsteady = 500 l/s ispumped through a DN 600 pi-peline of ductile cast materialwith a total length of L = 2624by three centrifugal pumps ope-rating in parallel at a total headof the pumps hsteady = 122.5 minto an overhead tank. The di-sturbance under investigation,which leads to excessive dyna-mic pressures, is the simultane-ous failure of all three pumps.The dynamic pressure peaksproduced by far exceed the per-missible nominal pressure of PN16 (see hmax curve) in Fig. 2.1-b;the minimum pressures drop tovapour pressure in wide areas ofthe system (see hmin curve) in Fig.2.1-b. The system can be protec-ted by installing an air vessel atthe inlet of the long-distance pi-peline. Although the vessel di-mensioned as shown in Fig. 2.1-b will initially prevent the deve-lopment of areas of low pressu-re, the water column in the pipe-line swinging back will still pro-duce dynamic pressure peaks inexcess of 16 bar. Therefore, thereverse flow into the air vesselhas to be additionally throttled;

a schematic diagram of the ope-rating principle is shown in Fig.8.1.1-a. In the present case, thethrottling action is achievedwith the aid of a short length ofDN 200 pipe fitted with a stan-dard DN 80 orifice. Fig. 2.1-bshows the calculated pressureenvelope with and without airvessel. The maximum head cur-ve obtained with an air vesselhmaxWK is now only slightly ab-ove the steady-state head curvehsteady and the associated mini-mum head curve hminWK runs at awide safety margin above thepeak point of the pipe.

Fig. 9.1 shows the head andflow curves of the system pro-tected by an air vessel arrange-ment plotted against time (headsexpressed in m above mean sealevel)

25

9Case Studies

Fig. 9.1: Time plots for the long-distance water supply pipeline (Fig.2.1-b); the example shows the head and flow curves of an air vessel-protected system as functions of time (heads expressed in m abovemean sea level)

H inlet [m above MSL]:KN=1/Pipe No. System with air vessel

Q inlet [l/s]:KN=1/Pipe No. 1 System with air vessel

Water vol. [m3]:KN=1/Air vessel No. System with air vessel

Time s

Time s

Time s

9.2 Case study: a stormwaterconveyance pipeline

Starting from a wastewaterpumping installation, a new DN350 stormwater pipeline with atotal length of L = 590 m waslaid to an aeration structure.Pumping operation was bymeans of three identical pumpsrunning in parallel, each equip-ped with a non-return valve anda motorised gate valve to controlpump start-up and run-down.The first 100 m of pipe made ofhigh-density polyethy lene werelaid under ground, the remai-ning 490 m were of steel andlaid above ground supported onpipe bridges. Fig. 9.2-a shows aschematic of the model installa-tion. The nodes connecting theabove-ground single pipes of themodel, are 90° elbows. Theengineering firm in charge ofplanning the plant neither per-formed ordered a surge analysisto accompany the project-planning phase.

During the first operating testsfollowing the plant’s comple-tion, several incidents, amongthem a power failure whichcaused all three pumps to fail atthe same time, caused the partof the piping laid above groundto shake considerably, damagingpipe fixtures and tearing offsome pipes altogether.

When a surge analysis was final-ly ordered, its objective was:

• to determine what caused thesurge pressures and forces thathad been observed,

• to devise some protective meas-ures or surge control equipmentthat would prevent the excessivedynamic pressures produced bya pump failure from occurring,and to prove their effectivenessmathematically.

Model parameters

Besides the parameters indicatedin Fig. 9.2-a, the following sys-tem data were entered into thecalculation:

Pump characteristic shown inFig. 9.2-c

Model pipeline L1:Material:

high-density polyethy-lene (HDPE)

Dinside: 354.6 mmk: 0.1 mma: 600 m/s (estimated value)Min. permissible pressure: vacuumPressure class: PN 6

26

9 Case Studies

Fig. 9.2-c: Characteristic curve of the pump used in the stormwaterconveyance system

Fig. 9.2-a: Schematic diagram of the stormwater conveyance pipelineused in the example

Aerator

Improved system with aeraor and

Stormwater pump 1470 rpm

Model pipeline L2 to L10:

Material: steelDinside: 349.2 mmk: 0.1 mma: 1012 m/s

(from equation 4.1)Min. permissible pressure: vacuumPressure class: PN 10

Nothing was known about thepump check valves. For the pur-pose of the model, it was there-fore assumed – correctly so, as itturned out – that the valveswould suddenly close upon re-verse of the flow direction.

