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Flowmeters

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Flowmeters

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Flowmeters

  1. 1. FlowmetersFlowmeters Andre PenningtonAndre Pennington Kat WitherspoonKat Witherspoon Pam BuzzettaPam Buzzetta
  2. 2. IntroductionIntroduction  Flowmeters are process instruments thatFlowmeters are process instruments that measure a fluid’s linear or non-linear flow atmeasure a fluid’s linear or non-linear flow at volumetric or mass flow ratesvolumetric or mass flow rates  A fluid can either be a liquid or a gasA fluid can either be a liquid or a gas
  3. 3. IntroductionIntroduction  Key features to consider in flow meterKey features to consider in flow meter selection:selection:  Fluid properties:Fluid properties:  Liquid or gasLiquid or gas  Temperature and pressureTemperature and pressure  DensityDensity  ViscosityViscosity  Chemical propertiesChemical properties  Presence of other phasesPresence of other phases
  4. 4. IntroductionIntroduction  Key features to consider in flow meterKey features to consider in flow meter selection:selection:  Installation considerations:Installation considerations:  OrientationOrientation  Flow directionFlow direction  Upstream/downstream pipe workUpstream/downstream pipe work  Location for servicingLocation for servicing  Location of valvesLocation of valves  Effects of local vibrationEffects of local vibration  Electrical connectionsElectrical connections  Effects of unsteady flowEffects of unsteady flow
  5. 5. IntroductionIntroduction  Key features to consider in flow meterKey features to consider in flow meter selection:selection:  Performance considerations:Performance considerations:  AccuracyAccuracy  RepeatabilityRepeatability  LinearityLinearity  Rangeability (turndown)Rangeability (turndown)  Pressure dropPressure drop  Output signal characteristicsOutput signal characteristics  Response timeResponse time
  6. 6. IntroductionIntroduction  Key features to consider in flow meterKey features to consider in flow meter selection:selection:  Economic considerations:Economic considerations:  Cost of ownership (i.e. purchase, installation, operation,Cost of ownership (i.e. purchase, installation, operation, maintenance, calibration, meter life, spares)maintenance, calibration, meter life, spares)  Pressure lossPressure loss  Environmental considerations:Environmental considerations:  Ambient temperature effectsAmbient temperature effects  Humidity effectsHumidity effects  Safety factorsSafety factors  Electrical interferenceElectrical interference
  7. 7. Positive Displacement FlowmetersPositive Displacement Flowmeters  Fluid goes through a chamber with a unitFluid goes through a chamber with a unit that repeatedly fills and discharges a fixedthat repeatedly fills and discharges a fixed volumevolume  The total volumetric flow rate can then beThe total volumetric flow rate can then be calculated from the rate of filling andcalculated from the rate of filling and discharging the discrete volumesdischarging the discrete volumes
  8. 8. Positive Displacement FlowmeterPositive Displacement Flowmeter  Accuracy: 0.25 to 1%Accuracy: 0.25 to 1%  Line sizes: ¼ to 3”Line sizes: ¼ to 3”  Rangeability: 2:1 to 10:1Rangeability: 2:1 to 10:1  Common Applications:Common Applications:  Fluids generally need a degree of lubricityFluids generally need a degree of lubricity  Clean, non-abrasive, medium to high viscosity liquidsClean, non-abrasive, medium to high viscosity liquids  Good for batch operation, low-tech plantsGood for batch operation, low-tech plants  Often used in oil and gas refining, chemical, pulp andOften used in oil and gas refining, chemical, pulp and paperpaper
  9. 9. Positive Displacement FlowmeterPositive Displacement Flowmeter Nutating DiscNutating Disc Rotating ValveRotating Valve
