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Spririnknklelerr____irirririgagatitionon _ ___systsyst emem____analanalysisysis____usinusin gg____EPANEPAN ETET____2.02.0 By
By GilbGilberto E. erto E. UrroUrroz, March 2012z, March 2012 Spri
Sprinklenklers ars are re commcommonly used only used to to irriirrigate hougate house se yardyards, parks, or s, parks, or agriagricultcultural ural plotsplots. . TheThe netw
network mapped below ork mapped below reprrepresentesents a s a sprisprinklenkler irrigr irrigation ation systesystem m for for a a smalsmall l parkpark..
The
The pipepipes in s in this networthis network have the k have the follfollowinowingg length, diameters, a
length, diameters, and nd Hazen-WilliamsHazen-Williams coefficients:
coefficients:
All
All nodnodes are es are at at zerzero o eleelevatvationion,, whi
while the le the resreservervoir Roir R1 1 has has a a tottotalal head (water surface elevation) of head (water surface elevation) of 10 ft.
10 ft.
---Pi
Pipe pe L(L(ftft) ) D(D(inin)) ---P P1 1 1100000 0 44 P P2 2 33000 0 44 P P3 3 44000 0 22 P P4 4 44000 0 22 P P5 5 55000 0 44 P P6 6 44000 0 22 P P7 7 44000 0 22 --- ---P
Pipipe e LL(f(ft) t) DD(i(in)n) ---P P8 8 44000 0 22 P P9 9 44000 0 22 P P110 0 55000 0 44 P P111 1 44000 0 22 P P112 2 44000 0 22 P P113 3 55000 0 44 P P114 4 55000 0 44 ---The
The sprisprinklenkler heads located atr heads located at jun
junctictions ons J6, J6, J7, J7, J8, J8, J9, J9, J10J10, , J11J11,, J12
J12, , J13J13, , J14J14, , and and J16 J16 havhave e emiemittetterr coefficients
coefficients of of 0.04 0.04 cfs/(psi)^0.5,cfs/(psi)^0.5, exc
except fept for or thothose at se at J13 J13 and and J14J14,, whos
whose e emitemitter ter coefcoefficificients aents are re 0.050.05 cfs/(psi)^0.5
cfs/(psi)^0.5
Sprinkler h
Sprinkler heads are eads are represented represented byby junc
junctiontions, ss, some ome of of whicwhich h are are termterminalinal junc
junctiontions (e.s (e.g., J7, g., J7, J8, J8, J10, J12,J10, J12, J13
J13, J14, and , J14, and J15J15). ). The discThe discharharge, ge, Q,Q, prod
produced by uced by a a sprinsprinkler kler head is head is relarelatedted to
to the the localocal pressurel pressure, p, by:, p, by: The
The pumpump p curcurve is ve is defdefineined d by by the the folfollowlowinging curve: curve: ---Q(c Q(cfs) fs) hP(hP(ft)ft) ---0 0..000 0 117700 0 0..667 7 113355 1 1..000 0 110000 ---p p E E C C Q Q In
In enteentering dring data for ata for this networthis network, we select CFS (cubic feek, we select CFS (cubic feet t per per secosecond) as nd) as the the defadefaultult unit of
unit of discdischargharge, e, and and H-W H-W (Haz(Hazen-Wien-Williamlliams)s) as the as the fricfriction ltion loss equatiooss equation to use. n to use. TheThe emit
emitter coeffiter coefficiencients ats are re enteentered in red in the the node node proppropertierties ies in n the the propproper units, i.eer units, i.e., ., inin this
this casecase, , in in CFS/CFS/(ft)(ft)^0.5^0.5.. Irri
Irrigatigation syston systems ems are are typictypically operaally operated under ted under steasteady-sdy-state cotate conditnditions for ions for a a givengiven peri
period of od of timetime. . ThusThus, for , for the the prespresent case a ent case a steasteady-stdy-state ate solusolution sution sufficffices.es. The
The figufigure below shows the re below shows the hydrhydraulic aulic gradgrade e line line elevelevatioations ans at t nodenodes s and and flow dischargflow dischargeses in
in the the pipepipes for s for the the steasteady statdy state solutioe solution.n.
