Fluid Mechanics:Properties of fluid basics

Fluid

1. Basics of Fluid
Mechanics
Let the fun begin…

2. DEGREEPROGRAM: MechanicalEngineering
COURSETITLE: FluidMechanics
COURSECODE: PCC-ME203
SEMESTEROFFERED:4th
REQUIREDCOURSEOR
ELECTIVECOURSE:
Requiredcourse
NameoftheFaculty: DipakKumarMandal
Contacts: 3L-0T-3P
Credit: 4.5
PREREQUISITES: PrerequisitesbyTopics:
??????Mathematics
??????GeneralPhysics

3. Module-Module:1(8lectures)
Definitionoffluid,Unitsanddimensions,Newton’slawofviscosity,Propertiesoffluids,mass,density,
specificvolume,specificgravity,viscosity,surfacetensionandcapillarity,vaporpressure,
compressibilityandbulkmodulus.Hydrostatics;fluidforceonplaneandcurvedsurfaces,
manometers,buoyancy,uniformlyacceleratedmotion.
Module-2(4lectures)
Kinematicsoffluidflow:Generalizedcontinuityequation,IrrotationalmotionandsolutiontoLaplace
equation.Conceptofstreamlines,EquipotentialLines,FlowNets.
Module-3(6lectures)
Dynamicsoffluidflow:Controlvolumeandcontrolsurface,applicationofcontinuityequationand
momentumequation,Bernoulli’sequationanditsapplications.
Module-4(4lectures)
Conceptofboundarylayer,boundarylayerthickness,Displacementthickness,momentumthickness,
energythickness.
Module-5(8lectures)
Laminarviscousflowthroughcircularconduits,CouetteandPoisuielleflow,Turbulentflowthrough
pipes,DarcyWeisbachequation,frictionfactorforsmoothandroughpipes,Moody’sdiagram.
Module-6(6lectures)Needfordimensionalanalysis,methodsofdimensionanalysis,Similitudeand
typesofsimilitude,Dimensionlessparameters,applicationofdimensionlessparametersModelanalysis.
Module-7(6lectures)
Forcesonimmersedbodies,conceptsofseparation,dragforce,circulationandliftforce.

4. PCC-ME203
FluidMechanics
RecommendedBooks:
1.SomandBiswas;FluidMechanicsandmachinery;TMH.
2.Cengal;FluidMechanics;TMH.
3.FluidMechanics&Machinery–R.K.Bansal,LuxmiPublications.

5. Courseoutcome
CO-1Understandthebasicprinciplesoffluidmechanics,including
propertiesoffluids.
CO-2Determineandinterpretpressureonimmersedplanarand
curvedsurfacesduetostaticfluids.
CO-3Analyzeandapplycontinuityandmomentumequationsto
solveproblemsrelatedtoflowthroughconduits,suchaspipes
andchannels.
CO-4Understandandapplydimensionalanalysistosimplifyfluid
mechanicsproblemsandcomprehendtheboundarylayer
concept,includingitsimplicationsforflowseparationand
drag.

6. INTRODUCTION
Statics, Kinematics and Dynamics
DEFINITION OF STRESS.

7. DEFINITION OF FLUID
DIFFERENCE BETWEEN SOLID AND FLUID .
If there is no flow or velocity. It means fluid is at rest, i. e., no shear
stress, i.e. persistence of all normal forces

8. CONTINUUM
FLUID PROPERTIES.
SIGNIFICANCE OF FLUID MECHANICS
Density or mass density
Specific Weight or Weight Density
Specific volume
Specific gravity (S)
SURFACE TENSION
CAPILLARY

9. Viscosity
Rate of shear strain
= Rate of shear deformation
= Velocity gradient
Water Density Specificweight
MKS 1000/9.81msl/m
3
1000Kgf/m
3
SI 1000Kg/m
3
1000X9.81N/m
3

10. VISCOSITY
.
VISCOSITYdy
du
 dy
du

Constantofproportionality=dynamicviscosity
•VISCOSITRateof shear strain=Rate of shear deformation = Velocity gradient 
dy
du

11. Viscosity
Rate of shear strain
= Rate of shear deformation
= Velocity gradient
Constant of proportionality
= dynamic viscosity dy
du

