EngineeringQuarterly
WhatbroughtyoutoMary?
Welcometothewinter issueofEngineering Quarterly,anewsletter publishedfourtimesa yearbytheUniversity ofMaryHammSchool ofEngineering.Init wetrytoincludearticlesfromeachofthesix engineeringmajorsthatwecurrentlyoffer: ElectricalEngineering,MechanicalEngineering,CivilEngineering,ComputerScience, ConstructionEngineering,andConstruction Management.
TheintendedaudienceoftheEngineeringQuarterlyareengineers,engineeringstudents,engineeringalumni,futureengineering students,andpeopleworkinginfieldsclosely relatedtoengineeringsuchasscience,computing,andmathematics.
Inthisissueweincludearticlesondesign projectsourstudentsareworkingon,trips theyhavegoneon,ourannualengineering alumnievent,serviceactivities,spectacular careersourgraduatesareembarkingon,and interestingassignmentsfromourcourses.Enjoy!
Dr.TerryPilling DeanofEngineering
I’vealwaysbeendrawntoMary,evenbefore Ibecameastudentin2010.Thereisasense ofpeaceandcalmthatyoufeeluponentering thecampus.Ihavewantedtoworkheresince thefirsttimeIcametoBismarckonHighway 1804andsawthebelltowerontopofthe hill.Notlongaftermyhusbandpassedaway inMarchof2022Isawtheadvertisement fortheAdministrativeAssistantpositionon thewebsite.Iwasintriguedbutdidn’tapply atthetimebecauseitwastoosoonafterhis death.AcoupleofmonthslaterIwentback tothewebsiteandtheadwasstillthere.Ifelt asthoughGodwastellingmesomethingsoI wentaheadandapplied.Astheysay,therest ishistory.
Whatdoyouliketodoinyoursparetime?
WhenI’mnotplayingfetchwithoneofmy dogs,whichshewoulddo24/7ifallowed, Iliketoread.EventuallyIdohopetojoina bowlingleaguebutIneedtopurchasemyown ball,shoesandbagsoI’mnotusingthehouse equipment.Ialsovolunteeratmychurch.
Doyouhavehobbies,interests,pets,etc?
Ihavethreedogs,atwelveyearBorderCollie/BlueHealerandtechnicallytwomutts, oneis3andtheotheris4.Bothofthem areBorderCollie/BlueHealer,Maltese/PoodleandAustralianShepherd.Thethreeyear oldmightalsohaveRedHealerinher.
Idooccasionallymakejewelrybutmostly Imakerosaries,prayerbeadsanddream catchers.IusedtocrochetandknitandI hopetostartthatbackupagainonceIgetinto amoreconsistentroutine.
Whatdoyouthinkofworkingheresofar?
AwardsBanquet.Theawardrecognizesa WelcomeWeekPeerLeaderwhoexcelledin theirposition.Theywarmlywelcomedall thosewhotheymetoncampus;workedwell withstudentsandfellowPeerLeaders;generatedenthusiasmandexcitementforWelcome Weekevents;andwentaboveandbeyond toservetheirfellowstudents.Therecipient ofthisawardisanexampletoallotherPeer LeadersandwasarolemodelfortheUniversity’sMissionandBenedictineValues.
TheWelcomeWeekPeerLeaderprogram isavolunteergroup.ThiswasDavid’sthird yearvolunteeringforthePeerLeaderprogram,andoverthosethreeyearshehasvolunteer134hours.Healsosteppedforwardthis pastyearandappliedforaPeerTeamLeader position,whichassistsintheplanning,development,andrunningoftheWelcomeWeek PeerLeaderprogram.
Ithinkthisawardiswelldeserved,and thatDavidisanamazingrepresentativeofthe HammSchoolofEngineering.
LOCKHEED-MARTINHIRES ELECTRICAL ENGINEERING SENIOR ByTERRYPILLING
Ourseniorelectricalengineeringstudent
PatriciaSmithjoinedtheHammSchoolof EngineeringthissemesterasournewadministrativeassistantandAdjunctProfessor.
Iloveworkinghere.Everyoneisreallynice andtheydon’tseemeasjustan“Admin. Asst.”butasanequal.Workinghereisgiving metheopportunitytodosomethingthatI’ve wantedtodomostofmylife,teach.
Ihavealwaysbelievedthateverything, boththegoodandthebad,happensforareason,thatGodhasaplanforallofusifwe trustinHimandletHimguideus,evenifit’s notwhatwethoughtitwouldbe.Thispast yearhasreinforcedthis.
TrishhasaBachelorsdegreeinAccounting, anMBAinAccounting,andhasservedas theDirectorofTaxEqualizationinMcIntosh County(2018-2022).Trishhasalsobeena CertifiedNursingAssistantfortheAshley MedicalCenterinAshley,ND.Trishworks morningswithusinEngineeringandafternoonsintheScienceandMathDepartmentin theHaroldMillerCenter.Trishwillalsobe teachingavarietyofcoursesfortheUniversityofMarybeginninginFall2023.
