some aspects of physical and numerical modeling of water hammer in pipelines

Nonlinear Dyn (2010) 60: 677–701DOI 10.1007/s11071-009-9624-7

O R I G I NA L PA P E R

Some aspects of physical and numerical modeling of waterhammer in pipelines

Kaveh Hariri Asli · Faig Bakhman Ogli Naghiyev ·Akbar Khodaparast Haghi

Received: 1 May 2009 / Accepted: 13 November 2009 / Published online: 10 December 2009© Springer Science+Business Media B.V. 2009

Abstract In this work, a computational method wasused for the prediction of water transmission failure.The proposed method allowed for any arbitrary com-bination of devices in the water pipeline system. Themethod used was by a scale model and a prototype(real) system for a city main water pipeline where tran-sient flow was caused by the failure of a transmissionsystem.

Keywords Transient flow · Water hammer ·Unaccounted for water · Method of characteristics

K.H. Asli (�)Department of Mathematics and Mechanics, NationalAcademy of Science of Azerbaijan “AMEA”, Baku,Azerbaijane-mail: [email protected]

K.H. AsliNo. 1045, Alley Azerbany 2, Farhang ring, Rasht41886-13133, Iran

F.B.O. NaghiyevAzerbaijan State Oil Academy, Baku, Azerbaijane-mail: [email protected]

A.K. HaghiUniversity of Guilan, Rasht, Irane-mail: [email protected]

A.K. Haghie-mail: [email protected]

Abbreviationsλ Coefficient of combinationI Moment of inertia (m4)w Weight (kg)P Fluid power (pa)z Elevation at the centroid (m)t Time (s)λ0 Unit of lengthp Pressure (N/m2)α Pipe cross section area (m2)V Velocity (m/s)s Length (m)f Friction factorτ Shear stress (Pa)H2–H1 Pressure difference (m-H2O)C Surge wave velocity (m/s)V Volume (m3)F Fluid force (N)W Frequencyq Flow rate (m3/s)D Diameter of each pipe (m)μ Fluid dynamic viscosity (kg/m s)R Pipe radius (m)γ Specific weight (N/m3)ν Fluid dynamic viscosity (kg/m s)J Junction point (m)y Surge tank and reservoir elevation

difference (m)K Volumetric coefficient (GN/m2)T Period of motionA Pipe cross-sectional area (m2)

mailto:[email protected]




678 K.H. Asli et al.

dp Is subjected to a static pressure rise (m)hp Head gain from a pump (m)hL Combined head loss (m)Eν Bulk modulus of elasticity (Pa)α Kinetic energy correction factorP Surge pressure (m)ρ Density (kg/m3)C Velocity of surge wave (m/s)g Acceleration of gravity (m/s2)K Wave numberTp Pipe thickness (m)Ep Pipe module of elasticity (kg/m2)Ew Module of elasticity of water (kg/m2)C1 Pipe support coefficientYmax Max. fluctuationMin. MinimumMax. MaximumLab. Laboratory

1 Introduction

Long-distance water transmission lines must be eco-nomical, reliable, and expandable. The present worktried to show safe hydraulic input to a network. Thisidea provided wide optimization and water hammerrisk-reduction strategy for the Rasht city water mainpipeline in northern Iran. The important effect of wa-ter hammer disaster is unaccounted for in the water“UFW” phenomenon. This work had particular exper-tise for designing safe pressurized pipeline segments.This means that by reduction of unaccounted for wa-ter, “UFW”, energy costs can be reduced. Water ham-mer disaster as a fluid dynamics phenomenon is an im-portant case study for designer engineers. Water ham-mer is a pressure surge or wave caused by the kineticenergy of a fluid in motion when it is forced to stop orchange direction suddenly [1]. The majority of tran-sients in water and wastewater systems are the resultof changes at system boundaries, typically at the up-stream and downstream ends of the system or at localhigh points. Consequently, the results of the presentwork can reduce the risk of system damage or failure.The study of hydraulic transients is generally consid-ered to have begun with the works of Joukowsky [2]and Allievi [3]. The historical development of this sub-ject makes for good reading. A number of pioneershave made breakthrough contributions to the field,including Angus and Parmakian [4] and Wood [5],

who popularized and refined the graphical calculationmethod. Wylie and Streeter [6] combined the methodof characteristics with computer modeling. The fieldof fluid transients is still rapidly evolving worldwideby Brunone et al. [7], Koelle and Luvizotto [8], Fil-ion and Karney [9], Hamam and McCorquodale [10],Savic and Walters [11], Walski and Lutes [12], Wu andSimpson [13]. Various methods have been developedto solve transient flow in pipes. These ranges havebeen formed from approximate equations to numericalsolutions of the non-linear Navier–Stokes equations.Hydraulic transient flow is also known as unsteadyfluid flow. During a transient analysis, the fluid andsystem boundaries can be either elastic or inelastic:(a) elastic theory describes the unsteady flow of a com-pressible liquid in an elastic system (e.g., where pipescan expand and contract); (b) rigid-column theory, de-scribes unsteady flow of an incompressible liquid ina rigid system. It is only applicable to slower tran-sient phenomena. Both branches of transient theorystem from the same governing equations. The conti-nuity equation and the momentum equation are neededto determine V (velocity) and p (surge pressure) in aone-dimensional flow system. Solving these two equa-tions produces a theoretical result that usually corre-sponds quite closely to actual system measurements,if the data and assumptions used to build the numeri-cal model are valid. Transient analysis results that arenot comparable with actual system measurements aregenerally caused by inappropriate system data (espe-cially boundary conditions) and inappropriate assump-tions [2, 3]. Among the approaches proposed to solvethe single-phase (pure liquid) water hammer equationsare the Method of Characteristics (MOC), Finite Dif-ferences (FD), Wave Characteristic Method (WCM),Finite Elements (FE), and Finite Volume (FV). Onedifficulty that commonly arises relates to the selec-tion of an appropriate level of time step to use for theanalysis. The obvious trade-off is between computa-tional speed and accuracy. In general, the smaller thetime step, the longer the run time but the greater thenumerical accuracy. The challenge of selecting a timestep is made difficult in pipeline systems by two con-flicting constraints. First, to calculate many boundaryconditions, such as obtaining the head and discharge atthe junction of two or more pipes, it is necessary thatthe time step be common to all pipes. The second con-straint arises from the nature of the MOC. If the adjec-tive terms in the governing equations are neglected (as

Some aspects of physical and numerical modeling of water hammer in pipelines 679

is almost always justified), the MOC requires that ratioof the distance �x to the time step �t be equal to thewave speed in each pipe. In other words, the Courantnumber should ideally be equal to one and must notexceed one by stability reasons. For most pipeline sys-tems, having as they do a variety of different pipeswith a range of wave speeds and lengths, it is impos-sible to satisfy exactly the Courant requirement in allpipes with a reasonable (and common) value of �t .Faced with this challenge, researchers have sought forways of relaxing the numerical constraints. Two con-trasting strategies present themselves. The method ofwave-speed adjustment changes one of the pipelineproperties (usually the wave speed, though more rarelythe pipe length is altered) so as to satisfy exactly theCourant condition [14].