  10. 10. Positive Displacement FlowmeterPositive Displacement Flowmeter Oscillating PistonOscillating Piston Oval GearOval Gear
  11. 11. Positive Displacement FlowmeterPositive Displacement Flowmeter  Advantages:Advantages:  Moderately inexpensiveModerately inexpensive  No Reynolds number constraintsNo Reynolds number constraints  No upstream/downstream requirementsNo upstream/downstream requirements  High accuracy – 0.25 to 1% of rateHigh accuracy – 0.25 to 1% of rate  Can measure very low and very viscous flowsCan measure very low and very viscous flows
  12. 12. Positive Displacement FlowmeterPositive Displacement Flowmeter  Disadvantages:Disadvantages:  Moving partsMoving parts  Can create large pressure dropsCan create large pressure drops  Maintenance is necessary; must disassembleMaintenance is necessary; must disassemble to unplug if using a dirty fluid and subject toto unplug if using a dirty fluid and subject to deteriorationdeterioration  Measures discrete fluid flows instead of actualMeasures discrete fluid flows instead of actual flow rateflow rate  May take up a lot of spaceMay take up a lot of space
  13. 13. Differential Pressure FlowmeterDifferential Pressure Flowmeter  Flow goes through a section with differentFlow goes through a section with different cross section areas that cause pressurecross section areas that cause pressure and velocity variationsand velocity variations  Employ Bernoulli equation by observingEmploy Bernoulli equation by observing relationship between pressure drop andrelationship between pressure drop and velocity to get volumetric flowvelocity to get volumetric flow
  14. 14. Differential Pressure FlowmeterDifferential Pressure Flowmeter  Most common method to measure flowMost common method to measure flow  Smart transmitters simplify useSmart transmitters simplify use  Accuracy: ±2% of full scaleAccuracy: ±2% of full scale  Line size: greater than ½”Line size: greater than ½”  Rangeability: 4:1Rangeability: 4:1  Common Applications:Common Applications:  Most gases and low viscosity fluidsMost gases and low viscosity fluids  Used for chemical, oil and gas refining, power, andUsed for chemical, oil and gas refining, power, and transfer of natural gastransfer of natural gas
  15. 15. Differential Pressure FlowmeterDifferential Pressure Flowmeter Orifice PlatesOrifice Plates Calculate mass flow: mCalculate mass flow: mactualactual = KA= KAtt*(2*(2ρ(pρ(p11-p-p22))))0.50.5
  16. 16. Differential Pressure FlowmeterDifferential Pressure Flowmeter Venturi TubeVenturi Tube Flow NozzleFlow Nozzle
  17. 17. Differential Pressure FlowmeterDifferential Pressure Flowmeter  Advantages:Advantages:  Well known system of measurementWell known system of measurement  VersatileVersatile  Line size flexibilityLine size flexibility  Inexpensive initiallyInexpensive initially  Highly repeatableHighly repeatable  East to maintainEast to maintain  Economical to correct sizing mistakeEconomical to correct sizing mistake
  18. 18. Differential Pressure FlowmeterDifferential Pressure Flowmeter  Disadvantages:Disadvantages:  High installation costsHigh installation costs  Moderate system accuracyModerate system accuracy  An abrasive or sticky process will erodeAn abrasive or sticky process will erode accuracy and increase maintenance costaccuracy and increase maintenance cost  Moderate rangeabilityModerate rangeability  High relative pressure lossHigh relative pressure loss
  19. 19. Turbine Flow MetersTurbine Flow Meters OverviewOverview  Uses flow to turn a turbineUses flow to turn a turbine rotorrotor  Magnetic sensor transmitsMagnetic sensor transmits a voltage pulse to aa voltage pulse to a processorprocessor  Axial-vane rotor is freeAxial-vane rotor is free turningturning  Rotor continuously movingRotor continuously moving under pressure of the liquidunder pressure of the liquid  Accuracy in the range of +/-Accuracy in the range of +/- 0.25% with 10:1 turndowns.0.25% with 10:1 turndowns.