Oneofourseniormechanicalengineering students,DavidRuiz, wasvotedthe2022OutstandingPeerLeader. Thewinnerofthis awardischosenbytheir fellowPeerLeadersand Davidwillreceivehis awardattheSpring
MargaretKuhar acceptedapositionwithLockheedMartinin NewJerseythis semesterstartinginMay2023.MaggiecametotheUniversityofMaryfromPhiladelphiatostudy ElectricalEngineeringattheHammSchool ofEngineeringwithaminorinComputerScience.Sincearrivingshehasbeenactivein peertutoring,designprojectssuchasbuilding thecontrolssystemsforaninvertedpendulum,andshehasspentsixsemestersonthe Dean’sHonorsList.MaggiealsotookadvantageofourStudyinRomeprogramandspent asemesterattheUniversityofMary’sRome campus.Inthesummerof2022,Maggiewas aninternat RelayandPowerSystems inPennsylvaniawheresheworkedonPythondata analysis,MachineLearning,andpublicoutreach.Maggiehasalwaysbeenafriendlyand outgoingstudenthereattheHammSchool ofEngineeringandweareveryproudofher manyaccomplishments.
ThepositionatLockheedMartinseems almostdesignedforourstudentsattheHamm SchoolofEngineeringinthattheskillsand educationalexperiencethattheyarelooking forareonesthatweemphasizehere.Remarkably,thesearealsoskillsthatare not usually providedatotherschoolsinthecountry.This givesourgraduatesanadvantageoverschools andputsourstudentsatthetopofthepile
whenapplyingatthesecompanies.Thefollowingisasummaryofthejobdescription Maggiehasaccepted:
• Abletoworkindependentlyorasa memberofateam.
• Strongleadership,administrative,and interpersonalskills.Strongwrittenand verbalcommunicationskills.
• ExperienceinworkingintheAgileenvironment
ThefacultyoftheUMaryEngineeringSchool arealwaysthrilledtohaveourgraduatesreturntocampusandtellusaboutallofthecool thingstheyhavebeenuptoandletusshow themournewdevelopmentsandthedesign projectsofourcurrentstudents.
AtLockheedMartinRotaryandMissionSystems,wearedrivenbyinnovationandintegrity.Webelievethatbyapplyingthehigheststandardsofbusinessethicsandvisionary thinking,everythingiswithinourreach–and yoursasaLockheedMartinemployee.LockheedMartinvaluesyourskills,trainingand education.Comeandexperienceyourfuture!
BasicQualifications
BSinElectricalEngineering,Computer Science/Engineering,Physicsorequivalent experience.
• Demonstratedpotentialtoworkina teamenvironmentononeormoreofthe followingareas:analysis,requirements development,design,modeling,simulation,integration,test.
• Familiaritywithcomputerarchitectures andalgorithmdevelopmentforarange ofsystem/subsystemapplications.
• ExperiencewiththeCprogramming language,algorithmandsoftwaredevelopmentisdesired.
• Performsrequirementsdevelopment, verificationandvalidation,costand risk,supportabilityandeffectiveness analysesfortotalsystems.
• AbilitytoobtainaSecretsecurityclearanceisrequired.
• Strongcommunicationsskills(written andverbal),strongteamleadership,administrativeandinterpersonalskillsdesired.
ExperienceWith
• Real-timedeterminismofRedHawk Linux
• SELinuxforRHEL6;Administration ofOpenStackCloudPlatform
• SoftwareintegrationinLinux
• Newtechnologyinvestigation
• GitandSubversion
• ShellScripting
• LinuxAdministration(multipledistributions)
• Abletoobtainandmaintainasecurity clearance.
DesiredSkills
ProficientintheuseofLinux,UnixOperatingSystemsandBash,C/C++programming languages.
JoinusatLockheedMartin,whereyour missionisours.Ourcustomerstacklethe hardestmissions.Thosethatdemandextraordinaryamountsofcourage,resilienceandprecision.They’redangerous.Critical.Sometimestheyevenprovideanopportunityto changetheworldandsavelives.Thoseare themissionswecareabout.
Weareplanningtoaddaspringsemester alumnieventeveryyeargoingforwardwhere weinviteourcurrentgraduates.Ourhope istohelpthemmakenewcontactsandbegincollaborationswithourformergraduates andgivethemaleg-upontheircareers.Itis alwaysfuntohangoutwithourgraduates–bothcurrentandformer.
OnFriday,November12th,anumberofour MechanicalandElectricalEngineeringstudentstraveledtoWatfordCity,ND.toattendanengineeringconferenceandmeeting withthecommunity.Watfordcityisarapidly growing,familyoriented,communityinwesternNorthDakotawithbrandnewfacilities andmanygreatcareeropportunitiesforengineers.
ALUMNI EVENT
OnNovember18,2022weheldourannual alumnieventoncampus.Thisyearwegave ourformerstudentsatourofthecompleted KelcyWarrenDepartmentofCivilEngineeringandallthelabsandnewequipment.