Newton’s law of viscosity
Water, air, mercury etc. is called Newtonian fluid.
The fluid which does not obey Newton’s law of viscosity, is called Non-
Newtonian fluid, i.e., blood, paint slurry etc.
Note:Frictionalforcecomesduetoshearstresswhichcomesfromviscosityorviscous
force.
Note:Shearstressiszerodoesnotmeanthatthereisnovelocity.Ifboththefluid
layersaremovingsamespeedthenshearstressbetweenthetwolayerswillbezero.
Unitsofviscosity
M,L,Tarebasicdimensions.
Or,
SIunit, orKg/ms.
CGSunit, orPoise.
1centipoise(CP)=1Poise/100
10Poise=1NS/m2. 
11
1
22
1
2
/



















 TML
T
LMLT
T
FL
dydu

 2
2



 FTL
length
timeForce
 2
/mNS 2
/cmdyneS

12. Viscosity
Rate
of
shear s
For Newtonian fluid, Coefficient of viscosity depends strongly on temperature
but varies very little with pressure.
For liquids: temperature , viscosity
For gases, temperature , viscosity
Causesofviscosity
(I) Intermolecularforceofcohesion:Duetostrongcohesiveforcesbetween
themoleculesandlayerinamovingfluidtrytodragtheadjacentlayerstomove
withanequalspeedandthusproducetheeffectofviscosity.
(II) Molecularmomentumexchange:Theindividualmoleculeofafluidis
continuouslyinmotionandthismotionmakesapossibleprocessofexchangeof
momentumbetweendifferentmovinglayersofthefluid.     

  TLMLTML
2311
/

 sm/
2
 scm/
2

KinematicViscosity
= Stoke

13. Viscosity
Rate
of
shear s
Idealfluid:thisisanimaginaryfluid.Afluidwhichisincompressibleandishavingno
viscosityisknownasidealfluidanditsmotionasidealorinviscidflow.
Different types of fluids ,0 0
Realfluid:Afluidwhichpossessesviscosityisknownasrealfluid.Actuallyallthe
fluidsarerealfluidsinpractice.
Newtonianfluid:WhichobeysthelawsofNewton`sviscositycalledNewtonianfluid,
i.e.,air,water.
NonNewtonianfluid:WhichdoesnotobeythelawsofNewton`sviscosity,i.e.,
blood,paint,milk,printerink,geleteneetc.
IdealBinghamPlastic:Shearstressisproportionaltoshearstrainaftersomeyield
value,i.e.,inarangeofshearstress,thereisnosheardeformation.Itviolatesbasis
ofdefinitionoffluid.Examples:toothpastewhere,continuousflowoccursafter
certainamountofshearforce.

14. Viscosity
Rate
of
shear s
Thegeneralequationofviscositycanbewrittenas
ForNewtonianfluid,consistencyindex,k=,andflowbehaviorindex,n=1
Ifn>1i.e.,Non-Newtonianfluid,calleddilatentorshearthickeningfluid.Where,
viscosityincreaseswithsheardeformation.Examples:Slurrywater,sugarwater
mixture,butteretc.Forthis,topumpshearthickeningfluid,pumpshouldrunatslow
speed.Ifspeedincreasesduetoincreaseofviscosity,morepowerisrequiredto
pumptheliquid
Forn<1,isalsonon-Newtonianfluid,calledPseudoplasticfluid.Here,viscosity
decreaseswithrateofsheardeformation.Examples:blood,paint,milkprinterink,
etc.Itisalsocalledshearthinningfluid.Thepracticalexamplehasbeenobservedfor
coloringbypaint.Withmoresheardeformationitiseasytocolorn
dy
du
k








 

15. Viscosity
Rate
of
shear s
P-1:Thevelocitydistributionofflowoveraplateisparabolicwithvertex
30cmfromtheplate,wherethevelocityis180cm/s.Iftheviscosityof
thefluidis0.9N.s/m
2
,findthevelocitygradientsandshearstressat
distancesof0,10and30cmfromtheplate.
P-2:Anoilfilmofthickness0.005misusedforlubricationbetweena
squareplateofsize40cm40cmandaninclinedplanehavinganangle
ofinclinationof30deg.Theweightofthesquareplateis4.5Nandit
slidesdownovertheplanewithauniformvelocityof12.5m/sec.Find
thedynamicviscosityoftheoil.Alsofindkinematicviscosityifdensityis
800Kg/m3.
P-3:Ina120mmlongjournalbearingarrangement,theclearance
betweenthetwoatconcentricconditionis1.5mm.Theshaftis400mm
diameterandrotateswith200rpm.Thedynamicviscosityofthe
lubricantusedis0.7kg/msandthevelocityvariationinthelubricantis
linear.ConsideringthelubricanttobeNewtonian,determinethetorque
requiredtoovercomethefrictioninbearingandpowerlossdueto
friction.