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HandMoveIrrigationSystemsSummaryThe‘handmove’irrigationsystemisaverysimplepipesetwhichcanbemovedbyhand.Twomainfactors——positioningandmovingschemeoftheequipmentbothaffecttheworktime.Herewedevelopamodeltocompletetheirrigationofthewholefieldbytheshortesttime.Firstly,wedecidethecertainnumberofsprinklersthroughthedesignatedparameter.Usingenumerativegeometry,wecomparetheirrigationareaofthesystemwithdifferentnumberofsprinklersandworkouttheoptimumnumberofsprinklers.Secondly,wetaketheadvantageofcombinatorialgeometrytodecidethepositioningandmovingschemeoftheirrigationsystem,inorderthatthemodelcanbeusedtorealizetheirrigationtaskbytheshortestworktime.Intheendwealsointroduceanewsprinklerwithsquareareaandcompareitsworkingefficiencywiththetraditionalsprinklerifweuseitonthisfield.1.IntroductionThereareawidevarietyoftechniquesavailableforirrigatingafield.Oneofthesystemsisthehandmoveirrigationsystemwhichisusedonsmallerranches.Lightweightaluminumpipeswithsprinklerheadsareputacrossfields,andtheyaremovedbyhandatperiodicintervalstoinsurethatthewholefieldreceivesanadequateamountofwater.Giventhatthistypeofirrigationsystemistobeused,howcanitbeconfiguredtominimizetheamountoftimerequiredtoirrigateafieldthatis80metersby30meters?Forthistaskwearegoingtofindanalgorithmtodeterminehowtoirrigatetherectangularfieldthatminimizestheamountoftimerequiredbyaranchertomaintaintheirrigationsystem.Onepipesetisusedinthefield.Wewilldeterminethenumberofsprinklersandthespacingbetweensprinklers,andwewillfindascheduletomovethepipes,includingwheretomovethem.Apipesetconsistsofanumberofpipesthatcanbeconnectedtogetherinastraightline.Eachpipehasa10cminnerdiameterwithrotatingspraynozzlesthathavea0.6cminnerdiameter.Whenputtogethertheresultingpipeis20meterslong.Atthewatersource,thepressureis420Kilo-Pascal,andhasaflowrateof150litersperminute.Nopartofthefieldshouldreceivemorethan0.75cmperhourofwater,andeachpartofthefieldshouldreceiveatleast2centimetersofwaterevery4days.Thetotalamountofwatershouldbeappliedasuniformlyaspossible.2.AnalysisoftheproblemOurobjectistodecidethenumberofsprinklersandthespacingbetweenthem.Andthenwehavetosetamovingschemetogetanoptimalmethodsothattheworktimeisshortestandthewholefieldcanbeirrigateduniformly.Thecombinationofirrigationsystemisacomplicatedproblem.Theirrigationcanbeaffectedbymanynaturalfactors.Ifwedon’tomitthesefactors,themodelmaybetoodifficulttobeappliedinpractice.What’smore,wehavetochooseonetypeofrotatingspraysprinkler.Aftersimplication,westarttoconstructourmodel.Firstly,wecananalyzethedataintheliteratureandsetsomelimitationsofflowrateandwaterpressureatthenozzles,whicharerelatedtothenumberandspacing.Therearealsolimitationstosprayintensityintheknowncondition.Throughtheabovelimitations,wecanworkoutthenumberofsprinklers.Thenthespacingandmovingmodecanbedecidedthroughcalculatingtheworktime.Worktimeincludeirrigationtimeandmovingtime.Irrigationtimeisrelatedtothesprayintensityandtheshapeofsprayareaafteroverlapped.Themovingtimeisrelatedtomovingmode.Ifwemakethemovingtimeshortest,theremustbeonlyonescheme.Wecandividethewholefieldtoseveralparts.Eachpartcanbecoveredbyonemovingunit.Thisunitisthesprayareaofirrigationsystem.Wetrytochoosedifferentspacingandmovingmodetocoverthesepartsasmuchaspossible.Iftheoverlappedareaisverysmall,thewholefieldcanbeirrigateduniformly.Iftheareaisverylarge,theseareascansupplementtoeachother.Wemayalsogetahighuniformityofirrigation.Afterdecidingthemodel,wehavetousesomeevaluationmethodtoanalysiswhetherourmodelisreasonable.Oneofthemostimportantindexesisuniformitycoefficient.Ofcourse,thisindexcanshowtherationalityofthemodel.Butifthiscoefficientsatisfiesthedemandofrealpractice,wecandrawaconclusionthatwecanuseourmodeltosolvetheproblem.3.Assumptions1.Takenoconsiderationtothereductionofthehydraulicpressure.2.Allnozzleshavethesameflowrate.3.Thewaterpumpcanbeputanywherearoundorinthefield.4.Eachpartoftheequipmentcanbecarriedbyonerancherandtheweightofeachpartdoesn’timpactonthewalkingpace.5.Neglecttheimpactofthewindtosprayirrigation.6.Thespraysprinklerrotatesalongthecirclesothesprayareaiscircular.7.Thesprayintensityatthesprayareaisconsistent.8.Thefieldislevelbasin.9.Therotatespeedofsprinklerisconsistent.4.SymbolsSymbolUnitDefinitionRmThesprayrangeQm3/hTheflowrateρscm/hThesprayintensitydmThediameterofthenozzlesn/Thenumberofthesprinklersμ/ThecoefficientofflowratethTheworktimeCU/UniformityCoefficientρd/Atomizationindex5.MathsModel5.1SinglesprinklerRotatingspraynozzlegenerallyhastwosprayingways:rotundityandsector.Hereweconsiderthemostusualway——rotundity,whichmeansthesprinkler’ssprayareaisarotundity.Andeachsprinklerhasonlyonenozzle.Underthiscondition,thesprayareaofeachsprinkleris:Astosinglesprinkler,itsflowrateisQs,sothesprayintensity(cm/h),i.e.precipitationdepthperhour,is:5-1-1Therelationshipbetweenflowrateandpressureofthesprinkleris:5-1-2Qsistheflowrateatonesprinkler.Histhewaterheightconvertedbywaterpressure.Therangeofthesprinklerisanimportantparameter.Itshouldbecalculatedinprocessofirrigationsystemdesign.Sofar,therearemanyexperiencefo