Every pipe system has a characteristic time pe-riod, T = 2L/a, where L is the longest possible paththrough the system and a is the pressure wave speed.This period is the time it takes for a pressure waveto travel the pipe system’s greatest length two times.It is recommended that the run duration equals or ex-ceeds T . Another factor to consider when determiningrun duration is to allow enough time for friction to sig-nificantly dampen the transient energy. If in doubt, runwork for a longer duration and examine the resultinggraphs and time histories. Run duration is measuredeither in seconds or as a number of time steps. Timesteps typically range from a few hundredths of a sec-ond to a few seconds, depending on the system andthe pressure wave speeds. The run duration has a di-rect effect on the modeling computation time, alongwith the time step selected for the simulation. Steady-state models, such as Water CAD or Water GEMS,are capable of two modes of analysis: steady state andextended period simulation (EPS). EPS solves a se-ries of consecutive steady states using a gradient algo-rithm and accounting for mass in reservoirs and tanks(e.g., net inflows and storage). Both methods assumethe system contains an incompressible fluid, so the to-tal volumetric or mass inflows at any node must equalthe outflows, less the change in storage. In additionto pressure head, elevation head, and velocity head,there may also be head added to the system, for in-stance, by a pump and head removed from the sys-tem by friction. These changes in head are referred toas head gains and head losses, respectively. Balancingthe energy across two points in the system yields theenergy or Bernoulli equation for steady-state flow: the

components of the energy equation can be combinedto express two useful quantities, the hydraulic gradeand the energy grade:

(P1/γ ) + Z1(V 2

1 /2g) + hp

= (P2/γ ) + Z2 + (V 2

2 /2g) + hL, (1.1)

Pressure head: p/γ

Elevation head: z

Velocity head: V 2/2g

where p—pressure (N/m2), γ —specific weight(N/m3), z—elevation (m), V —velocity (m/s), g—gravitational acceleration constant (m/s2, ft/s2).

Unsteady or transient friction Compared to a steadystate, fluid friction increases during hydraulic transientevents because rapid changes in transient pressure andflow increase turbulent shear. The MOC model cantrack the effect of fluid accelerations to estimate the at-tenuation of transient energy more closely than wouldbe possible with quasi-steady or steady-state friction.Computational effort increases significantly if tran-sient friction must be calculated for each time step.This can result in long model-calculation times forlarge systems with hundreds of pipes or more. Typ-ically, transient friction has little or no effect on theinitial low and high pressures and these are usually thelargest ever reached in the system. This is illustratedfrom the following present work simulation resultscomparing steady, quasi-steady, and transient frictionmethods. The steady-state friction method yields con-servative estimates of the extreme high and low pres-sures that usually govern the selection of pipe classand surge-protection equipment. However, if cyclicloading is an important design consideration, the un-steady friction method can yield less conservative es-timates of recurring and decaying extremes. In thepresent work, this method has provided a suitableway for detecting, analyzing, and recording transientflow (down to 5 milliseconds). Transient flow hasbeen solved for the pipeline in the range of approx-imate equations. These approximate equations havebeen solved by numerical solutions of the non-linearNavier–Stokes equations in a method of characteris-tics “MOC”. So, experiences have been ensured forthe reliable water transmission for the Rasht city mainpipeline in northern Iran (research pilot).


2 Materials and methods

The method of characteristics “MOC” is based on afinite difference technique where pressures are com-puted along the pipe for each time step [15]. Two casesare considered for modeling [2, 3]:

(1) The combined elasticity of both the waterand the pipe walls is characterized by the pressurewave speed (Arithmetic method—combination of theJoukowski formula and Allievi formula):

Joukowski formula

H2 − H1 = (C/g)(v2 − v1) = ρC(v2 − v1), (2.1)

Allievi formula

c = 1

2[ρ((1/k) + (dC1/Ee))] (2.2)

With the combination of the Joukowski formula andAllievi formula:

λ[(∂v/∂t) + (1/ρ)(∂p/∂s)

+ g(dz/ds) + (f/2D)v|v|]

+ C2(∂v/∂s) + (1/p)(∂p/∂t) = 0,

λ = +c and λ = −c

(2.3)

Hence, water hammer pressure or surge pressure(�H) is a function of independent variables (X) suchas

�H ≈ ρ,K,d,C1,Ee,V,g, (2.4)

(2) The method of characteristics (MOC) based ona finite difference technique where pressures are com-puted along the pipe for each time step,

HP = 1

2

(C/g(VLe − Vri) + (HLe + Hri)

− C/g(f �t/2D)(VLe|VLe| − Vri|Vri|

)), (2.5)

VP = 1

2

(VLe + Vri) + (g/c)(HLe − Hri)

− (f �t/2D)(VLe|VLe| + Vri|Vri|

)), (2.6)

f —friction, C—slope (deg), V —velocity (m/s), t—time (s), H—head (m).

The present work used the method of characteris-tics “MOC” to solve virtually any hydraulic transientproblems.

Dateline for field tests and lab. Model data collec-tion was: at 12:00 a.m., 10/02/07, until 05/02/09. Lo-cation of work field tests and lab. Model was at Rashtcity in the northern part of Iran. Pilot subject was: “In-terpenetration of two fluids at parallel between platesand turbulent moving in pipe”. For the data collectionprocess, the Rasht city water main pipeline has beenselected as a field test model. The pipeline was in-cluded in the water treatment plant pump station (inthe start of water transmission line), 3.595 (km) of twolines of 1200 (mm) diameter pre-stressed cement pipesand one 50,000 (m3) water reservoir (in the end of wa-ter transmission line). All of these parts have been tiedinto existing water networks.

The curve estimation procedure was formed by es-timating regression statistics and producing relatedplots. The model summary and parameter estimateshave been provided a set of results. Also, numeri-cal modeling and simulation which was defined bymethod of characteristics “MOC” have been provideda set of results. The present work has compared thesetwo sets of results (method of characteristics “MOC”numerical modeling and simulation results against thecurve estimation procedure which was formed by es-timating regression statistics). The method of charac-teristics “MOC” approach transforms the water ham-mer partial differential equations into the ordinary dif-ferential equations along the characteristic lines de-fined as the continuity equation and the momentumequation are needed to determine V and P in a one-dimensional flow system. Solving these two equationsproduces a theoretical result that usually correspondsquite closely to actual system measurements if the dataand assumptions used to build the numerical modelare valid. Transient analysis results that are not com-parable with actual system measurements are gener-ally caused by inappropriate system data (especiallyboundary conditions) and inappropriate assumptions.Comparisons between the models and validation datacan be grouped into the following three categories:

(a) Cases for which closed-form analytical solutionsexist given certain assumptions if the model candirectly reproduce the solution, is considered validfor this case.

(b) Laboratory experiments with flow and pressuredata records—The model is calibrated using oneset of data and, without changing parameter val-ues, it is used to match a different set of results. Ifsuccessful, it is considered valid for these cases.