OnWednesday,October19th,University ofMaryobserved“DayofService,”canceling classesandencouragingstudentsandfaculty togivebacktothecommunity.Inthepast, theengineeringschoolhasbeeninvolvedwith creatinggagaballpits.Thisyear,however, Dr.CarricoandIgotonabuswithover40 studentandfacultyfromtheSchoolofEducationtotraveltotheStandingRockreservation.
AnhoursouthofMandan,theStandingRock reservationhasamissionschoolinFortYates. Togetherwithstudentsintheeducationprogram,theengineeringprofessorsunloaded theirboxesofmaterialandheadedinsideto meetthestudents.Thegoaloftheday?Well, thereweretwoactivitiesplanned.Forthe4th through8thgraders,itwasdroppinganegg fromthetopofstairsandengineeringsolutionstomakesuretheydidn’tbreak.Forthe Kthrough3rdgraders,itwasallaboutmaking paperairplanes.
Dr.Carricodesignedboxesofmaterials fortheolderstudents,givingthemacardboardboxwithsomematerials,includinga foamcup,asmallsquareofStyrofoam,aballoon,string,andafewotheritems.Thestudentsweretaskedwithfirstidentifyingmaterialsthatmayprotecttheiregg,thento sharetheirideastotheothermembersoftheir groups.Givenonly15minutesthestudents devisedmanywaystoprotecttheeggand allfourteamsweresuccessfulthefirsttime around!
dayended,allthestudentslinedupthrewtheir planesallatonce.
OnethingIlearnedfrompasteventsisthat children,especiallyyoungerones,willnotrememberthewholeactivityortheexactsciencebehindit,buttheywillrememberthe peopleandthefuntheyhad.So,theultimate goalofthedaywastohavesomefunandleave thestudentswithastorytotelltheirfamilies andhopefullyanewmemoryassociatedtothe word“engineer.”
CHRISTMAS TOY ADAPT-A-THON ByJERIKACLEVELAND
TheHammSchoolofEngineeringstarted theirfirstyearoftheToyAdapt-a-thon.A weekofmodifyingtoysforchildrenwithmotordisabilitiestouseaccessibilitybuttonsrunningfromDecember1to8th.Childrenlearn throughplaying,sohavingmanytoysfora childtochoosefromisimportant.
Thiswasnotourplan.Manystudents whodothisactivitywillfailthefirsttime andyetthepowerofacardboardboxwasthe mainthemeofthefirstround.MaybeAmazonshouldfollowtheirexampleforhowthey packedtheboxes,butIdigress.Westillhad another20minuteswiththestudents.Well, thinkingonourfeet,Dr.Carricosaidthe seconddesigncouldnothavethecardboard boxes,andwithgroansthestudentsobliged butwerenottoohappy.Afteranother15minutesanewwaveofideasformedanddropped withonlyoneoutofthefourgroupsfailingby onlyahairlineofafracture.Theideathestudentsdecidedwasallaboutreducingspeed: parachutes.Someusedbags,someusedballoons,thebestteamusedabagwithaballooninside:whichmadesuretheparachute waskeptopen.
However,familiesofchildrenwithmotor disabilitiesoftenhavetoconsiderthattheaccessibilitybuttonsarebetween$50-$200.On topofthat,thecostfortoysthatworkwith thesebuttons,canmakearegular$15atTargetincreaseto$115,theyalsomustbebought online,andoftendonotincludefavoritecharactersfromnewmovies.Thegoodnewsis studentvolunteerscantakealmostanybattery poweredtoyandadaptittoworkwiththeaccessibilitybuttonforroughly$3atoy.The $3iscoveredthroughdonations,makingthis afreeserviceforchildrenandtheirfamilies andschools.
TohelpfamiliesinBismarck/Mandanand surroundingcommunitiesweareofferingto adapttoysforfreeforfamiliesandschools. Wecanevenrepairtoysthatwerealready beenadapted.Weevenhavebrandnew,donatedtoysthatwearegivingawaytochildren andtheirfamiliesforfree!
Thestudentspresentedtheirprototypedesignsatapostersessionheldattheendofthe semester.
Nextwastheyoungercrowd,makingpaperairplanes!Imaybeshouldhavethought thatthroughalittlebitbetter,butIhavenot heardofstudentsusingthisnewknowledge formischief.Amajorhurdleforthepaperairplaneswasthatnoneofthestudents knewhowtomakeoneontheirown!Luckily,wehadmorevolunteersthanstudentsand wereabletohelpstudentsmakethepaperairplanes.Oncedone,wetraveleddownstairs tothelunchareaandthestudentstookturns throwingtheplanesandmeasuringhowfar theywent.Sincemakingtheairplanestook moretimethanplanned,thelessonhadtobe shortened.Thestudentswereinstructedto placetwopaperclipsontheirplanesandsee howthatchangedtheirdistance.Astheschool
MECHANICAL ENGINEERING DESIGN
Thisyearnineseniormechanicalengineeringstudentsdividedintotwogroupsfocusingonthedesignoftwotrackedvehicles foruseinthesnow.Thevehicleswereconceivedofanddesignedentirelybythestudents.