  20. 20. Turbine Flow MetersTurbine Flow Meters Common ApplicationsCommon Applications  Turbine flow meters are widely used forTurbine flow meters are widely used for both liquid and gas applicationsboth liquid and gas applications  Typical applications include:Typical applications include:  Oil and gas, refining, chemical, semiconductor,Oil and gas, refining, chemical, semiconductor, agricultural, pharmaceutical, food beverageagricultural, pharmaceutical, food beverage dispensing, photo development, processdispensing, photo development, process control, and morecontrol, and more
  21. 21. Turbine Flow MetersTurbine Flow Meters Benefits/AdvantagesBenefits/Advantages  High degree of accuracy at low cost, especiallyHigh degree of accuracy at low cost, especially when combined with a flow computerwhen combined with a flow computer  Flexibility in connecting to associated electronicFlexibility in connecting to associated electronic readout devices for flow control and computerreadout devices for flow control and computer interfaceinterface  Wide flow rangeabilityWide flow rangeability  Construction materials that permit use with manyConstruction materials that permit use with many process fluidsprocess fluids  Simple, durable, field-repairable constructionSimple, durable, field-repairable construction  Operation over a wide range of temperatures andOperation over a wide range of temperatures and pressurespressures
  22. 22. Turbine Flow MetersTurbine Flow Meters Limitations/DisadvantagesLimitations/Disadvantages  Poor interchangeability from unit to unitPoor interchangeability from unit to unit  Bearings depend on lubricity and cleanliness ofBearings depend on lubricity and cleanliness of process fluidprocess fluid  Turbine blades are susceptible to wear andTurbine blades are susceptible to wear and must be frequently calibratedmust be frequently calibrated  Liquid applications may be suspect to problemsLiquid applications may be suspect to problems involving cavitation, specific gravity, andinvolving cavitation, specific gravity, and viscosityviscosity  Intended for clean fluid applicationsIntended for clean fluid applications
  23. 23. Magnetic Flow MetersMagnetic Flow Meters OverviewOverview  Nonmagnetic tubeNonmagnetic tube surrounded by coilssurrounded by coils  Must pump conductive liquidsMust pump conductive liquids  Flow rate inferred by sensingFlow rate inferred by sensing linear velocitylinear velocity  Principle of operation basedPrinciple of operation based on Faraday’s Law, E=kBDVon Faraday’s Law, E=kBDV  30:1 rangeability30:1 rangeability  Accuracy 0.5% of volumetricAccuracy 0.5% of volumetric raterate  Line size of 0.15” to 60”Line size of 0.15” to 60”
  24. 24. Magnetic Flow MetersMagnetic Flow Meters Common ApplicationsCommon Applications  Turbine flow meters are widely used forTurbine flow meters are widely used for corrosive, dirty, or slurry-like liquidscorrosive, dirty, or slurry-like liquids  Typical applications include:Typical applications include:  Wastewater applications or any dirty liquid which isWastewater applications or any dirty liquid which is conductive or water based (large water flows)conductive or water based (large water flows)  Pulp & paper industry, acid flows or other highlyPulp & paper industry, acid flows or other highly corrosive liquids, abrasive fluids such as mining orecorrosive liquids, abrasive fluids such as mining ore slurries and pulp stockslurries and pulp stock  Also ideal for applications where low pressure dropAlso ideal for applications where low pressure drop and low maintenance are requiredand low maintenance are required
  25. 25. Magnetic Flow MetersMagnetic Flow Meters Benefits/AdvantagesBenefits/Advantages  Relatively unaffected by changes in liquid densityRelatively unaffected by changes in liquid density or viscosity (compatible with wide range of processor viscosity (compatible with wide range of process fluids)fluids)  Liquid turbulence has a very limited affectLiquid turbulence has a very limited affect  Suitable for high viscosity and slurriesSuitable for high viscosity and slurries  Low maintenance, high accuracy and rangeabilityLow maintenance, high accuracy and rangeability  No pressure lossNo pressure loss  Obstructionless flowObstructionless flow  Flow profile has minimum effect on measurementFlow profile has minimum effect on measurement accuracy (Re# constraints and little flowaccuracy (Re# constraints and little flow conditioning needed)conditioning needed)
  26. 26. Magnetic Flow MetersMagnetic Flow Meters Limitations/DisadvantagesLimitations/Disadvantages  Measures conductive liquids onlyMeasures conductive liquids only  High initial costHigh initial cost  4-wire device (requires external power source)4-wire device (requires external power source)  Must be lined with non-conductive materialMust be lined with non-conductive material (lower temperature and pressure limits)(lower temperature and pressure limits)  Grounding problemsGrounding problems  Unstable zero with empty meterUnstable zero with empty meter