1/5 1/5
Notice that the suction side of the pump, J1, shows a negative pressure, as expected, whereas the discharge side, J2, shows a positive pressure. Since all elevations are set at the same level (zero), the pressure difference across the pump is related to the pump head as follows:
γ p J1 p J2 hP
where γ is the specific weight of water. Taking γ 62.4 lbf/ft^3, the pump head, in this case, is:
3 ft lbf 62.4 psi 24.4483 psi 27.09
hP , i.e., hP 118.9345ft , while the
pump supplies a total of 0.83 cfs to the irrigation system network. The pressures at the sprinklers vary from 1.25 psi (J10, J12) to 9.08 psi (J7,J8).
The following figure shows the node demands, which, in this case, basically represent the sprinkler discharges. The figure also shows the discharge directions in the pipes.
In most cases, sprinkler irrigation system discharges are given in GPM (gallons per minute) rather than in CFS (cubic feet per second). For practice, you should repeat this exercise using GPS for the default discharge units. The network properties are basically the same except for the emitter coefficient values which should be given in gpm/(psi)^0.5. Thus, the values to use are:
s 3 ft cfs min gal gpm 2 1 psi gpm 17.9532 2 1 psi cfs 0.04 2 1 psi gpm 22.4416 2 1 psi cfs 0.05
Also, the pump curve needs to have the discharges, Q, converted from CFS to GPM:
gpm
300.7169
cfs
0.67 1.00cfs 448.8311gpm
Thus, the resulting pump curve is:
---Q(gpm) hP(ft) ---0.0 170 300.7 135 448.8 100 ---Booster__pump
Since all the sprinklers are set at a zero elevation and the source reservoir, R1, is at a higher elevation, theoretically a pump is not needed to supply water to the system. However, in this case, an elevation of 10 ft will produce much smaller pressures at the sprinkler heads if the pump were not present. The following figure shows the pressures and flows for the case in which the pump is removed:
The pump, in this case, is referred to as a booster pump because it "boosts" the discharge delivered to the system.
Calculating__prinkler's __emitter__coefficient
Manufacturers provide data detailing the discharge characteristics of sprinkler heads.
For example, the figure below shows performance data for different nozzle sizes fora particu model.
The emitter coefficient can be calculated from the discharge and pressure data listed in the table above. For example, for the 1/8" nozzle size, the p and Q data ar
50 45 40 35 30 25 p 3.20 3.03 2.86 2.68 2.48 2.26 Q
The following code calculates the emitter coefficients:
for k p k Q k C E .. n 1 k length p n 0.4525 0.4517 0.4522 0.453 0.4528 0.452 C E (psi) (gpm) ps gpm
An average value for the emitter coefficient for this case is
n = n 1 k k C E C E_ave psi gpm psi cfs 0.001 psi gpm 0.4524 => C 0.4524 E_ave or
NOTE:_ _ _Modeling _ _ _free-discharging _ _pipelines _ _in _ _EPANET
The solution for Q found using SMath Studio was Q = 1.38 cfs. To solve such a system in EPANET, point (2) should be represented as a node with a very large emitter
coefficient. Since the pressure at that point should be zero (or very close to zero in the EPANET solution), then a very large emitter coefficient will ensure that the demand at that node has a reasonable value. In addition, to account for the velocity head at the free-discharging node (2), a loss coefficient of 1.0 must be included in the pipe connecting reservoir (1) with outlet (2). In the problem statement it is indicated that minor losses (in this case, reservoir entrance losses only) are to be ignored. However, the loss coefficient of 1.0 is necessary for a complete solutio In setting up the EPANET model we created the following map (here showing the pressures and the flow discharge after running the mode
We use a total head of 60 ft for R1, and an elevation of 55 ft for J1. Pipe P1 has a length of 100 ft, a diameter of 6 inches, a Hazen-Williams coefficient of 110, and a
(minor) loss coefficient of 1.0. Node J1 uses a emitter coefficient of 1000 cfs/psi^0.5. After running the program you get a warning that negative pressures were detected in the system. Ignore this message and check the final result, Q = 1.39 cfs, very close to the value found using SMath Studio (Q = 1.385 cf