ThegroupledbyBenNiemuth,Brett Thompson,DavidRuiz,andElizabethHersheydesignedasnowbike.
CivilEngineeringstudentsinECI351and ConstructionManagementstudentsinCMT 321workedtogethertodesignandconstruct woodentrussbridgesthathadtomeetcertain deflectioncriteria.Studentsweretaskedtodesign,build,andtestatrussbridgethatspana 10footgaponlyusing 2 × 2’sand 1/2inplywood.
Theyhadtodesignthebridgetonotdeflect morethanL/400(0.3in.)andL/800(0.15in.) whenloadedwiththreeteammembersand justtheprofessor,respectively.Studentsperformedanalysisofmaterialstrengths,influencelines,deflectionsusingenergymethods,andmodelingusingRISAtodothedesignwork.Studentssuccessfullyconstructed bridgestosatisfyprojectrequirements.
timethissemester.Eachofourdegreeprogramshasrequiredtechnicalelectives.These arecourseswhichareofferedperiodicallyon arotationandaresubjectswhicharethearea ofresearchinterestandexpertiseforoneof ourfacultymembers.Hereisthecoursedescription:
FundamentalsofAntennasandCommunicationElectronicswilluseahands-onapproach tolearnaboutandcreatecommunicationcircuitswhilelearningaboutthetheoryandapplication.Additionally,thefundamentalsof antennas,EMI/EMC,radiationpatterns,directivity,andgainwillallowstudentstounderstandandcreatesimulationstovalidate basicPCBantennadesign.
R
ProfessorAnthonyWaldenmaier’sCurlingteam: AlfredoAnthonyandtheMeatballs wonthe2022RoughriderBonspielonDecember11th,2022thisyearattheCapital CurlingClubinBismarck.
tips.Thiscanbeunderstoodinthecontextof tensilestress(forceperunitarea)andultimate strength.Theultimatestrengthofamaterial isthemaximumvalueoftensilestressthata materialcanwithstand.
Anidealizedmodelofaniciclepresumes itshomogeneity(constantdensity ρ0)and ascribestoitaregularconicalgeometry(circularcross-sectioninplanesperpendicularto itsaxisofsymmetry,andopen-half-angle θ).
(a) Theicelyingbelowtheimaginarysurface atdistance x fromthetipisheldinplace bythetensileforceexertedthroughthe surface,whichcancelsitsweight.
(i) Computethevolumeoficelying withindistance x fromthetip.
(ii) Determinetheweightofthisice (W = ρ0 × Volume × g).
(b) Theforcecountertotheweightdeterminedin(a)isdistributedacrossthe cross-sectionalfaceoftheicicle(ata distance x fromthetip).Computethe tensilestressandverifythatitisproportionalto x
Sincethetensilestressincreaseswithdistancefromthetip,sotoodoesthelikelihood ofreachingorexceedingtheultimatetensile strengthoftheice.
SECRET SANTA ByTOMVOLKMANOnDecember9,electricalengineeringseniors heldapostersessionshowcasingtheirfirst semesterdesignprojectsintheSeniorDesign CenteroftheHammSchoolofEngineering. MaggieKuharandDerekFauldevelopeda deviceintendedtohelpincreasetheindependenceandsafetyofblindindividuals.The deviceiscapableofnavigatingagivenpath whileavoidingobstaclesandusesanarrayof ultrasonicsensorsinadditiontoalidarsensortodetectobstaclesandusessteppermotor positionstotrackpathing.
PROBLEMSTOTRY
Herearesomeproblemsfromourcoursesthis semesterthatyoumightliketotry.Thesolutionscanbefoundattheendofthisissue.
Pythonisanobject-oriented,easy-tounderstandinterpretedprogramminglanguagethatcanbeusedtowritequickprogrammingapplications.It’sanidealcoding languageforthosewhowanttowritedorapid developmentwithouthavingtohaveadeep understandingofadvancedprogrammingconcepts.Pythoniswidelypopularduetomany reasons:
• ItisEasytoUse:Itisrelativelyeasy tolearn,makingitagoodfirststepin learninghowtoprogram.
• IthasSimpleSyntax:Itiseasytoread andunderstand,sinceitreadslikeEnglish.
• IthasaThrivingCommunity:Sinceit isanopen-sourcelanguage,anyonecan usePythontocode.
• IthasVersatility:Itcanbeusedfor manydifferentuses;datamanipulation,artificialintelligence,webdevelopment,gamedevelopment,andmore.
Question: WriteapythonapplicationtocreateaSecretSantalist,whichcanbeadapted toanynumberofgivers/receivers.