Calculation of actual dutydata, first results

The steady-state flow calculatedby the surge software for the pa-rallel operation of three pumpsamounted to Qsteady = 187 l/s.The first surge calculation of thesimultaneous failure of all threepumps showed that macro-cavi-tation and, as a result of it,dynamic pressure peaks as highas 15 bar would occur inside theHDPE pipeline, i.e. considerablyin excess of the given nominalpressure of the pipe of PN 6.The calculation showed that thepipe bridges between each pairof 90° elbows had to temporari-ly withstand longitudinal forcesof just under 100 kN, or interms of weight, the equivalentof a thrust somewhere in the re-gion of 10 t. Figs. 9.2-d and 9.2-eshow some examples of the sys-tem behaviour without surgecontrol plotted over time. Fig.9.2-d shows the pump speed,head and flow at the entrance ofmodel pipe L1 (head in m abovepipe centreline); the curve in Fig.9.2-e shows the axial forces act-

ing on L8. This explained theviolent shaking and resultingdamage observed.

27

9Case Studies

Fig. 9.2-d: Operating characteristics of the stormwater line withoutsurge control plotted over time

-120

-100

-80

-60

-40

-20

0

20

40

0 5 10 15 20 25 30 35 40 45 50

Zeit s

Kra

ft k

N

Längskraft auf L8 ohne Druckstoß -Sicherungen

Fig. 9.2-e: Longitudinal force acting on L8 if the stormwater line iswithout surge control

Pump failure without surge control

Pump failure without surge control

Q inlet [l/s]:KN=1/Pipe No. 1

H inlet [m]:KN=1/Pipe No. 1

Time s

Time s

Time s

Pump failure without surge control

Longitudinal force acting on L8 without surge control

Time s

Forc

e k

N

Surge control measures

To eliminate the macro-cavita-tion developing after pump fail-ure, a second simulation calcula-tion was run with a DN 150 ae-rator at the outlet of L2, the hig-hest point of the piping. Despitethe addition of a surge controldevice, the HD-PE pipe was stillfound mathematically to containunacceptably high pressure in-creases a few seconds afterpump failure. In order to elimi-nate these highly undesirablepressure peaks, it was eventuallydecided to add a shut-off valvewith a bypass between the inletof L1 and the pump suctiontank which would be automati-cally opened by a maintenance-free electro-hydraulic lever andweight type actuator if all threepumps were to fail at once. Tovalve manufacturers today, sys-tems like this are more or lesspart of their standard productrange. After adding surge con-trol devices, i.e. an aerator and abypass fitted with an automati-cally opening shut-off valve, thesimulation finally showed thatthe dynamic pressure peaks re-mained below the steady-stateinitial pressure, and that thelongitudinal forces acting on thepipe bridge sections laid aboveground had diminished to nomore than 5% of the initialvalue. The calculation furtherrevealed that the existing checkvalves could be dispensed with.Fig. 9.2-f shows – on the samescale as in Figs. 9.2-d and 9.2-eto facilitate comparison – the n,H and Q curves of the surge-protected system plotted overtime; Fig. 9.2-g shows the forces

28

9

Längskraft auf L8 mit Belüfter und Bypass

-100

-80

-60

-40

-20

0

20

40

0 5 10 15 20 25 30 35 40 45 50

Zeit s

Kar

ft k

N

Fig. 9.2-g: Longitudinal force acting on L8 if the stormwater line issuitably protected

Fig. 9.2-f: Operating characteristics of the stormwater line withsurge control plotted over time

Pump failure in a system equipped with an aeratorand a bypass as surge control devices

Pump failure in a system equipped with an aeratorand a bypass as surge control devices

Pump failure in a system equipped with an aeratorand a bypass as surge control devices

Case Studies

Longitudinal forces acting on L8 if the system is protected by an aerator-bypass combination

time {s}

Q inlet [l/s]:KN=2/Pipe No. 1

H inlet [m]:KN=2/Pipe No. 1

Time s

Time s

Time s

of the surge-protected systemplotted over time. The globalpressure envelope of the rehabi-litated installation, as well as thecurves of the system withoutsurge control, are shown in Fig.9.2-h.