Table 1 Rasht citylaboratory model technicalspecifications

*—Laboratory test results:If liquid density and pipecross section are constant,the instantaneous velocity isthe same in all sections.These rigidity assumptionsresult in an easy-to-solveordinary differentialequation; however, itsapplication is limited to theanalysis of surge. Newton’ssecond law of motion (2.7)is sufficient to determinethe dynamic hydraulic of arigid water body during themass oscillation (Fig. 1)

Laboratory model technical specifications Notation Value Dimension

Pipe diameter d 22 mm

Surge tank cross section area A 1.521 × 10−3 m2

Pipe cross section area a 0.3204 × 10−3 m2

Pipe thickness t 0.9 mm

Fluid density ρ 1000 kg/m3

Volumetric coefficient K 2.05 GN/m2

Fluid power P * *

Fluid force F * *

Friction loss hf * *

Frequency W * *

Fluid velocity ν * m/s

Max fluctuation Ymax * *

Flow rate q * m3/s

Pipe length L * m

Period of motion T * *

Surge tank and reservoir elevation difference y * m

Surge wave velocity C * m/s

(c) Field tests on actual systems with flow and pres-sure data records—These comparisons requirethreshold and span calibration of all sensor groups,multiple simultaneous datum, and time basechecks and careful test planning and interpreta-tion. Sound calibrations match multiple sensorrecords and reproduce both peak timing and sec-ondary signals—all measured every second orfraction of a second.

2.1 Laboratory models

A scale model shows transient flow in a prototype(real) system. It was designed by Kaveh Hariri Asli.Its patent was recorded in the inventions organizationof Iran (record No.: 44242—date of record: 11/24/07).It was used for PhD research laboratory tests.

2.2 Laboratory model technical specifications

The model has been calibrated by a water hammer lab-oratory instrument on 05/02/09. The calibration instru-ment belonged to Iran science and Technology Univer-sity. The model specifications are as the flowing Ta-ble 1 and Figs. 1, 7(a).

Specialist “Transient View” analysis software forRasht city laboratory model was capable of window-

ing down to one sample. Sensor input analogue sup-plied with quick fit connector, 0–35 (bar), accuracy±0.25% recording up to 8,000,000 readings. Loggingmemory was programmed to read continuously (cyclicmode) or for a features specific period of time (block).Frequency 1, 5, 10, 20, and 25 samples were per sec-ond. Logger ID had up to 8 alphanumeric characters.Communications programmed with Serial RS232 byMIL connector for connection to laptop or desktop PC115,200. Portable ultrasonic flow meter “UFM” withpressure transient data logger pressure transient was aspecialized data logger for monitoring rapid pressurechanges in water pipe systems (e.g., water hammer). Itwas supplied in portable mode only. Pressure transientloggers were completely waterproof, submersible, andbattery powered for at least 5 years.

Newton second law for laboratory model

ρaldv

dt= ρgaH1 − ρga(H2 + y)

+ ρgaL sin θ − ρgahf. (2.7)

For steady-state flows condition, if dV/dt = 0, thenthis equation simplifies to the Darcy–Weisbach for-mula for computation of head loss over the length of


Fig. 1 Laboratory experiments for Rasht city with flow and pressure data records

the pipeline. However, if a steady-state flow conditionis not established because of flow control operations,then three unknowns need to be determined: H1(t)

(the left-hand head), H2(t) (the right-hand head), V (t)

(the instantaneous flow velocity in the conduit) to de-termine these unknowns, the boundary conditions atboth ends of the pipeline must be known. Using thefundamental rigid-model equation, the hydraulic gradeline can be established for each instant. The slopeof this line indicates the head loss between the twoends of the pipeline, which is also the head neces-sary to overcome frictional losses and inertial forcesin the pipeline. For the case of flow reduction causedby a valve closure (dQ/dt < 0), the slope is re-duced. If a valve is opened, the slope increases, po-tentially allowing vacuum conditions to occur. Thechange in slope is directly proportional to the flowchange. At fast transients, down to 1 second, surgepressure, and velocity of surge wave are found by

approximate equations to numerical solutions of thenon-linear Navier–Stokes equations. Hydraulic tran-sient flow is also known as unsteady fluid flow. Forlaboratory models of the work, the maximum transienthead envelope calculated (2.8)–(2.15) by rigid watercolumn theory (RWCT) is a straight line, as shownin the following figure (Fig. 7a). The rigid model haslimited applications in hydraulic transient analysis be-cause the resulting equations do not accurately modelpressure waves caused by rapid flow control opera-tions. The rigid model applies to slower surge or massoscillation transients, as defined in “wave propagationand characteristic time”.

L

g× dv

dt+ y + hf = 0, av = A

dy

dt+ Q,

H2 = H1 + k, L sin θ = k,

L

g× d

dt

(A

a

dy

dt+ Q

a

)+ y + hf = 0,


d2y

dt2+ ga

LAy = 0,

d2y

dt2+ W 2y = 0, (2.8)

L

g× d

dt

(A

a

dy

dt+ Q

a

)+ y + hf = 0,

d2y

dt2+ ga

LAy = 0,

d2y

dt2+ W 2y = 0, W 2 = ga

LA,

if: f and Q, equal to zero

y = ymax sin 2πt

T, (2.9)

T = 2π

W= 2π

√LA

ga, (2.10)

ymax = u

W= u

√LA

ga,

ymax = y − 0.6hf,

(2.11)

Fluid power = δQh, (2.12)

Fluid power = δ(H − �h)V A (2.13)

Head friction = fL

D

V 2

2g⇒ (2.14)

Fluid power = δV A(H − KV h

). (2.15)

2.3 Regression

The curve estimation procedure allows quick estimat-ing regression statistics, and producing related plotsfor different models (Tables 2–7). Curve estimation isthe most appropriate when the relationship betweenthe dependent variable(s) and the independent variableis not necessarily linear. Linear regression is used tomodel the value of a dependent scale variable basedon its linear relationship to one or more predictors.Non-linear regression is appropriate when the relation-ship between the dependent and independent variablesis not intrinsically linear. Binary logistic regression ismost useful in modeling of the event probability fora categorical response variable with two outcomes.The auto-regression procedure is an extension of ordi-nary least-squares regression analysis specifically de-signed for time series. One of the assumptions under-lying ordinary least-squares regression is the absenceof auto-correlation in the model residuals. Time se-ries, however, often exhibit first-order auto-correlation

of the residuals. In the presence of auto-correlatedresiduals, the linear regression procedure gives inac-curate estimates of how much of the series variabil-ity is accounted for by the chosen predictors. This canadversely affect the choice of predictors, and hencethe validity of the model. The auto-regression pro-cedure accounts for first-order auto-correlated resid-uals. It provides reliable estimates of both goodness-of-fit measures and significant levels of chosen predic-tor variables. The auto-regression procedure by regres-sion software “SPSS 10.0.5” has been selected for thecurve estimation procedure in the present work. Theregression model (3.1)–(3.8) has been built based onfield test data and in the final procedure it has beencompared (Figs. 5, 6) with the method of character-istics “MOC” numerical modeling and simulation re-sults.