ENR304:VOLTAGE DIVIDER SIX SIGMA
FundamentalsofAntennasandCommunicationElectronicsisbeingofferedasaElectricalEngineeringtechnicalelectiveforthefirst
Theiciclesthat arefoundonthe eavesofhouses inthewintertime, aswellasthestalactitesfoundin subterraneancaverns,tendtofracturenearertotheir basesthantotheir
Writeasimulationofavoltagedividercircuitwheretheresistorsaregivenresistorvalueswithinof1%,5%,and10%tolerances. Thesimulationshouldrunaspecifiednumber oftimeswiththeresistorvaluesrandomized withinthetolerancerangesandthevoltagedivideroutputplacedintoahistogram.Writea gnuplotscripttoshowtheresultinghistogram.
TheMandelbrotsethasitsoriginincomplexdynamics,afieldfirstinvestigatedbythe FrenchmathematiciansPierreFatouandGastonJuliaatthebeginningofthe20thcentury. Inthe1980’s,BenoitMandelbrotworkedat IBM’sThomasJ.WatsonResearchCenterin YorktownHeights,NewYork.
oneiterationitisacertainscaleofgray,aftertwoiterationsadarkershadeofgray,etc. Hereisanimplementationofthisalgorithm, writteninC,whichcreatesaPortablePixel Map(PPM)imageandthenuses imagemagick toconvertittoaPortableNetworkGraphics (PNG)filethatcanbeviewedwithanimage viewer.
mandelbrot.c
#include <stdio.h> #include <stdlib.h> #define DIVERGE2.0
int usage( char * ); int main( int argc, char ** argv){ if (argc!=8) return usage(argv[0]);
double xmin=atof(argv[1]);
double xmax=atof(argv[2]); double ymin=atof(argv[3]); double ymax=atof(argv[4]); int num_iterations=atoi(argv[5]); int width=atoi(argv[6]);
FILE * fp=fopen(argv[7],"wb"); double dx=(xmax−xmin)/width; int height=(ymax−ymin)/dx; int i,j,k;
double x,y,u,v,U,V; fprintf(fp,"P6\n#Mandelbrot,"); fprintf(fp,"xmin=%lf,xmax=%lf,",xmin,xmax); fprintf(fp,"ymin=%lf,ymax=%lf",ymin,ymax); fprintf(fp,"num_iterations=%d\n",num_iterations); fprintf(fp,"%d\n%d\n",width,height); fprintf(fp,"%d\n",(num_iterations<256?255: num_iterations)); for (j=0;j<height;j++){
BecauseofhisaccesstoIBM’scomputers, Mandelbrotwasabletousecomputergraphicstocreateanddisplayfractalgeometricimages,leadingtohisdiscoveryoftheMandelbrotsetin1980.Heshowedhowvisual complexitycanbecreatedfromsimplerules. TheMandelbrotsetappearedonthecoverof ScientificAmerican inAugust1985andbecameprominentinthemid-1980sasacomputergraphicsdemoonpersonalcomputers.
}
Acomplexnumber c isamemberoftheMandelbrotsetif,whenstartingwith z0 =0 and repeatedlyapplyingtheiteration: zn+1 = z2 n + c,theabsolutevalueof zn remainsbounded.
Forexample,for c =1,thesequenceis 0, 1, 2, 5, 26,... whichtendstoinfinity → so 1isnotanelementoftheMandelbrotset.On theotherhand,for c = 1,thesequence is 0, 1, 0, 1, 0,... whichisbounded → so
1 doesbelongtotheset.
Wecanvisualizethisonacomputerby takingeverypixelofthescreenandthinkingofthe (x,y) coordinatesofthepixelasa pointinthecomplexplane.Wecanusethat complexpointasour c intheabovealgorithm anditerateitafewtimes.Ifthevaluepasses agivensizeweconsideritas‘divergent’and ifnotweconsideritasbounded.Wemake itmoreinterestingbycoloringthepixelaccordingtohow fast itbecomesdivergent.For example,ifitisbounded(i.e.ifitisamemberoftheMandelbrotset)wecolorthepixel black,ifitdivergespastourthresholdafter
y=ymax−j * dx; for (i=0;i<width;i++){
x=xmin+i * dx;
u=0.0;
v=0.0; for (k=1;k<num_iterations&&(u * u+v * v< DIVERGE);k++){
U=u * u−v * v+x;
V=2* u * v+y;
u=U;
v=V;
} if (k>=num_iterations){ char black[]={0,0,0,0,0,0}; fwrite(black,6,1,fp);
} else { char color[6]; color[0]=k>>8; color[1]=k; color[2]=k>>8; color[3]=k; color[4]=k>>8; color[5]=k; fwrite(color,6,1,fp); }
} fclose(fp); return 0;}
int usage( char * name){
fprintf(stderr,"Usage:%s<xmin><xmax><ymin>< ymax><num_iterations><width><out.ppm>\n", name); fprintf(stderr,"Example1:%s0.270850.27100
0.0046400.00481010001024pic.ppm\n",name) ; fprintf(stderr,"Example2:%s0.2709860.270990 0.0048040.00480710001024pic.ppm\n",name) ; fprintf(stderr,"Converttopngusing:\n"); fprintf(stderr,"convert−normalizepic.ppmpic.png \norcolorwith\n"); fprintf(stderr,"Seehttp://www.imagemagick.org/ Usage/color_mods\n"); return 1;}
Bymodifyingtheinputparametersyoucan zoominonvariousregionsoftheset.You mightenjoyplayingwiththecodetoexplorethebeautyofthismathematicalcuriosity.Youcanalsoeasilyfindcolorfulphone appsandonlinegeneratorsoftheMandelbrotsetwhichallowyoutoselectregions andzoominsmallerandsmaller.Iencourageyoutotrythem!Youmightalsowant tocheckouttheYouTubevideo youtu.be/ FFftmWSzgmk foraninterestingdiscussion oftheMandelbrotSetandofJuliaSetsingeneral.
