Viscosity Measurement

This slide contains a brief description of viscosity and the methods and devices to measure it.

1. Viscosity
Measurement
ER.FARUKBINPOYEN
FARUK.POYEN@GMAIL .COM

2. Content:
Definition
Coefficient
Units
Measuring Devices
2

3. Viscosity –Definition and Formula
Viscosityisthemeasureofasubstance'sresistancetomotionunderan
appliedforce.
Theformulaformeasuringviscosityisfairlysimple:
????????????�??????��??????��=μ= �ℎ�??????��������ℎ�??????��??????��=τ/γ
Shearstressistheforceperunitarearequiredtomoveonelayeroffluid
inrelationtoanother.
Shearrateisthemeasureofthechangeinspeedatwhichintermediate
layersmovewithrespecttooneanother.
3

4. Viscosity –Coefficient of Viscosity
ViscousDrag(DragForce)(F)-Thefrictionalbackwardforceexisting
betweenthetwosurfaces.
??????∝??????;??????∝ �??????��
CoefficientofViscosity(μ)
??????=
??????
??????
∗
��
�??????
A=Areaofthelayers;V=Velocity; �??????��=velocitygradient;
z=distancebetweensurfaces.
CoefficientofViscosityisthetangentialbackwardforcethatacts
betweentwofluidlayersofunitarea,situatedunitdistanceapartand
havingunitrelativevelocity,whenthefluidisinstreamlinemotion.
4

5. Viscosity –Newtonian and Non Newtonian Fluid
NewtonianFluid-Atagiventemperatureandshearstress,theviscosity
ofafluidwouldremainconstantregardlessofchangestotheshearrate.
E.g.,Petrol,kerosene,mineraloils,water,saltsolutionsetc.
Non-NewtonianFluid-Mostfluids,however,haveviscositiesthat
fluctuatedependingontheshearrate.ThesearecalledNon-Newtonian
fluids.
Therearefivetypesofnon-Newtonianfluids:thixotropic,rheopectic,
pseudoplastic,dilatant,andplastic.
E.g.,Printer’sink,starch,peanutbutter,tar,chewinggumetc.
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6. Viscosity –Units of Viscosity
CGS Unit –Poise (P).
Centipoise (cP) = 0.01 Poise.
SI Unit of μ–(kg/mt-s) = 10 Poise.
SI Unit of Viscosity –(Newton*Sec/square mt.) = Poiseuille(PI).
Other Unit –Pascal Second (Pa.s).
1 PI = 10 Poise = 1000 cP
1 cP= 1 mPa.s
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7. Viscosity -Types
Therearetwodifferentmeasurementsofviscosityusedtodescribe
fluids,dynamicandkinematicviscosities.
Theseareinterchangeableifthefluiddensityρisknown.
DynamicViscosity(μ)measurestheratiooftheshearstresstotheshear
rateforafluid.
??????=
�ℎ�??????�??????��������
�ℎ�??????�??????���??????��
=
??????
??????
= (????????????)( �??????��)
Kinematicviscosity(ν)measurestheratiooftheviscousforcetothe
inertialforceonthefluid.Kinematicviscosityisanalogoustodiffusivity
ofmassandheat,beingthediffusivityofmomentum.
ν= ??????�
UnitofKinematicViscosityinCGSisStokes(St)=SquareMt/Sec.
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8. Viscosity –Hagen PoiseuilleFormula
HagenPoiseuilleLawisaphysicallawthatgivesthepressuredropin
anincompressibleandNewtonianfluidinlaminarflowflowingthrough
alongcylindricalpipeofconstantcrosssection.
∆�=
8????????????�
��
4
Q=Volumetricflowrate;L=pipelength;R=piperadius;ΔP=pressuredifference;
μ=dynamicviscosity;
�
�????????????=��
2
∆�
�
8