2.4 Regression model compared with “MOC” model

High pressure approaches

The regression model and “MOC” model showedwater-column separation and the entrance of air (e.g.,Fig. 3) into the pipeline. Field tests focused on theactual system’s model. But in the second case, water-column separation was not what happened. This wasthe effect of the air release from the leakage point lo-cation. Also, work results showed Max. transient pres-sure line was completely over the steady flow pressureline Max. The pressure value was 156.181 (m). Thispressure was too high for old piping and it must beconsidered as a hazard for piping (for transmissionline with surge tank and in leakage condition).

2.5 Field test and regression equations definition

The main approach of this work was the definitionof a model by regression of the relationship be-tween the dependent and independent data or vari-ables. (Numerical modeling and simulation of waterhammer disaster). The variables are as follows: P —surge pressure (as a dependent variable with nomen-clature “Y ”), several factors (as independent variableswith nomenclature “X”) such as: ρ—density (kg/m3),C—velocity of surge wave (m/s), g—accelerationof gravity (m/s2), �V —changes in velocity of wa-ter (m/s), d—pipe diameter (m), Ep—pipe moduleof elasticity (kg/m2), Ew—module of elasticity of


Fig. 2 Laboratory experiments for Rasht city with flow and pressure data records

water (kg/m2), C1—pipe support coefficient, T —time (s), Tp—pipe thickness (m). For the data collec-tion process, advanced flow and pressure sensors havebeen selected as field test data collection. They wereequipped with high-speed data loggers and “PLC” inthis work. So, by this ability, they recorded fast tran-sients data, down to 5 milliseconds. Methods suchas inverse transient calibration and leak detection incalculation of unaccounted for water “UFW” usedsuch data. For district and zone monitoring, Multi-Log GPRSTM were used for monitoring flow, pres-sure, and/or water quality parameters were assessedfor demand, leakage, and conformance. MultiLogGPRSTM were used to perform dynamic flow andpressure analysis of water pipeline modeling, particu-larly where hourly data were updated for near real time

monitoring. Digital uni- or bi-directional pulses wereused as instrument powered or non-powered sensors,e.g. PD100 (Up to 128 pulses per second) for internalpressure transducer Sensor (0–20 bar/0–200 metershead/0–300 (psig), repeatability ±0.1%). Input ana-logue external pressure transducer (volt) or transmit-ter (mA) 0–20 (bar)/0–200 meters head/0–300 (psig),accuracy ±0.1% 4–20 (mA) from isolated sensor0–1 (V), 1–5 (V), or 0–100 (mV) Primary recording48,720 readings (memory expandable to 245,280 read-ings) were used. Memory were programmed to readcontinuously (cyclic mode) or for a specific period oftime (block). Secondary recording used 6,144 read-ings, frequency 15 minute sample rate (for hourly datadownload). Optional alarms sent by SMS. Minimumor maximum threshold alarm equipped with persis-


tence logging alarms factor per channel (7 Alarms perlogger). Each alarm had out comment field of 16 char-acters. Features were programmed to auto dial up to 4telephone numbers on alarm. Logger ID had up to 8alphanumeric characters that were programmed withgeography Information System (GIS) number. Clockon board 24-hour real time showed clock with datefacility. It was programmed to record either fast data,average minimum, average maximum, or channel timeinterval between pulses (for data smoothing). Loggingmodes counted with Serial RS232 by MIL connectorfor connection to Rad Link hand held programmingand data collection unit, laptop PC, or desktop PC.It was programmed up to 19,200 Baud. Communica-tions GPRS (email) typically 1 × email per day totransmitted 1 or 2 channels of communications com-pressed data at a 15-minute sample rate. SMS (Text)with SMS message transmitted on Alarm. GSM (Data)with SIM card was enabled for GSM service, office PCcould establish communications real time, communi-cations with Logger for reconfiguration, etc. Pressuretransient logger was supplied with one input for anexternal pressure transducer.

3 Results and discussion

Water hammer software version 07.00.049.00 resultshave been compared with regression software “SPSS10.0.5”. Regression software “SPSS” has fitted thefunction curve and provided regression analysis. So,the regression model has been found in the final proce-dure. By this model, field test results have been com-pared by lab. model results. This was the main prac-tical aim of the present work. In the final procedure,a condition base maintenance (CM) method has beenfound for all water transmission systems. The resultsare as follows: At fast transients, down to 1 second,surge pressure and velocity of surge wave have beenrecorded. Curve estimation procedure has used thesedata which have been detected (Fig. 6) on actual sys-tems (field tests). Also, flow and pressure were col-lected by lab. test model. Those data have been com-pared by flow and pressure data which have been col-lected from actual systems (field tests). The model iscalibrated using one set of data, without changing pa-rameter values. It is used to match a different set of re-sults [16]. The regression model (3.1)–(3.8) has been

built based on field test data. The curve estimation pro-cedure (Figs. 3, 4) was formed by estimating regres-sion statistics (Tables 2–7) and producing related plotsfor the field test model with two assumptions:

Assumption (1): p = f (V ).Assumption (2): p = f (V,T ,L).

Assumption 1 p = f (V ), V —velocity (flow para-meter) is the most important variable. Dependent vari-able: P —pressure (bar), for starting point of waterhammer condition (Table 2). The independent variableis Velocity (m/s). Regression software “SPSS 10.0.5”performs multi-dimensional scaling of proximity datato find least-squares representation of the objects in alow-dimensional space

Linear function ∴ pressure

= 6.062 + 0.571 Flow, (3.1)

Quadratic function ∴ pressure

= 6.216 − 0.365Flow4 + 0.468Flow3, (3.2)

Cubic function ∴ pressure

= 6.239 − 0.057Flow2 + 0.174Flow, (3.3)

Compound function ∴ pressure

= 1.089(1 + Flow)n,

n = compounding period, (3.4)

Growth function ∴ pressure

= 1.804(0.085)Flow/0.05, (3.5)

Exponential function ∴ pressure

= 6.076eFlowLn 0.085, (3.6)

Logitic function ∴ pressure

= 1/(1 + e−Flow) or

pressure = 0.165 + 0.918Flow. (3.7)

Assumption 2 p = f (V,T ,L), V —velocity (flow)and T —time and L—distance, are the most importantvariables.

Input data are in relation with water hammer con-dition. Regression software “SPSS 10.0.5” fitted thefunction curve (Figs. 3–4) with regression analysis forwater hammer condition (Tables 3, 4a).


Table 2 Rasht city model summary and parameter estimates (start of water hammer condition)

Equation Model summary Parameter estimates

R Square F df1 df2 Sig. a0 a1 a2 a3

Linear y = a0 + a1x 0.418 15.831 1 22 0.001 6.062 0.571

Logarithmica . . . . . . .

Inverseb . . . . . . .

Quadratic 0.487 9.955 2 21 0.001 6.216 −0.365 0.468

y = a0 + a1x + a2x2

Cubic 0.493 10.193 2 21 0.001 6.239 0 −0.057 0.174

y = a0 + a1x + a2x2 + a3x

3

Compound A = Cekt 0.424 16.207 1 22 0.001 6.076 1.089

Powera . . . . . . .