COMPUTATIONAL FLUID DYNAMICS ByASSALHADDAD
basicknowledgeofphysicsandmathematics isworkingtogethertodescribehowadropof waterdecidestomove.Althoughthereisa feelofrandomnesswhenwatchingawaterfallorwhensomeonespillsaglassofwater,it isactuallythecompleteopposite.Thewhole scenarioisalmostpredeterminedwhereevery dropofwaterhaspreciselyoneuniquepathto followunderthegivencircumstances.
Inadditiontobeingcrucial,itisalsoexcitingforengineerstomathematicallydescribe a“random”naturalphenomenon.Itisvery challengingtogetascloseaspossibletothe realthing,anditrequiresadeepunderstandingofeverysignificantandinsignificantvariablethatmightaffectthenaturalbehavior. Computationalfluiddynamics(CFD)utilizes thecomputercapacitytorunnumerouscalculationstosolvetheNavier-Stokesequations in3Dwhichprovides,forexample,engineers withanaccuratedescriptionofstreamlines aroundanairplanewingalongwithanestimationofthepressurevariations.
However,suchaprojectwouldbebeyond thescopeofafluidmechanicsundergraduatecourseandwouldalsorequirecertain specializedsoftwareandprogrammingabilitieswhichmaynotnecessarilyberequired fromcivilandmechanicalengineeringstudents.Thus,inthisFallsemester,fluidmechanicsstudentswereabletoprovideamathematicaldescriptionofasimplefluidproblem ofajetofwaterspewingoutofaholeina tankthatisbeingfilleditselfataconstantrate. Relatingthechangesinthewaterlevelofthe tankandtheprojectileshapeofthewaterjet requiredunderstandingofmassbalanceconcepts,Bernoulli’sconcepts,andparticledynamics.Themainchallengeforstudentswas togiveareal-timefeeltothedynamicsystem.Theprojectrequiredstudentstowrite acodeusingV-Python3.2thatcontinuously printsthetrailofwaterjet.Theintendedobjectivesbytheendoftheprojectwere:
1. Visualizingtherelationbetweenthe Bernoulli’sterms(mainly V2/2g andZ)
2. Visualizingtherelationbetweenthe continuityequationterms(Accumulationandinfluentandeffluentflowrates)
3. Investigatingthenonlineareffectof elapsedtimeonwaterheightinsidethe tank,andtheshapeofthewaterprojectileejectingoutsidethetank
4. Understandingthecomplexityinmodelingawaterjetunderacontinuousdomainoftime(i.e.,everydropofwaterwillhavedifferent Vx onceitleaves theopening);andrealizingthevalue ofsimplifyingcontinuoustimeintodiscretetimefragments(dt),whichhelps invisualizingthesignificanceofintegration
5. Designinganalgorithmthatcontinuouslycalculatesanumberofvariables thatprogressintimewithinaloopthat hasaspecifiedlimit.
InArabicslang,“likewater”isusedtodescribeaneasyandsimpleconceptorprocess. Agoodexamplewouldbeifonewouldwant todescribehoweasyitistoshareanimage fromFacebooktoafriendonWhatsApp;one wouldsayitis“likewater”.Oddly,onewould arguethatfluidmechanicsisdefinitelynot “likewater”.Itisasubjectwheretheentire
Studentshadfunwritingtheircodeafter ProfessorRodrigodaCostaAparecido,who wasassistingwiththecourse,explainedthe basicbuildingblocksoftheV-Pythonsoftwareandwalkedthemthroughthetrickyparts ofthecodingprocess.Studentswereexperiencingthegradualbuildupoftheirmodelsand
visualizinghowtheirmodelscometolifeand starttolookreal.