9. Viscosity –Stokes Law
StokesLawdelineatesthefrictionalforce,alsocalleddragforce(F)
exertedonsphericalobjectswithverysmallReynoldsnumbersina
viscousfluid.
The force of viscosity on a small sphere moving through a viscous fluid
is given by
??????=6�??????��
F = drag force, μ= dynamic viscosity, R = radius of spherical object;
v = flow velocity relative to the object.
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10. Viscosity Reynolds Number
Reynoldsnumberisadimensionlessvaluewhichisappliedinfluid
mechanicstorepresentwhetherthefluidflowinaductissteadyor
turbulent.
Thisvalueisobtainedbycomparingtheinertialforcewiththeviscous
force.
TheReynoldsnumberiddenotedbyRe.
��=
��??????
??????
TheKindofflowisbasedonthevalueofRe
1.IfRe<2000,theflowiscalledLaminar
2.IfRe>4000,theflowiscalledturbulent
3.If2000<Re<4000,theflowiscalledtransition.
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11. Viscosity –Measurement Methods
Viscositymeasurementiscarriedoutonthebasisonanyoneofthe
followingthreephenomena.
1.Flowthroughcapillarytube.
2.Dragexperiencedbyafallingballthroughafluid.
3.Dragexperiencedbyoneoftheconcentriccylinderscarryingfluid
betweenthem,whentheoutercylinderisrotating.
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12. Viscosity –Flow through Capillary Tube
Thecapillaryviscometermeasuresthetimebetweenthevolumeof
liquid/sampletopassthroughthelengthofthecapillarytubes.
ViscosityismeasuredemployingHagenPoiseuillelaw.
??????=
&#3627409163;∆&#3627408451;&#3627408453;
4
8&#3627408452;??????
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13. Viscosity –Flow through Capillary Tube
InaCapillaryTubeViscometer,theliquidtobetestedisdrawnintothe
tubetoalevelabovethetopetchedline.
Thetimeisthenobtainedfortheliquidtodraintothebottometched
line.
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14. Viscosity –Falling Sphere Viscometer
Measurestheviscositybydroppingasphereofaspecificweight&
densityandmeasuresthetimeittakesthespheretoreachdesignated
junctures.
Weightbringsthespheredownwhereasthedragforceandbuoyancy
pushthesphereupward.
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15. Viscosity –Falling Sphere Viscometer
Iftheparticlesarefallingintheviscousfluidbytheirownweight,then
aterminalvelocity,alsoknownasthesettlingvelocity,isreachedwhen
thisfrictionalforcecombinedwiththebuoyantforceexactlybalancethe
gravitationalforce.
Theresultingsettlingvelocity(orterminalvelocity)is??????
&#3627408481;&#3627408466;&#3627408479;givenby
??????
&#3627408481;&#3627408466;&#3627408479;=
2
9
∗
&#3627408453;
2
&#3627408468;(&#3627409164;
&#3627408480;−&#3627409164;
&#3627408467;)
??????
Viscosityismeasuredbythefollowingexpression
??????=
??????
2
&#3627408468;(&#3627409164;
&#3627408480;−&#3627409164;
&#3627408467;)
18??????
&#3627408481;&#3627408466;&#3627408479;
D&R–Diameter&Radiusofsphererespectively;
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16. Viscosity –Rotational or Concentric Cylinders
Measuresthetorquerequiredtorevolveanobjectwithinthevolumeof
liquid.
Rotationoftheoutercylinder(typically)withinnercupbeingstatic,
generatesshearonthefluid,causingthefluidtoflowwithinthe
viscometer.
Therotationalviscometerconsistsoftwobasicpartsseparatedbythe
fluidbeingtested.
Thetwopartsmaybe:concentriccylinders(cupandbob),parallel
plates,alowangleconeandplate,oraspindleinsideofacylinder.
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17. Viscosity
Angular velocity of inner cylinder = ω; Tangentialvelocity=&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627409172;;
&#3627408454;ℎ&#3627408466;??????&#3627408479;??????&#3627408475;&#3627408468;&#3627408453;??????&#3627408481;&#3627408466;=γ=
&#3627409173;&#3627408483;
&#3627409173;??????
=
&#3627408453;
&#3627408476;&#3627408482;&#3627408481;&#3627409172;
(&#3627408453;&#3627408476;&#3627408482;&#3627408481;−&#3627408453;
??????&#3627408475;)
;
 μ=&#3627408454;ℎ&#3627408466;??????&#3627408479;&#3627408454;&#3627408481;&#3627408479;&#3627408466;&#3627408480;&#3627408480;&#3627408454;ℎ&#3627408466;??????&#3627408479;&#3627408453;??????&#3627408481;&#3627408466;=τ/γ=>??????=??????∗??????
Polar Moment of Inertia ??????=
??????&#3627408453;
4
2
&#3627408455;&#3627408476;&#3627408479;&#3627408478;&#3627408482;&#3627408466;&#3627408455;=
&#3627408454;&#3627408481;&#3627408479;&#3627408466;&#3627408480;&#3627408480;∗??????&#3627408476;&#3627408473;??????&#3627408479;&#3627408448;&#3627408476;&#3627408474;&#3627408466;&#3627408475;&#3627408481;&#3627408476;&#3627408467;&#3627408444;&#3627408475;&#3627408466;&#3627408479;&#3627408481;????????????