  27. 27. Ultrasonic Flow MeterUltrasonic Flow Meter OverviewOverview  Use transmitted sound wavesUse transmitted sound waves to determine flow rateto determine flow rate  Measures liquids and gasesMeasures liquids and gases with different designswith different designs  Accuracy 1-5% forAccuracy 1-5% for microprocessor-based unitsmicroprocessor-based units  Rangeability 20 to 50:1Rangeability 20 to 50:1  Can be divided into 2 typesCan be divided into 2 types  Transit Time (pulsed type)Transit Time (pulsed type)  Doppler (frequency shift type)Doppler (frequency shift type)
  28. 28. Ultrasonic Flow MeterUltrasonic Flow Meter Transit Time (Pulsed Type)Transit Time (Pulsed Type)  Sonic transducers areSonic transducers are mounted diagonally onmounted diagonally on opposite sides of a pipeopposite sides of a pipe  Requires clean liquid andRequires clean liquid and uniform flow profileuniform flow profile  Rangeability: 10:1Rangeability: 10:1  Accuracies:+/- 1% of rateAccuracies:+/- 1% of rate  Advantages:Advantages:  Bi-directional and non-Bi-directional and non- intrusiveintrusive
  29. 29. Ultrasonic Flow MeterUltrasonic Flow Meter Doppler (Frequency Shift Type)Doppler (Frequency Shift Type)  Established 1843 by ChristianEstablished 1843 by Christian DopplerDoppler  Measures the shift inMeasures the shift in frequency due to motion offrequency due to motion of particles or bubbles in theparticles or bubbles in the process pipeprocess pipe  Turndowns: 10:1Turndowns: 10:1  Accuracy: +/- 1% of rateAccuracy: +/- 1% of rate  Not suitable for clean liquidsNot suitable for clean liquids  Requires straight pipe runs forRequires straight pipe runs for installationinstallation  Pipe must have goodPipe must have good acoustical propertiesacoustical properties
  30. 30. Open Channel (Weirs and Flumes)Open Channel (Weirs and Flumes)  Oldest method to measureOldest method to measure flow, used by Romans toflow, used by Romans to measure flow in theirmeasure flow in their aqueductsaqueducts  Any time the fluid flows with aAny time the fluid flows with a free surfacefree surface  Examples: aqueducts, logExamples: aqueducts, log flumes, channels, etc.flumes, channels, etc.  Flow measured by inserting aFlow measured by inserting a calibrated restriction to thecalibrated restriction to the channelchannel  Two types of restrictionsTwo types of restrictions  WeirsWeirs  FlumesFlumes
  31. 31. Ultrasonic Flow MetersUltrasonic Flow Meters Common ApplicationsCommon Applications  Liquids and some gas applicationsLiquids and some gas applications  Doppler flowmeters require entrained gas or particlesDoppler flowmeters require entrained gas or particles to reflect ultrasonic energyto reflect ultrasonic energy  Where non-wetted sensors are applicableWhere non-wetted sensors are applicable  Existing installations where pipe modifications areExisting installations where pipe modifications are difficult or uneconomicaldifficult or uneconomical  Where exotic materials make other flowmeterWhere exotic materials make other flowmeter uneconomicaluneconomical  Large pipes where in-line meters are uneconomicalLarge pipes where in-line meters are uneconomical  Temporary installationsTemporary installations  Typical applications include:Typical applications include:  Water and wastewater, chemical, refining, oil and gasWater and wastewater, chemical, refining, oil and gas
  32. 32. Ultrasonic Flow MetersUltrasonic Flow Meters Benefits/AdvantagesBenefits/Advantages  Some designs allow measurement to beSome designs allow measurement to be made external to the pipe (utilize no wettedmade external to the pipe (utilize no wetted parts)parts)  Low maintenanceLow maintenance
  33. 33. Ultrasonic Flow MetersUltrasonic Flow Meters Limitations/DisadvantagesLimitations/Disadvantages  Fluid changes (% solids, bubbles, etc) affectFluid changes (% solids, bubbles, etc) affect measurementmeasurement  Proper installation is criticalProper installation is critical  Longer upstream/downstream straight pipingLonger upstream/downstream straight piping requirementsrequirements  Minimum Reynolds number constraintMinimum Reynolds number constraint  4-wire operation (external power source)4-wire operation (external power source)  Low user confidenceLow user confidence  Only mixed success in industrial flowOnly mixed success in industrial flow applicationsapplications
  34. 34. Oscillatory FlowmetersOscillatory Flowmeters  Two types:Two types:  Vortex SheddingVortex Shedding  FluidicFluidic Vortex Shedding Flowmeter Fluidic Flowmeter
  35. 35. Vortex SheddingVortex Shedding  Vortex shedding is caused by fluid flowing around anVortex shedding is caused by fluid flowing around an objectobject  Blunt object placed in the flowing streamBlunt object placed in the flowing stream  The frequency of the vortices is measuredThe frequency of the vortices is measured  The relationship between flow and frequency is: V = k*d*fThe relationship between flow and frequency is: V = k*d*f  The frequency is directly proportional to the flow rate.The frequency is directly proportional to the flow rate.