SecretSanta: HereisthePythoncode: secretSanta.py
import random
myList=["Reagan","Ryan","Madison","Taylor"," Lucy","Grant","Adam"] listCount= len (myList)
#FunctiondisplaySantaList def displaySantaList(santaList,giftList): for index inrange (listCount): print (f"{santaList[index]}SecretSantafor {giftList[index]}")
#mainfunction def main():
#Createtwoarraysforstoringuniquelists santaList=[] giftList=[] #Createtwolists for name in myList: santaList.append(name) giftList.append(name)
#randomlyshufflebothlists random.shuffle(santaList) random.shuffle(giftList)
duplicate=True
#loopuntiltherearenomatchesinthelists while duplicate==True: duplicate=False random.shuffle(giftList)
#Comparethelists for index inrange ( len (myList)): if santaList[index]==giftList[index]: duplicate=True displaySantaList(santaList,giftList); #Callthemainfunction. main()
fluid.py
#Numberofsamples=n n=10
#height1=h1
h1=3
#height2=h2
h2=2
#Areaofthehole
Ah=0.2
#Areaofthetank
At=1
#Waterin
Qi=1
#Farthestsplash fp=sqrt(2 * 9.81 * h1) * sqrt((2 * h2)/(9.81))
#EqualibriumHeight
hf=((Qi/Ah) ** 2)/(2 * 9.81)
T=0
while h1>=0:
vx=sqrt(2 * 9.81 * h1) totaltime=sqrt((2 * h2)/(9.81))
totalx=vx * totaltime
mytank=box(pos=vector(−1,.5 * (h2+h1) * 1.2,0), length=2,height=(h1+h2) * 1.2,width=.01)
mywaterfull=box(pos=vector(−1,h2 * .5,0),length =2,height=h2,width=.01,color=color.blue) horizontalaxis=curve(vec(−2,0,0),vec((totalx * 1.2)+2,0,0)) rate(100)
water=sphere(pos=vec(0,h2,0),radius=0.1,color= color.blue,make_trail=True,retain=(n+1)) mywater=box(pos=vector(−1,h2+(h1/2),0),length =2,height=h1,width=.01,color=color.blue)
t=0
dt=totaltime/n
T=T+dt while t<totaltime: water.pos.x=vx * t water.pos.y=h2−0.5 * 9.81 * (t ** 2) rate(100) dt=totaltime/n t=t+dt
Vh=(Qi−(Ah* vx))/At
dh=Vh* dt print ("FinalHeight="+hf) print ("h1="+h1) print ("ChangeinHeight="+dh) if Qi<=0: print ("Time="+T) print ("FarthestSplash="+fp)
h1=h1+dh mywater.visible=False water.clear_trail()
SOLUTIONSTO PROBLEMS
Herearethesolutionstotheproblemsthat werepresentedearlierinthisissue.
BrokenIcicles:
(i) Volumeofconeofheight x is πx3 3 tan2(θ)
Thinkforcirculardiscs dV = πR2 dx, where R = x tan(θ)
(ii) W = πρ0 gx3 3 tan2(θ)
Tensilestress = W Area = W πR2 = ρ0 gx 3
Sincetensilestressincreaseswith x,the longericiclesbreakandtheybreakfar fromthetip(neartothebase).
ENR304:VoltageDividerSixSigma
Thefollowingcodewillperformagivennumberoftrialsonvoltagedividerswithgiven resistorvaluesandtolerancesandoutputthe resultingvoltagedividervoltage.
divider.c
#include <stdio.h>
#include <stdlib.h>
#include <time.h> int usage( char * name); int main( int argc, char ** argv){ if (argc!=6) return usage(argv[0]); srand(time(NULL)); float R1=atof(argv[1]); float R2=atof(argv[3]); int dR1=atoi(argv[2]); int dR2=atoi(argv[4]); int Trials=atoi(argv[5]); float voltage,sign,dr1,dr2; int stats[101]; for ( int i=0;i<101;i++)stats[i]=0; for ( int i=1;i<=Trials;i++){ //dr1is+/−apercentageofR1 sign=(rand()%2)?1.0:−1.0; dr1=sign *R1 * (( float )((rand()%dR1)+1))/100.0; //dr2is+/−apercentageofR2 sign=(rand()%2)?1.0:−1.0; dr2=sign *R2 * (( float )((rand()%dR2)+1))/100.0; //inputvoltageis1 //outputvoltagefraction //comesfromresistorvalues voltage=(R2+dr2)/(R1+dr1+R2+dr2); stats[( int )(100 * voltage)]++; } for ( int i=0;i<101;i++) printf("%0.2f\t%0.2f\n",( float )i/100.0,(( float ) stats[i])/(( float )Trials)); return 0; } int usage( char * name){ fprintf(stderr,"Usage:%sR1dR1R2dR2Trials\n", name); fprintf(stderr,"R1,R2aretheresistornominal values\n"); fprintf(stderr,"dR1,dR2arethetolerances.I.e. 5%%is5\n"); fprintf(stderr,"Trialsisthenumberofrandom trials\n"); return 1; }
Ifyouruntheprogramwithtwo 100Ω resistorswith1%,5%,and10%tolerance valuesrespectivelyandplotthehistogram withthefollowingGnuplotscript.
divider.gnuplot
set termx11 settitle "VoltageDividerOutputasaFractionof InputVoltage" setxlabel "OutputVoltage" setylabel "FractionofTrials" setgrid setxtics 0.01 setxtics rotateby−45 setstyle fillsolid border −1 setkey topright setxrange [0.4:0.6] plot "divider1.dat" using 1:2 with boxes title "1% tolerance",\ "divider5.dat" using 1:2 with boxes title "5% tolerance",\ "divider10.dat" using 1:2 with boxes title "10% tolerance"
Thehistogramoftheoutputvoltagesareas follows
Thissametechniquecanbeusedwithany electriccircuit,mechanicalmachine,orphysicalstructurewhenthematerialsusedhave givenmanufacturingtolerances.Yousimulate theparametersoftheresultingwholebyrandomizingtheinputvaluesbasedonthetolerances.Thisallowsyoutooptimizetheproductcostswithingivenqualityspecifications.
