2006-2363: A HYDRODYNAMIC WHEATSTONE BRIDGE FOR USE AS A TEACHING TOOL IN INSTRUMENTATION LABORATORY COURSES David Bloomquist, University of Florida Michael McVay, University of Florida Scott Wasman, University of Florida Clinton Slatton, University of Florida Page 11.56.1 Page © American Society for Engineering Education, 2006 A HYDRODYNAMIC WHEATSTONE BRIDGE FOR USE AS A TEACHING TOOL IN INSTRUMENTATION LABORATORY COURSES Abstract Undergraduate engineeringstudentsoftenfindsystemscomposedofelectricalcircuitsdifficult tograsp becausevariablessuchascurrent,voltage,resistance,capacitance,andinductanceare noteasilyvisualizedastheiranalogsinmechanicalsystems.Thus,a HydrodynamicWheatstone bridge,usingthe analogyofflowinpipes,wasdevelopedtoserve asateachingtoolinthe classroom.Aseriesoftestswere performedtosimulate¼,½,full,andshuntedbridgecircuits, wheretheincreaseordecreaseinresistanceinthe straingageisanalogoustopartially closingor opening avalveina pipenetwork.Thedifferenceinheadpotential(i.e., ∆V)wasmeasuredwith manometerslocatedbetweenthevalves.Theresultsagreewiththe¼,½,full,andshunted Wheatstone bridgecircuits.Futureenhancementsincludetheadditionofflowmeterstorelate waterflowtocurrentflow,scaledfullturnvalvestomoreaccuratelyrepresentchanging resistances,andaflexibletubesection,inplaceofavalve,toreplicateastraingageintension. Introduction In1994,CivilEngineering professorsatthe Universityof Floridadevelopedanundergraduate course,"INSTRUMENTATION FORENGINEERS",inwhichstudentsareexposedtothe fundamentalsofcircuitrythroughbasicanalysisofDCandACcircuits.Exercise problemsare routinely performedintheclassroomandgiventothestudentsforreinforcementthrough independent practice.Accompanyingthecourseisaweeklytwohourlabwhichprovidesthe studentshandsonpracticewithcivilengineeringinstrumentation:e.g.,loadcells,displacement transducers (LVDT),accelerometers,and pressuretransducers.Since the Wheatstone bridge circuitisfrequentlyusedintheseinstruments,analysisofitis paramounttothestudents’success inthecourse.Unfortunately,thistopicisonethatcausesthemost angst(perhapssecondonlyto Thevenins!),andthuswefeltitwouldbehelpfultodevelopadevicethatwouldallowthe studentstoobservewhat happenstowater pressureswhenflowingina “bridge circuit” pipe network. Hence,usingthe analogyofflowinpipes,a bridgecircuitwasdevelopedasateachingtool. Thesimilarity betweenhydrodynamics(flow,pressure,andvalve position)toelectricity(current, voltage,andresistance) providesauseful analogy.Forexample,astraingageina bridgecircuit canbemodeledwithaneedlevalveina pipenetworksothatanincreaseordecreasein resistance (viatensionor compression)inthe straingageisanalogoustoclosingoropening a valveina pipe system.Thiswill,inturn,createa ∆V(assuminga¼bridge)thatcanbe representedbyadifferenceinwaterheightsinmanometerslocatedatthe mid-pointsofthe “bridge”. Similarly,½,full,andshuntedbridgecircuitscanbe modeleddependingonthevalvesettings. Forexample,thestudentscan'balance'the bridge byadjustingthevalvesuntilthewaterheights 11.56.2 Page inthemanometersareequal.Then,byopening(lessresistance =compressionofagage)oneor morevalves,they canseetheeffectthishasonthewaterlevels.Stopping theflowattheoutlet