29

9

Druckeinhüllenden mit und ohne Druckstoß-Sicherungen (DS)

40

60

80

100

120

140

160

180

200

220

0 100 200 300 400 500 600

abgewickelte Rohrlänge m

Ko

te m

üN

N

Rohrkote

hmax mit DS

hmin ohne DS

hmin mit DS

hmax ohne DS

Fig. 9.2-h: Pressure envelope of the stormwater conveyance pipeline with and without surge control

Case Studies

Pressure envelope with and without surge control equipment (SC)

Pipeline section m covered by the analysis

Elev

atio

n in

m a

bove

mea

n se

a le

vel

Elevation of pipelinehmax with SC

hmax with SC

hmax without SC

hmax without SC

Additional Literature:

1. Dynamische Druckänder-ungen in Wasserversor-gungsanlagen (Dynamicpressure changes in watersupply systems), Techn.Mitteilung, MerkblattW303, DVGW, Sept. 1994

2. Horlacher, H.B., Lüdecke,H.J.: Strömungsberechnungfür Rohrsysteme (Flow mo-delling for piping systems),expert Verlag, 1992

3. Zielke, W.: ElektronischeBerechnung von Rohr- undGerinneströmungen (Compu-ter analysis of flows in pipesand channels), Erich SchmidtVerlag, 1974

4. Wylie, E.B., Streeter, V.L.:Fluid Transients, FEB Press,Ann Arbor, MI, 1983

5. Chaudry, H.M.: AppliedHydraulic Transients, VanNostrand Reinhold Com-pany, New York, 1987

6. Sharp, B.B.: Water Hammer,Edward Arnold, 1981

7. Parmarkian, J.: Water-hammer Analysis, DoverPublications, 1963

8. Publication of all paperspresented at the Internatio-nal Conference on “PressureSurges” held by bhra fluidengineering, Great Britain,in the years 1976, 1980,1986, 1992, 1996, 2000

9. Engelhard, G.: Zusammen-wirken von Pumpen, Armatu-ren und Rohrleitungen (Inter-action between pumps, valvesand pipelines), KSB 1983

10. Raabe, J.: HydraulischeMaschinen und Anlagen (Hydraulic machines andsystems), VDI Verlag, 1989

Authors:

Prof. Dr. Horst-Joachim Lüdecke,born in 1943, Diplom-Physiker,developed process engineeringand fluid dynamics softwarewhilst employed with BASF AG,Ludwigshafen; professor at Hoch-schule für Technik und Wirtschaft(HTW) des Saarlandes (Universityfor Technology and Economics ofSaarland) since 1976; numerouspublications on the subject of flu-id flows in pipelines; co-author ofthe book “Strömungsberechnungfür Rohrsysteme” (Flow model-ling for piping systems) (expertVerlag); as a member of the WaterHammer Committee of DVGW(German Association of the Gasand Water Sector), involved in therevision of Surge Guideline W303; currently supports andadvises KSB in the field of surgeanalysis

Dipl.-Ing. Bernd Kothe, born in1955; graduate from “Otto vonGuericke” Technical University atMagdeburg; joined PumpenwerkeHalle as a development engineerfor power station pumps. From1993 to 1998, whilst employed inthe engineering division of KSBAG, in charge of surge analysesand complex flow modelling forwaste water systems. Since 2002,Manager Sales Support of theWaste Water Competence Centerat Halle.

Edited by:

KSB Aktiengesellschaft,Communications

Dipl.-Ing. (FH) Christoph P. Pauly

30

10 Additional Literature

Authors

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