Irememberonetimeinelementaryschool wehad“TrackandFieldDay”whereabunch ofschoolsgottogethertocompeteinvarious runningandjumpingcompetitions.Theparentswerethereanditwasbeforetheschool agewherekidsareseparatedintoteams.Everybodycompetedineveryevent.Itismore aboutthefunandexerciseinthesunrather thanaboutoneschoolbeatinganother.Obviouslyitwasstillcompetitiveandeveryone wantedtocomehomewithvictoryribbonsin aneventortwo.
Anyway,Ihadabestfriendatthetime, Calvin,whoIdideverythingwith.Tothis dayIamconvincedthatCalvinhadthefunniestsenseofhumorofanyoneIevermet–andthatsayssomethingsincewewereonly somethinglike8yearsold!Theproblemwas thatCalvinwasasthmaticandwasnotoriously badatsportingeventsasaresult.Iremember itwastimeforthe‘highjump’competition andIcouldtellthatitterrifiedCalvin.He couldn’tjumpveryhigh.Thewaythecompetitionworkedwasthattherewasasandpit (weweren’toldenoughyettohighjumpin thetechnicalwaywhereyoubackfliponto amat)andthegoalwasjusttohopfromone sideoverthebarintothesandontheother side.Allthestudentslinedupand,oneaftertheother,theywouldruntothebarand hopoverit.Ifyouknockedthebardownyou wouldrunbackaroundwhiletherefereesreplacedthebarandyouwouldrunatitagain. Ifyouknockeditdownthreetimesyouwould beeliminated.Aftertheentirelineofkids hadfinished,therefereeswouldraisethebar anotchandgothroughthelineofkidsagain andthiswouldcontinueuntilonlyonekidwas left.Thelastthreestandingwouldbeawarded thefirst,second,andthirdplaceribbonsfor theevent.
AsIsaid,Calvinwasterrified,andwith goodreason.BeinghisbestfriendIknewthat hewasgoingtodomiserably.Hecouldbarely runandhecertainlycouldn’tjumpveryhigh. However,evenIwassurprisedbyhowpoorly hedid.Thebarwasonthefirstsettingwhen heknockeditdown.Thiswastheeasiest level!Sortofthe‘warm-up’levelwhereall ofthekidswereexpectedtoeasilyclearit.A
confidenceboosteryoumightsay.AndCalvin knockeditdown.Icouldseehisfacegrowingredwithhumiliationashelumberedback aroundforhissecondattempt.Heknocked itdownagain!Onhiswaybackaroundfor hisfinalattemptIcouldseeafearanddeterminationinhiseyes.He needed toclearthe bar.Thisdaywouldhaunthimforeverifit endedinthisworstkindofhumiliation.To failattheeasiestsettingwitheveryoneinthe worldwatching...Heknockeditoveragain. Hewaseliminated.Heslowlywalkedtothe sidelinesastherefereesreplacedthebar.Up tothatpointhewastheonlyonewhoeven knockedthebardownonce,letalonebeing eliminated.Howhorriblehemusthavefeltat thatmoment.
Afewstudentslateranditwasmyturn.I knockedthebardown.Icouldseemymom onthesidelinesandtheconfusionthatap-
pearedonherface.Didmyfootsnagon something?Shemusthavethought.Iranback aroundandknockeditdownyetagain!Now shewasreallyconfused.Iwasalittlemonkey atthatageandsheknewthatjumpingover thatmeaslyheightwasatrivialityforme.On myfinalattemptIknockeditoveryetagain andwaseliminated.
Iwalkedovertomymomandshe,althoughconfused,gavemeahugandsaid, “don’tworry,it’sokay,you’lldobetternext time.”IthenwanderedovertoCalvinwho wasstandingwithhismom.“Igoteliminated,”Isaid.“Iknow,”hereplied,“metoo. Youwanttogogetacokefromtheconcessionstand?”“Ya”,Ismiled,“let’sgo!”The restofthedaywasabunchoffun.Calvin’s humorhadreturnedinfullforceandheforgot allaboutthetraumatichumiliationofthehigh jumpevent.
Calvinnowmanagesafarmimplement storeinmyhometownandishappilymarried withthreewonderfulkids.Idon’tthinkhe evenremembersthatTrackandFielddaylet alonethinkingofitasafailure.Asforme?I havethoughtaboutthatdaysometimes.For me,oneoftheproudestsuccessesinmyearly lifewas losing thathighjumpcompetition.
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