Sb . . . . . . .

Growth (dA/dT ) = KA 0.424 16.207 1 22 0.001 1.804 0.085

Exponential y = abx + g 0.424 16.207 1 22 0.001 6.076 0.085

Logistic y = axb + g 0.424 16.207 1 22 0.001 0.165 0.918

aThe independent variable contains non-positive values. The minimum value is 0.00. The logarithmic and Power models cannot becalculated.bThe independent variable contains values of zero. The Inverse and S models cannot be calculated. Regression equation defined instages (2–3–7–8) is meaningless. Stages (1–4–5–6–9–10–11) are accepted, because their coefficients are meaningful.

Fig. 3 Scatter diagram for Rasht city water transmission lines (start of water hammer condition)


Table 3 Rasht city modelsummary and parameterestimates (water hammercondition)

Model Un-standardized Standardized Beta T sign

coefficients coefficients

std. error

1 (Constant) 28.762 29.73 – 0.967 0.346

Flow 0.031 0.01 0.399 2.944 0.009

Distance −0.005 0.001 −0.588 −4.356 0

Time 0.731 0.464 0.117 1.574 0.133

2 (Constant) 14.265 29.344 – 0.486 0.632

Flow 0.036 0.01 0.469 3.533 0.002

Distance −0.004 0.001 −0.52 −3.918 0.001

3 (Constant) 97.523 1.519 – 64.189 0

4 (Constant) 117.759 2.114 – 55.697 0

Distance −0.008 0.001 −0.913 −10 0.033

5 (Constant) 14.265 29.344 – 0.486 0.632

Flow 0.036 0.01 0.469 3.533 0.002

Distance −0.004 0.001 −0.52 −3.918 0.001

Fig. 4 Scatter diagram forlab. tests (Rasht cityresearch Field Test Model)

Regression equation defined in stage (1) is ac-cepted, because its coefficients are meaningful:

pressure = 28.762 + 0.031Flow − 0.005Distance

+ 0.731Time. (3.8)

3.1 Field tests

Numerical modeling and simulation included threecases: The first case was the water pipeline with waterleakage and equipped with a surge tank. The secondcase was the water pipeline without a surge tank, but

it had water leakage. Field test results showed water-column separation and the entrance of air into thepipeline. Results showed that at point P25:J28 of theRasht city water pipeline, air was interred to the sys-tem. Max. volume of penetrated air was 198.483 (m3)and current flow was 2.666 (m3/s).

But in the second case, water-column separationdid not happen. This was the effect of air release fromthe leakage location (Figs. 10, 11). Work results haveshown Max. Transient Pressure line was completelyover the steady flow pressure line. Max. Pressure was156.181 (m). This was pressure was too high for old


Table 4 Rasht city waterhammer condition data andmodel summary andparameter estimates

aAll requested variablesenteredbAll requested variablesremovedcDependent variable:pressure

(a) Rasht city water hammer condition data

Pressure Flow Distance Time

(m-Hd) (l/s) (m) (s)

86 2491 3390 0

86 2491 3390 1

88 2520 3291 0

90 2520 3190 1

95 2574 3110 1.4

95 2574 3110 1.4

95 2574 3110 1.5

95 2590 3110 2

95 2590 3110 2

95.7 2600 3110 2

95.7 2600 3110 3

95.7 2600 3110 4

95.7 2600 3110 5

95.7 2605 3110 0.5

100 2633 2184 1.3

100 2633 2928 1.3

101 2650 2920 1.4

106 2680 1483 1.4

107 2690 1217 1.4

109 2710 1096 1.4

109 2710 1096 1.4

110 2920 1000 1.5

(b) Model summary and parameter estimates

Model Variables Variables Method

entered removed

1 Time, distance, flowa Enter

2 Time Stepwise (Criteria:Probability-of-F-to-enter ≤0.050,Probability-of-F-to-remove ≥0.100)

3 a Flow, distanceb Remove

4 Distance Forward (Criterion:Probability-of-F-to-enter ≤0.050)

5 Flow Forward (Criterion:Probability-of-F-to-enter ≤0.050)

piping and it must be considered as a hazard for pip-

ing (Rasht city water pipeline transmission line with

surge tank and in leakage condition). Comparison be-

tween three parts (Fig. 11) for cases (Flow-Time &

Head-Time & Head-Distance transient curve) proved

the surge tank had an effective role. The flow was de-

creased from 3014 (l/s) down to Min. value 2520 (l/s)

after 0.6 (s). So, in 0.4 (s), it had grown to 3228 (l/s).

This was the effect of the water release from the leak-

age location. Hence, in one second, 494 (l/s) water

flows have been interred and exited to the surge tank

(for transmission line with surge tank and in leakage


Table 5 Rasht cityregression model summaryand parameter estimates(water hammer condition)

aPredictors: (constant),time, distance, flowbPredictors: (constant),distance, flowcPredictor: (constant)dPredictors: (constant),distanceeDependent variable:pressure

Model Sum of squares df Mean square F Sig.

1 Regression 972.648 3 324.216 62.223 0.000a

Residual 93.791 18 5.211

Total 1066.439 21

2 Regression 959.744 2 479.872 85.455 0.000b

Residual 106.695 19 5.616

Total 1066.439 21

3 Regression 0.000 0 0.000 . .c

Residual 1066.439 21 50.783

Total 1066.439 21

4 Regression 889.663 1 889.663 100.655 0.000d

Residual 176.775 20 8.839

Total 1066.439 21

5 Regression 959.744 2 479.872 85.455 0.000b

Residual 106.695 19 5.616

Total 1066.439 21

Table 6 Rasht city regression model summary and parameterestimates

Model R R square Adjusted Std. error of

R square the estimate

1 0.955a 0.912 0.897 2.283

2 0.949b 0.900 0.889 2.370

3 0.000c 0.000 0.000 7.126

4 0.913d 0.834 0.826 2.973

5 0.949b 0.900 0.889 2.370

aPredictors: (constant), time, distance, flowbPredictors: (constant), distance, flowcPredictor: (constant)dPredictors: (constant), distance

condition). The surge pressure was 110 (m) nearbythe pump station (i.e. at the start of transmission line).The leakage happened near the location of the watertreatment plant. So, water flow was decreased from3000 (l/s) to 2500 (l/s). This was unaccounted for thewater “UFW” alarm.

This work found the location and rate of unac-counted for water “UFW” in the pipeline. Results haveshown the location and the rate of unaccounted forwater “UFW” in the pipeline (Fig. 11). Min. pressureline curve was under the transmission line profile, inthe near of 50,000 (m3) water reservoir. Hence, this

showed that there was minus pressure in that zone ofthe transmission line. So, it must be removed from thesystem. Max. Transient pressure line was completelyover the steady flow pressure line. Max. pressure in thesystem was 156.181 (m). This pressure is to high forold piping and it must be considered a hazard for thepiping system (Tables 8–10).