  36. 36. Measuring the VorticesMeasuring the Vortices  Different objects manufactured to produceDifferent objects manufactured to produce stable vorticesstable vortices  Vortices are measured by:Vortices are measured by:  High frequency pressure transducersHigh frequency pressure transducers  Measuring variations in heat transfer from aMeasuring variations in heat transfer from a heated resistorheated resistor  UltrasonicsUltrasonics
  37. 37. Pros & ConsPros & Cons ProsPros  Good accuracy (+/- 0.5%)Good accuracy (+/- 0.5%) and rangeability (40:1)and rangeability (40:1)  No moving parts, less toNo moving parts, less to breakbreak  Moderate costsModerate costs  Can handle liquid, gas,Can handle liquid, gas, and steamand steam  Low pressure dropLow pressure drop  Not affected by fluidNot affected by fluid density changesdensity changes ConsCons  Intrusive, obstruct flowIntrusive, obstruct flow  If using ultrasonics toIf using ultrasonics to measure the vortices,measure the vortices, straight runs of pipe arestraight runs of pipe are neededneeded  Re < 20,000 (high) forRe < 20,000 (high) for linear performancelinear performance  Sensitive to increasingSensitive to increasing ViscosityViscosity  Expensive in larger sizesExpensive in larger sizes
  38. 38. Common ApplicationsCommon Applications  Low viscosity fluidsLow viscosity fluids  Pressurized gasesPressurized gases  Steam and other utility fluidsSteam and other utility fluids  Pressurized gases with high densitiesPressurized gases with high densities  Single-phase fluids (no particulate matter)Single-phase fluids (no particulate matter)
  39. 39. FluidicFluidic  As fluid enters device, flows along one interior wallAs fluid enters device, flows along one interior wall  Some fluid diverted back to inlet (feedback flow) causing the fluid toSome fluid diverted back to inlet (feedback flow) causing the fluid to be pushed against other wallbe pushed against other wall  The flow shifts from side to side creating oscillationsThe flow shifts from side to side creating oscillations  Oscillations sensed by an electronically heated thermistor on oneOscillations sensed by an electronically heated thermistor on one sideside  Alternating flow causes the thermistor to be cooled, this signal isAlternating flow causes the thermistor to be cooled, this signal is directly proportional to velocitydirectly proportional to velocity
  40. 40. Pros & ConsPros & Cons ProsPros  Accuracy betweenAccuracy between 0.5% and 1.0% of0.5% and 1.0% of raterate  MinimumMinimum maintenancemaintenance  InexpensiveInexpensive ConsCons  Can only be used onCan only be used on clean low-viscosityclean low-viscosity fluidsfluids  ReRe ≥ 3,000 (requires≥ 3,000 (requires turbulent flow)turbulent flow)  Only used in pipes 4”Only used in pipes 4” or less diameteror less diameter
  41. 41. Target FlowmetersTarget Flowmeters
  42. 42. Target FlowmeterTarget Flowmeter  Use an object that is placed in the fluid flowUse an object that is placed in the fluid flow  Object mounted at right angleObject mounted at right angle  Force exerted on the target is measured byForce exerted on the target is measured by strain gaugesstrain gauges  Gauges produce electronic output that isGauges produce electronic output that is proportional to the square of flow rateproportional to the square of flow rate  Optimum size of target depends on liquid beingOptimum size of target depends on liquid being studiedstudied
  43. 43. DrawbacksDrawbacks  While accuracy is good at low scale, at fullWhile accuracy is good at low scale, at full scale the accuracy can vary as much asscale the accuracy can vary as much as 5+%5+%  Straight pipe length requirementsStraight pipe length requirements  20 x diameter upstream20 x diameter upstream  10 x diameter downstream10 x diameter downstream
  44. 44. Mass FlowmetersMass Flowmeters  ThermalThermal  Angular MomentumAngular Momentum  CoriolisCoriolis  Two general categoriesTwo general categories  Inferred mass (uses density to convertInferred mass (uses density to convert volumetric to mass flow)volumetric to mass flow)  Direct Mass (actually measure mass)Direct Mass (actually measure mass)