&#3627408465;??????&#3627408480;&#3627408481;??????&#3627408475;&#3627408464;&#3627408466;&#3627408467;&#3627408479;&#3627408476;&#3627408474;&#3627408464;&#3627408466;&#3627408475;&#3627408481;&#3627408466;&#3627408479;&#3627408481;&#3627408476;&#3627408480;&#3627408481;&#3627408479;&#3627408466;&#3627408480;&#3627408480;&#3627408466;&#3627408465;&#3627408480;&#3627408482;&#3627408479;&#3627408467;??????&#3627408464;&#3627408466;
=
??????∗&#3627408445;
&#3627408453;
;
??????&#3627408476;&#3627408479;??????>0.99,&#3627408454;ℎ&#3627408466;??????&#3627408479;&#3627408454;&#3627408481;&#3627408479;&#3627408466;&#3627408480;&#3627408480;??????= &#3627408455;2&#3627409163;??????&#3627408453;
??????&#3627408475;
2
??????=
??????&#3627408475;&#3627408475;&#3627408466;&#3627408479;&#3627408479;??????&#3627408465;??????&#3627408482;&#3627408480;
&#3627408476;&#3627408482;&#3627408481;&#3627408466;&#3627408479;&#3627408479;??????&#3627408465;??????&#3627408482;&#3627408480;
>0.99
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18. Viscosity
Viscosity for concentric cylinders is given by the expression
??????=
&#3627408455;∗(&#3627408453;
&#3627408476;&#3627408482;&#3627408481;−&#3627408453;
??????&#3627408475;)
2??????&#3627408453;
??????&#3627408475;
2
&#3627408453;&#3627408476;&#3627408482;&#3627408481;&#3627409172;&#3627408447;
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19. Viscosity –Syboltor Redwood Viscometer
TheRedwood(Sybolt–calledinUSA)viscometerconsistofvertical
cylindricaloilcupwithanorificeinthecentreofitsbase.Theorifice
canbeclosedbyaball.
Thecylindricalcupissurroundedbythewaterbath.
Thewaterbathmaintainthetemperatureoftheoiltobetestedat
constanttemperature.
Theoilisheatedbyheatingthewaterbathbymeansofanimmersed
electricheaterinthewaterbath
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20. Viscosity -Syboltor Redwood Viscometer
Thisviscometerisusedtodeterminethekinematicviscosityoftheoil.
KinematicViscosity(ν)isgivenincentistokesas
ν=0.226∗t−
195
&#3627408481;
&#3627408467;&#3627408476;&#3627408479;&#3627408481;<100&#3627408480;;0.200∗&#3627408481;−
135
&#3627408481;
&#3627408467;&#3627408476;&#3627408479;&#3627408481;>100&#3627408480;
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21. Viscosity –Zahn Cup
AZahncupisaviscositymeasurementdevicewidelyusedinthepaintindustry.
Itiscommonlyastainlesssteelcupwithatinyholedrilledinthecentreofthebottom
ofthecup.
Measuresbyobservingthetimeittakesthevolumeofliquidtoemptythecupthougha
smallholeinthebottomofacontainer/cups.
Thereisalsoalonghandleattachedtothesides.
Todeterminetheviscosityofaliquid,thecupisdippedandcompletelyfilledwiththe
substance.
Afterliftingthecupoutofthesubstancetheusermeasuresthetimeuntiltheliquid
streamingoutofitbreaksup,thisisthecorresponding"effluxtime".
Effluxisdefinedastherateatwhichaliquidflowsoutofasystem.
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22. Viscosity -Vibrational Viscometer
Bymeasuringthevibrationalwavesusingavibratingrodsubmergedin
fluid,viscosityiscalculatedbyanalyzingthedampeningofthe
vibration.
Thevibroviscometerworksbysendinguniformfrequencyvibrations
outfromtwosensorplateswhichsitsubmergedinthesamplefluid.
Thethicker(moreviscous)thesubstancethemoredrivingcurrentis
requiredtomaintainthevibrationfrequency,theviscosityisthen
workedoutbythepositivecorrelationbetweenthedrivingelectric
currentandtheviscosity.
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23. Viscosity -Vibrational Viscometer
Theviscosityismeasuredbythefollowingequation.
&#3627408453;
??????=
??????
??????&#3627408466;
????????????&#3627408481;
=??????&#3627409163;&#3627408467;??????&#3627409164;&#3627408453;
??????
&#3627408453;
??????=ViscousResistance
F=Force
f=vibrationalfreq.
A=planardimensions
23

24. Viscosity -VROC Viscometer
Viscometer-Rheometer-on-a-Chip)combinesmicrofluidicandMEMS
(Micro-Electro-MechanicalSystems)technologiestomeasuredynamic
viscosityoverawidedynamicrangeofoperation.
Thisviscometerispressuredrivenusingapumpingsystemthatthe
laminarflowtopushtheliquidintoarectangularslitwithpressure
sensors,measuringtheviscosityofafluidthroughthechangein
pressureafterpassingeachpressuresensorwithinthemicrochip.
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25. Reference:
https://www.cscscientific.com/viscosity#targetText=
https://blog.rheosense.com/different-ways-to-measure-
viscosity#targetText
https://www.odinity.com/stokes-law-reynolds-number-measuring-liquid-
viscosity/
https://www.chegg.com/homework-help/
http://encyclopedia.che.engin.umich.edu/Pages/ProcessParameters/Visco
meters/Viscometers.html
http://www.area4.info/Area4%20Informations/Instrumentation-15.htm
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