The most important points that were observed inlab. and field test results:

Influence of the rate of discharge from local leak tototal discharge in the pipeline. It has an effect on thevalues of the oscillation’s period and wave celerity.

Influence of the rate of discharge from the local leakon the maximal value of pressure

The reason for the high decease in water transmissionpressure was related to the leakage condition in thetransmission of the Rasht city waterline (local leak-age effect for a high decrease in water pressure atthe pipeline) [17]. This was done to explain repeatedpipe breaks. Water hammer has been analyzed in threemanners: (1) water leakage assumption for transmis-sion line, (2) no leakage assumption for transmissionline, (3) water leakage assumption for transmissionline which was equipped by a pressure vessel or a one-way surge tank (actual condition). Head-time tran-


Fig. 5 Analysis & comparison results for calculations of modeling results and field test results Rasht city water pipeline pilot research

Table 7 Regression modelsummary and parameterestimates excludedvariables (Rasht city waterhammer condition)

aPredictors in the model:(Constant), distance, flowbPredictor: (constant)cPredictors in the model:(Constant), distancedDependent variable:pressure

Model Beta In t Sig. Partial Co-linearity statistics

correlation tolerance

2 Time 0.117a 1.574 0.133 0.348 0.887

3 Time 0.122b 0.552 0.587 0.122 1.000

Flow 0.905b 9.517 0.000 0.905 1.000

Distance −0.913b −10.033 0.000 −0.913 1.000

4 Time 0.189c 2.274 0.035 0.463 0.995

Flow 0.469c 3.533 0.002 0.630 0.298

5 Time 0.117a 1.574 0.133 0.348 0.887

sient curve for transmission line without surge tankand in leakage condition showed 1.2 (s), head valuerises from 1.2 (m) to 146 (m), and down to 131 (m) at1.5 (s). In the end, the transient curve showed 135 (m)at 5 (s).

3.2 Comparison of present work results with otherexpert’s research

Comparison of the present work results (water ham-mer software modeling and SPSS modeling), with


Fig. 6 Flow (l/s) and time (s) records: (a) for total length of pipeline, (b) for leakage effects observation, at water hammer field testsof Rasht city water pipeline

other expert’s research results show similarity and ad-vantages: Apoloniusz Kodura and Katarzyna Weine-rowska, 2005: In the present work, water hammer hasbeen run in pressurized pipeline with the local leak.The experiments in Fig. 7a and numerical analysis re-sults in Tables 8, 9, 10, 11, 12 were presented. If the

pipeline with the local leak was considered, the waterhammer phenomenon was influenced by some addi-tional factors [18]. Detailed conclusions were drawnon the basis of experiments and calculations for thepipeline with a local leak. Hence, the most impor-tant effects that have been observed were as follows:


Fig. 7 Rasht city water pipeline (modeling results and field test results, comparison)

The influence of the ratio of discharge from the lo-cal leak has been restricted. Total discharge effect inthe pipeline on the values of period wave oscillationshas been investigated. The outflow to the overpres-sure reservoir from the leak affected the value of wavecelerity (Fig. 8b).

3.3 Experimental equipment comparison of presentwork results with other expert’s research

Experiments were carried out in the laboratory of theWarsaw University of Technology, Environmental En-gineering Faculty, Institute of Water Supply and WaterEngineering (Fig. 8b).

The physical model is schematically shownin Fig. 8b. The main element was the pipeline singlestraight pipe of the length L, extrinsic diameter D, andthe wall thickness e, or the pipeline consisted of sec-tions of varied parameters. The pipeline was equipped

with the valve at the end of the main pipe, which wasjoined with the closure time register. The water ham-mer pressure characteristics were measured by exten-someters, and recorded in the computer’s memory. Thesupply of the water to the system was realized with theuse of the reservoir which enabled inlet pressure sta-bilization.

The experiments were carried out for four cases:

• Simple positive water hammer for the straightpipeline of constant diameter; the measured char-acteristics were the basis for estimation of the influ-ence of the diameter change and local leak on waterhammer run.

• Positive water hammer in pipeline with singlechange of diameter: contraction and extension.

• Positive water hammer in pipeline with local leak intwo scenarios: with the outflow from the leak to theoverpressure reservoir and with free outflow from


Table 8 Field test model System (water pipeline of Rasht cityin northern Iran—Software hammer version 07.00.049.00)

Type Keyword Value

1 Title Untitled

2 Units for flow cms

3 Units for head m

4 Units for volume m3

5 Units for diameter mm

6 Units for length m

7 Units for mass kg

8 Time increment 0.0148

9 Number of time steps 339

10 Simulation time 5.003

11 Wave speed 1084

12 Vapour pressure −10

13 File name E:\k-Hariri Asli\daraye nashti.inp

14 Date of run 10/10/2008

15 Time of run 11:09.4

16 Number of nodes 27

17 Number of pipes 26

18 Licensee name HMI

19 Licensee address Waterbury, CT

20 EHG name Haestad Methods, Inc.

21 EHG address Waterbury, CT

22 Units for force N

23 Force reports No

24 Volume scale factor 1

25 Flow scale factor 1

26 Labels Short

27 Units for pressure mH

28 Specific gravity 1

29 Courant number Cr = 0.997

the leak (to atmospheric pressure, with the possibil-ity of sucking in air in a negative phase). This wasthe reason for the sucking air in the negative phase(Fig. 10a) for Rasht city water pipeline.

Local leakage rate effect on the maximal value ofpressure

The reason for the high pressure drop in water trans-mission was related to the leakage effect (local leak-age water pipeline). It was done to explain the effecton high pressure deceasing in repeated pipe breaks.This work led to improved standards for precessiondesigns and installation techniques in the field of sub-

Table 9 Field test model nodes (water pipeline of Rasht city innorthern Iran—Software hammer version 07.00.049.00)

Category and type Node Elevation (m) Branch pipes

Junction 2 or more J10 38.3 2

J11 38.6 2

J12 39.7 2

J13 41 2

J14 42.3 2

J16 43.4 2

J18 43 2

J19 42.3 2

J2 35.5 2

J21 42.5 2

J22 44.6 2

J23 69.9 2

J24 81.8 2

J27 36.5 2

J4 37.2 2

J6 36.3 2

J7 36.3 2

J8 36.1 2

Prot equip air valve J15 45.2 2

J17 45 2

J20 44.2 2

J26 37.2 2

J28 95.2 2

J9 38 2

Pump Shut J3 35.5 2

Reservoir 1 or more J1 40.6 1

N1 95.9 1

atmospheric transient pressures that can suck contam-inants into the water system.

The leakage has happened near the location of thewater treatment plant. So, water flow was decreasedfrom 3000 (l/s) to 2500 (l/s). In this case, the pipelinewas equipped with a sure tank. So, leakage happenedon point P3:J7 (P3:45.00%) at elevation 36.2 (m) andat a distance 140 (m) far from the water pump station(Fig. 11), Max. head at 155 (m) dropped to 135.1 (m).Vapor pressure was equal to −10.0 (m). Initial headand Min. head did not have any changes (Tables 1–6).