alsoshowsthatregardlessofthevalve(s) position,thewaterlevelsareequalfornoflow conditions. Instrument Description TheHydrodynamicWheatstoneBridge (HWB)showninFigure1,wasdesignedforuse asa hands-onlabinstrument. Itutilizesa1000mL graduatedcylinder filledwithwaterandplaced adjacenttothe bridgetocreatetheappliedpressure(voltage)tothe pipenetwork(circuit). Swagelokvalvesrepresentthefourstraingagesinthelegsofthecircuit.Thevalvesare connectedby¼"ODtubingand45º brassfittings.Manometertubes,(Fig.2)arelocatedin- betweenthevalves,allowingthestudents tomeasurethewatercolumnheight orhead(voltage) andthechangescausedby openingorclosingone ormorevalves.Thevalvescanbe adjustedto a prescribedsetting,simulatingthestrainingofthegage(s) ( ∆R).Themanometertubesserveas the “voltmeter”tomeasurethedifferenceinvoltage acrossthe twolegsof the bridge. Inelectrical circuits,Wheatstone bridges are oftenusedtomeasure medium resistance values (1). Verysmallresistancesaredifficulttomeasure becauseofthermoelectric voltages generatedat the junctionsofdissimilarmetalsandthermalheatingeffects.Verylargeresistancesaredifficult tomeasureaccurately becauseofleakagecurrents.Thereisnodirectanalogtothesetwo phenomenainthehydrodynamicWheatstone bridge.Whiletheopening andclosingofvalvesis nota perfectanalogy for electricalresistors,thehydrodynamiccircuitdoesserveas anaccurate analogaslongasthevalvesarenot completelyclosedoropen. Thewaterinthehydro-bridge circuitis pumpedintothegraduatedcylinderfromareservoir locatedbelowthe circuit (Fig1).Outflow fromthecircuitischanneledbackintothereservoirto maintainaconstantflow condition.Tapwater withfooddyeservesasthefluidtohelpobserve waterheightsineachmanometer(Fig.2). Page 11.56.3 Page NEEDLE VALVE 1000mlGRADUATED CYLINDER Ho MANOMETERS HB HI HA HF 2 VALVE S 1 3 4 WATER RESERVOIR PUMP TANK Figure1.HydrodynamicWheatstone Bridge 11.56.4 Page Figure2.HydrodynamicBridgeCircuit Test Setup Afterconstruction,aseriesoftestswereconductedtoverifytheconcept.Thetestswere planned tosimulate¼,½,Full,andshuntedbridgecircuits.Table1providesthedetailsofeachtest,i.e., valvesettings. 11.56.5 Page Table1.TestSimulations Bridge Configuration ¼ ½ Full Shunt (Valve 2) Valve Settings Valve1 ½Open ¼Open ¼Open ½Open Valve2 ½Open ½Open ¾Open 9/16 Open Valve3 ¼Open ¼Open ¼Open ½Open Valve4 ½Open ½Open ¾Open ½Open Thereadingsofthemanometertubesforthedifferentvalve configurationsarethemeasured watercolumnheights.Settingallthevalvestothesameopenposition(e.g.½open)represents a balancedbridgeinwhichallthe straingagesareorientedinthesamedirectionwithequal resistances.Thisscenario produceszerovoltagedifference betweenthelegs,henceVA–V B or ∆V=0(RefertoFigure 3.below).A balancedWheatstone bridge conditioncanbedescribedby Equation1. i 1 + i 2 VI R1 R 2 + i 1 i2 VO VA VB _ i3 i4 R4 R 3 VF ∆V Figure3.Wheatstone BridgeCircuit R1 R2 = Eq.1 R4 R3 Inthe caseoftheHydrodynamic bridge,settingvalves1and4tothesame settingandvalves2 and3toadifferent,butequalsetting,alsoresultsina balancedbridge (∆V =0).Itwas 11.56.6 Page anticipatedthatmanometersH AandHBwouldbeequalandhalfof theinitialmanometer(HI) waterheight.Opening eachvalvetoadifferentsetting resultsinanunbalancedbridge( ∆V ≠0), inwhichcasemanometerheightsHA andHBwould bedifferent. Fora¼bridge,asingle