The authors compared the formulation and computational performance of two numerical methods for modeling hydraulic transients in water distribution systems. One method is Eulerian-based, and the other is Lagrangian-based. The Eulerian approach explicitly solves the hyperbolic partial differential equations of continuity and momentum and updates the hydraulicstate of the system in fixed grid points as time is advanced in uniform increments. The Lagrangian approach tracks the movement and transformation of pressure waves and updates the hydraulic state of the system at fixed or variable time intervals at times when a change actually occurs. Each method was encoded into an existing hydraulic simulation model that gave initial pressure and flow distributionand was tested on networks of varying size and complexity under equal accuracy tolerance. Results indicated that the accuracy ofthe methods was comparable, butthatthe Lagrangian method was more computationally efficient for analysis of large water distribution systems.
Numerical methods for modeling transient flow
in distribution systems
BY DON J. WOOD. SRINIVASA LlNGIREDDY, PAUL F. BOULOS.BRYAN W KARNEY. AND DAVID L. MCF'HI::RSON
ompurcr models for simularing rhe hydraulic and water qualitv hehav101' of water di~trihution S\stellls havc heen availahlc for many years. Rccenth these lllodc!" ha\l: hccn extended to analyze hniraulic tran"iCllt, as \\'ell. In thc p~l';t, most transient analvscs were pcrformed onlv on large translllission mains u,ing highly skcletonized modcls forengincering design; propriet,HY transicnt computer prograllls \VelT largely Iilllired to "pecialist conslllting companies, research organizatiotls, and univcrsitics. In ,1ddition to improvcd design and opcration ()f \Varer distrihlltion sysrellls, a driving force behitld the tremi toward increased analysis of hvdralllic tratl,icnts has heen rhe gro\\'ing ,l\varctless th,n hydralllic transicnts canClTate lltleXpecred opportutlitics for pathogens prescnt in the externai environlllcnt to intrllde into the distrihlltiotl system with disastrous consequcnces to puhlic hcalth. Modem managelllCtlt of water distrihutiotl S\stellls reqllircs sillllllation Illodels that are ahlc to accurately predict tr,1l1siCllt flow and preSSllre variatiotls wirhin the distriblltion s\·;,tem etlVirOtllllent.PRESSURE TRANSIENTS
Effect O" water quality. It is \\cll-recognized that pressllrc transients Illa) adversel\ affccr the l]llality of treated water. Pressure transients in water distrihlltion s\ stems reslllt from ,1n ahrllpt chatlge in the flow \'Clocit)" and G1n he callsed Iw main breab, sudden changcs in denlalld, llllcolltrolled pump startillg
JULY 2005 I JOURNAL AWWA· 977
WOOD ET AL
or stopping, fire hydrant opening and c!osing, power failure, air-valve sbm, FIGURE 1 Pipeline and data for comparison of MDC, WCM, and flushing operations, fccd-t~11lk drainexact solution ing, overhead storagc tank loss, pipe filling and draining, and other conditions (Karim et ai, 2(03). Thesc e\ents can gcncrate high intensitics of f1uid shear and ma)' causercsuspeJ1sioJ1 of scttlcd particles as \I/ell as biofilm detachmeJ1t. So-called rcd water cvents have often becn associated with tranori/ice ......... sient disturbanccs. Morcover, a low-prcssurc transicnt event-arising from a power failure or pipc hreak, for cxample-has the Valve Data potential to cause contalllinatcd groundwatcr to illtrude into a pipc at a Icakv joint or brcak. Dcpcnd11lg Hex-hydraulicgrade at pipe exit, Ho-hydraulic grade outside the orifice, H R reservoir hydraulic grade, MOC-method of characteristics, qo-initial flow rate through the on thc sizc of thc Icaks, the volumc of pipeline, WCM-wave characteristic method intrusion can range from a fcw galCase 1 (no orifice): H R = Ho = 45 ft (13.7 m), Hex = O; case 2 (orifice): H R = 135 ft (41.2 lons to hundrcds of ga\lons (Funk...