Air entrance approaches

Modeling of air influence on hydraulic similarity withtwo different types of air content models have been


Table 10 Field test model pipes (water pipeline of Rasht cityin northern Iran—Software hammer version 07.00.049.00)

Pipe Length Diameter Velocity Hazen–Williams

(m) (mm) (m/s) friction coef.

P3 311 1200 2.21 90

P4 1 1200 2.65 90

P5 0.5 1200 2.65 91

P6 108.7 1200 2.65 67

P7 21.5 1200 2.21 90

P8 15 1200 2.21 86

P9 340.7 1200 2.21 90

P10 207 1200 2.21 90

P11 339 1200 2.21 90

P12 328.6 1200 2.21 90

P13 47 1200 2.21 90

P14 590 1200 2.21 90

P15 49 1200 2.21 90

P16 224 1200 2.21 90

P17 18.4 1200 2.21 90

P18 14.6 1200 2.21 90

P19 12 1200 2.21 90

P20 499 1200 2.21 90

P21 243.4 1200 2.21 90

P22 156 1200 2.21 90

P23 22 1200 2.21 90

P24 82 1200 2.21 90

P25 35.6 1200 2.21 90

P0 0.5 1200 2.65 90

P1 0.5 1200 2.65 90

Note: Results showed at point P25:J28 of Rasht city waterpipeline air was interred to pipeline. Max. Vol. of air was198.483 (m3) and current flow was 2.666 (m3/s). Data table cre-ated by hammer—Version 07.00.049.00 compared to the equa-tion of regression software SPSS

proposed in the literature in predicting the transientpressure behavior: the concentrated vaporous cavitymodel (Brown, 1968; Provoost, 1976) [19] and the dis-crete air release model (Lee, 1991–1995; Wylie, 1993)[19]. The concentrated vaporous cavity model pro-duces satisfactory results in slow transients, but pro-duces unstable solutions for rapid transients, such asthe pump’s stoppage with reflux valve closure. Thediscrete air release model produces satisfactory re-sults in pump shut down cases, but is susceptible tolong term numerical damping (Ewing, 1980; Jonsson,1985) [19]. Typically, in the discrete air release model,

the wave speed distribution along with a pipeline (withnode points i = 0,1, . . . ,N) was given by Lee (1991)[19]. In this work, at first was a simulated transientpressure in the system due to an emergency power fail-ure without any protective equipment in service. Aftera careful examination of results, it was selected pro-tective equipment and the system was simulated againusing modeling to assess the effectiveness of the de-vices which selected to control transient pressures. Atpresent, work analysis and comparison were includedin first and second model results. It was shown thatat point P24:J28 of the water pipeline, air was in-terred to the system. Max. vol. of penetrated air wasequal to 198.483 (m3) and current flow was equalto 2.666 (m3/s). Treated or modeled air entrainmentproblems in real prototype systems and results wasshown in Tables 10, 11, 12, 13, 14.

Consistency between the observed values of max-imal pressure in the first amplitude and correspond-ing values were calculated according to Joukowski’sformula, irrespective of the rate of discharge from theleak.

Significant influence of the rate of the dischargefrom the leak on the vivid decrease of duration of thewater hammer phenomenon, which suggests the pos-sibility of utilization of this fact to the pipeline leaktightness assessment, especially that the duration timedecreased with the increase of the outflow from theleak. This was the strong reason for the high deceas-ing in duration time for Rasht city water pipeline.

Column separations due to the turned off pump forthe Rasht city water pipeline were carried out for twocases:

(a) With surge tank and local leakage condition as-sumption: In this case, air was sucked into thepipeline at a negative phase (Fig. 10a).

(b) Without surge tank and local leakage condition as-sumption: In this case, air was not sucked into thepipeline at a negative phase (Fig. 10b).

4 Conclusion

It is always a good idea to run research to check ex-treme transient pressures. It is necessary for the sys-tem with large changes in elevation and long pipelineswith large diameters (i.e., mass of water). Also, it isnecessary for the initial (e.g., steady-state) velocities


Table 11 Field test modelextreme pressures andheads (water pipeline ofRasht city in northernIran—Software hammerversion 07.00.049.00)

End Upsurge Max. pressure Min. pressure Max. head Min. head

point ratio (m) (m) (m) (m)

P2:J7 1.25 120.5 96.7 156.8 133

P3:J7 1.25 120.5 96.7 156.8 133

P3:J8 1.25 118.7 95.1 154.8 131.2

P4:J3 1.1 109.4 99.5 144.9 135

P4:J4 1.1 107.7 97.8 144.9 135

P5:J4 1.1 107.7 97.8 144.9 135

P5:J26 1.1 107.7 97.8 144.9 135

P6:J26 1.1 107.7 97.8 144.9 135

P6:J27 1.25 120.8 97 157.3 133.5

P7:J27 1.25 120.8 97 157.3 133.5

P7:J6 1.25 120.9 97 157.2 133.4

P8:J8 1.25 118.7 95.1 154.8 131.2

P8:J9 1.25 116.7 93.1 154.7 131.1

P9:J9 1.25 116.7 93.1 154.7 131.1

P9:J10 1.26 114.5 90.8 152.9 129.2

P10:J10 1.26 114.5 90.8 152.9 129.2

P10:J11 1.27 113.1 89.4 151.7 128

P11:J11 1.27 113.1 89.4 151.7 128

P11:J12 1.27 109.5 86.4 149.2 126

P12:J12 1.27 109.5 86.4 149.2 126

P12:J13 1.28 106.3 83.1 147.3 124.1

P13:J13 1.28 106.3 83.1 147.3 124.1

P13:J14 1.28 104.7 81.5 147 123.8

P14:J14 1.28 104.7 81.5 147 123.8

P14:J15 1.31 98.2 59.3 143.4 104.5

P15:J15 1.31 98.2 59.3 143.4 104.5

P15:J16 1.3 99.6 60.5 143 104

P16:J16 1.3 99.6 60.5 143 104

P16:J17 1.32 97.2 57.5 142.3 102.6

P17:J17 1.32 97.2 57.5 142.3 102.6

P17:J18 1.3 98.5 59.2 141.5 102.2

P18:J18 1.3 98.5 59.2 141.5 102.2

P18:J19 1.3 99.1 60.3 141.4 102.7

P19:J19 1.3 99.1 60.3 141.4 102.7

P19:J20 1.31 97.2 57.9 141.4 102.1

P20:J20 1.31 97.2 57.9 141.4 102.1

P20:J21 1.3 95.1 56.5 137.6 99

P21:J21 1.3 95.1 56.5 137.6 99

P21:J22 1.32 91.8 52.9 136.4 97.5

P22:J22 1.32 91.8 52.9 136.4 97.5

P22:J23 1.52 66 24.5 135.9 94.4

P23:J23 1.52 66 24.5 135.9 94.4

P23:J24 1.71 53.9 12.2 135.7 94

P24:J24 1.71 53.9 12.2 135.7 94


Table 11 (Continued)End Upsurge Max. pressure Min. pressure Max. head Min. head

point ratio (m) (m) (m) (m)