  45. 45. Thermal MassThermal Mass  Measures heat loss from a heat sourceMeasures heat loss from a heat source  Measures temperature rise as flow passesMeasures temperature rise as flow passes a hot tubea hot tube  Mass flow isMass flow is inferredinferred from known physicalfrom known physical properties of fluidproperties of fluid  Usually used for gas applicationsUsually used for gas applications
  46. 46. CoriolisCoriolis  Operates on gyroscopicOperates on gyroscopic principleprinciple  Based on coriolis forcesBased on coriolis forces (angular velocity of earth(angular velocity of earth imparts force on a movingimparts force on a moving object)object)  Fluid flows through U- orFluid flows through U- or S-shaped tube whichS-shaped tube which vibrates at its naturalvibrates at its natural frequencyfrequency
  47. 47. CoriolisCoriolis  Motion of fluid in theMotion of fluid in the tubes resist thistubes resist this vibration (the tubesvibration (the tubes twist)twist)  Velocity of the tubeVelocity of the tube deflection isdeflection is proportional to massproportional to mass flowflow
  48. 48. Pros & ConsPros & Cons ProsPros  Extremely accurateExtremely accurate (0.15%)(0.15%)  Directly measures massDirectly measures mass  No Re constraintsNo Re constraints  Low maintenanceLow maintenance  Can measure density,Can measure density, temperature, mass andtemperature, mass and volumetric flowvolumetric flow ConsCons  High initial capitalHigh initial capital costscosts  Small pipe diametersSmall pipe diameters needed cause largeneeded cause large pressure droppressure drop  Not recommended forNot recommended for measurementsmeasurements involving gasesinvolving gases
  49. 49. Angular MomentumAngular Momentum  Measures the force required toMeasures the force required to resist the angular momentumresist the angular momentum of flowing fluidof flowing fluid  This force proportional to massThis force proportional to mass  Device consists of:Device consists of:  MotorMotor  Impeller (imparts theImpeller (imparts the momentum)momentum)  Turbine to resist theTurbine to resist the angular momentum torqueangular momentum torque is appliedis applied  The torque needed to resistThe torque needed to resist rotation of the turbine isrotation of the turbine is transmitted to a displaytransmitted to a display
  50. 50. DrawbacksDrawbacks  Only clean liquids can be usedOnly clean liquids can be used  Lots of moving parts that often requireLots of moving parts that often require maintenancemaintenance  ExpensiveExpensive
  51. 51. SourcesSources  http://www.manufacturing.net/ctl/article/CA185726http://www.manufacturing.net/ctl/article/CA185726  http://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_pd.cfmhttp://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_pd.cfm  http://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_dp.cfmhttp://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_dp.cfm  www.manufacturing.net/ctl/article/CA325984www.manufacturing.net/ctl/article/CA325984  http://www.jlcinternational.com/gas_liquid_turbine_flowmeters.htmhttp://www.jlcinternational.com/gas_liquid_turbine_flowmeters.htm  http://www.ddc-online.org/inout/inout_chapt02_ana_06flow.aspxhttp://www.ddc-online.org/inout/inout_chapt02_ana_06flow.aspx  http://www.omega.com/prodinfo/magmeter.htmlhttp://www.omega.com/prodinfo/magmeter.html  http://www.envitech.co.uk/Product_Images/FlowMeter4210.jpghttp://www.envitech.co.uk/Product_Images/FlowMeter4210.jpg  http://www.seilenterprise.co.kr/English/Technology/flowmetertypes.htmhttp://www.seilenterprise.co.kr/English/Technology/flowmetertypes.htm  http://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_tar.cfmhttp://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_tar.cfm  http://www.omega.com/literature/transactions/volume4/images/10_Fig_01_l.GIFhttp://www.omega.com/literature/transactions/volume4/images/10_Fig_01_l.GIF

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