gageisstrainedincompressionortension.Thestrainingincreasesor decreasesthe resistance(∆R),whichifhigherordertermsareneglected,producesadifferencein voltage,describedbyequation2. GF ∆V = ε V Eq.2 4 o where: GFisthe gagefactor, εthestrainandV o,the excitationvoltage Forthe½bridgecircuit,twogages(R 1andR 3)arestrainedincompressionortension,resulting inavoltagedifferencetwicethatofthe¼bridge.Thechangeinvoltageis describedby equation3. (GF ) ε ∆V = V Eq.3 2 o Therefore,itwas expectedthat thedifferenceinreadings between H AandH Bwouldproduce similarresults,assuming equallengthsofthetubinginthecircuit. Tosimulateashuntedcircuit,weadjustedthevalvesetting toreplicatethe parallelcombination ofR 2andashuntresistor,R S.ThehighresistanceofR ScombinedwiththeresistanceofR 2 resultsinavaluethatisslightly lessthanR 2.Therefore,valve2wasopenedslightlymorethan theothervalves.Thesettingfortheothervalves isdescribedinTable1.Asaresult,thereisa smallincreaseinV Band ∆V(i.e.,VA–V B).This wasobservedinthemanometerreadingsof HA andHB aswell. Test Results Testswere performedontheHWBtosimulate¼,½,full,andshunted bridge circuit configurations.Theresultsofeachtestare presentedinTables2-5. ¼ Bridge ThedifferenceinwaterheightsofHAandHBwas 4.1cm.ConsideringOhm'slaw(V= IR),for constantcurrent,astheresistanceincreasessodoesthevoltagedropor difference.Forthese tests,thewaterflow was maintainedataconstant,lowrate.Inthe caseoftheHWB,headloss duetotheflow path(pipefriction,fittinglosses etc.fromthesourcetothe firstmanometer)was negligible.Wemeasureda0.5cm.difference(orloss) betweenthesetwopoints.Itisimportant tonotethattheflowrate hadtobeadjustedinorderforthe bridgetoworkproperly.Thiswas done bytrialanderror andonceset,theremainderofthetestsworkedproperly.Whilewedid nothaveaflowmetersensitiveenoughtomeasure it,we plantoincorporatearotameterto monitortheflowinthenextmodel. 11.56.7 Page Table2.Resultsofthe ¼Bridge Simulation Valve Source Head (36 cm) Manometer Reading Settings Valve1 ½Open HI 35.5cm Valve2 ½Open HB 30.2cm Valve3 ¼Open HF 0cm Valve4 ½Open HA 26.1cm Figure4.ManometerHI 11.56.8 Page ½ Bridge Theexpectedresultsofthe½bridgesimulationwasadifferenceinheadbetweenH A andH B approximatelytwicethat ofthe¼bridge.Table3presentsthetestresults.Weseethat ∆Hwas closeto2xthe¼ bridge setup. Table3.Resultsof½BridgeSimulation Valve Source Head (36 cm) Manometer Reading Settings Valve1 ¼Open HI 35.7cm Valve2 ½Open HB 30.4cm Valve3 ¼Open HF 0cm Valve4 ½Open HA 22.5cm Full Bridge InTable4theresultsofthefull bridgesimulationareshown.As expected,theheightdifference wasapproximately16.9cmor4.12timesthe¼bridgedifference(asopposedto4).Again,the flowratehasasubstantialeffectontheheightsanditwasnecessarytoreduceittoaminimumin ordertomaintainthecorrect bridgeoutputeffects. Table4.ResultsoftheFullBridgeSimulation Valve Source Head (36 cm) Manometer Reading Settings Valve1 ¼Open HI 34.6cm Valve2 ¾Open HB 28.6cm Valve3 ¼Open HF 0cm Valve4 ¾Open HA 11.7cm 11.56.9 Page Shunted Bridge Table5presentstheresultsoftheshuntsimulationforvalve2.Thereadingsof HAandH B indicateasmalldifference,approximately0.4cm.Thisagreeswiththetrendwhenshunting a bridgewithalargekiloohmresistorinparallelwithoneofthestandardgages(120or350ohms).