P24:J28 2.07 36.4 5 131.6 100.2

P25:J28 2.07 36.4 5 131.6 100.2

P25:N1 1 16.7 16.7 112.6 112.6

P0:J1 0 0 0 40.6 40.6

P0:J2 1.09 5.5 4.7 41 40.2

P1:J2 1.09 5.5 4.7 41 40.2

P1:J3 1.12 5.7 4.5 41.2 40

Table 12 Field test model pipes (water pipeline of Rasht city in northern Iran—Software hammer version 07.00.049.00)

Node Label Category Type Elev. X-cord. Y -cord. Branch Vapour Maximum Type of Code

ID pipes pressure volume volume

1 J2 Junction 2 or more 35.5 7.32 0 2 −10 0 Vapour 68

2 J4 Junction 2 or more 37.2 20.52 0.34 2 −10 0 Vapour 68

3 J1 Reservoir 1 or more 40.6 0 0.3 1 −10 0 Vapour 23

4 J3 Pump Shut 35.5 14.33 0.3 2 −10 0 Vapour 74







11 J18 Junction 2 or more 43 133.05 18.76 2 −10 0 Vapour 68






17 J26 Prot equip Air valve 37.2 25.22 0.16 2 −10 0 Air 76

18 J9 Prot equip Air valve 38 55.2 7.47 2 −10 0 Air 76



21 J17 Prot equip Air valve 45 123.39 15.06 2 −10 0 Air 76




25 N1 Reservoir 1 or more 95.9 219.75 28.79 1 −10 0 Vapour 23


27 J13 Junction 2 or more 41 85.73 17.14 2 −10 0 Vapour 68


Fig. 8 Scheme of the water hammer experimental equipment (a) Rasht city water hammer laboratory model, (b) water hammerlaboratory model with local leak (Kodura and Weinerowska)

in excess of 1 (m/s). In some cases, hydraulic tran-sient forces can result in cracks or breaks, even withlow steady-state velocities. In this work, positive wa-ter hammer in the pipeline was introduced with localleaks in two scenarios; first, with the outflow fromthe leak to the overpressure reservoir, and secondly,with free outflow from the leak (to atmospheric pres-sure, with the possibility of sucking air in the nega-tive phase). Consistency between observed values ofmaximal pressure in first amplitude and correspond-ing values were calculated according to the explicitmethod of characteristics. This was related to the rateof discharge from the leak. The discharge rate of theleakage point, reduced the time duration significantly.So, the duration time was decreased due to the in-crease of water outflow from the leak. The compar-ison showed similarity in results between this workdiscussion and other expert works. Field test results

showed in the leakage condition at a negative phasethat air was sucked into the Rasht city water pipeline(Fig. 10a). There was minus pressure in the zone of thenear 50,000 (m3) water reservoir. This volume of airmust be removed from the system; it was shown thatat 110 M surge pressure in the near to pump station(start of transmission line). The leakage has happenednear the location of the water treatment plant. So, wa-ter flow was decreased from 3,000 (l/s) to 2,500 (l/s).This was unaccounted for water “UFW” alarm. Thiswork found the location and rate of unaccounted forwater “UFW” in the pipeline. Results have shown lo-cation and the rate of unaccounted for water “UFW” inthe pipeline (Fig. 11). This was the main practical aimof the present work. In the final procedure, a conditionbase maintenance (CM) method has been found for allwater transmission systems.


Fig. 9 Laboratory modelpressure characteristic(observed and calculated)for present research andKodura and Weinerowskaresearch

Table 13 Model extremeheads for pipes (waterhammer condition)

Point Distance Elev. Init. head Max. head Min. head Vap. pr.

+P3:J7 0.0 36.3 132.8 156.8 105.1 0.000 −10.0

P3:5.00% 15.6 36.3 132.7 156.6 105.3 0.000 −10.0

P3:10.00% 31.1 36.3 132.6 156.3 105.1 0.000 −10.0

P3:15.00% 46.7 36.3 132.4 156.1 105.0 0.000 −10.0

P3:20.00% 62.2 36.3 132.3 155.8 104.9 0.000 −10.0

P3:25.00% 77.8 36.3 132.2 155.6 104.7 0.000 −10.0

P3:30.00% 93.3 36.2 132.1 155.5 104.4 0.000 −10.0

P3:35.00% 108.9 36.2 131.9 155.3 104.3 0.000 −10.0

P3:40.00% 124.4 36.2 131.8 155.2 104.2 0.000 −10.0

P3:45.00% 140.0 36.2 131.7 155.0 104.0 0.000 −10.0

P3:50.00% 155.5 36.2 131.6 135.1 103.8 0.000 −10.0

P3:55.00% 171.1 36.2 131.4 134.9 103.7 0.000 −10.0

P3:60.00% 186.6 36.2 131.3 134.7 103.5 0.000 −10.0

P3:65.00% 202.2 36.2 131.2 134.4 103.4 0.000 −10.0

P3:70.00% 217.7 36.2 131.1 134.6 102.9 0.000 −10.0

P3:75.00% 233.3 36.2 130.9 134.4 102.7 0.000 −10.0

P3:80.00% 248.8 36.1 130.8 134.0 102.7 0.000 −10.0

P3:85.00% 264.4 36.1 130.7 133.9 102.4 0.000 −10.0

P3:90.00% 279.9 36.1 130.6 133.6 102.3 0.000 −10.0

P3:95.00% 295.5 36.1 130.4 133.5 102.1 0.000 −10.0

+P3:J8


Fig. 10 Column separations due to the turned off pump—Rasht city water pipeline: (a) with surge tank—pipeline in leakage condi-tion—pipeline sucked air in the negative phase, (b) without surge tank—pipeline in no leakage condition

Table 14 Modeling of air influence on hydraulic similarity (water pipeline of Rasht city in northern Iran—Software hammer version07.00.049.00)

Node Label Category Type Elevation X-cord. Y -cord. Branch Vapour Max. Type of Code

ID pipes pressure volume volume

24 J28 Prot equip Air valve 95.2 211.71 35.02 2 −10 198.483 Air 76


Fig. 11 (a) location and rate of unaccounted for water “UFW”, (b) flow variation, (c) head variation related to “UFW” in Rasht citywater pipeline

The personal contribution of the corresponding au-thor:

All substantive provisions of the work are receivedby the authors personally. All parts of the experimentswere made by the authors of the manuscript.

Acknowledgements The authors thank Prof. Soltan Aliev,Prof. Mir Ahmad Lashteneshaee, Prof. Amir Hossien Mahvi,Dr. Alireza Pendashteh, Dr. Babak Noroozi, and all specialistsfor their valuable observations and advice, and to the referees forrecommendations that improved the quality of this paper. Thiswork was a part of the Ph.D. thesis of Kaveh Hariri Asli (corre-

sponding author) at contract No: 2, dated: 05/02/2007, with theNational Academy of Science of Azerbaijan “AMEA”, Instituteof Mathematics and Mechanics.

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