1.1. Fluid Properties.pdf

Fluid Properties

1. Fluid Mechanics
Presented by:
Suman Acharya

2. 2
INTRODUCTION
Fluid mechanics deals with liquids and
gases in motion or at rest.
Fluid mechanics:It is the branch of science
which deals with the behavior of fluid (Liquids
or Gases) at rest as well as in motion.
FluidStatics:The study of fluid at rest is
called fluid statics
FluidKinematics:The study of fluid in motion
where pressure forces are not considered
FluidDynamics:The study of fluid in motion,
where pressure forces are considered

3. 3
Automobile
Application Areas of Fluid Mechanics

4. 4
Aerospace
Application Areas of Fluid Mechanics

5. 5
Application Areas of Fluid Mechanics
Fluid dynamics is used extensively
inthe design of artificial hearts.
Shownhere is the Penn State
Electric TotalArtificial Heart.
Biomedical

6. 6
Sports
Application Areas of Fluid Mechanics

7. 7
Buildings
Application Areas of Fluid Mechanics

8. 8
Environment
Application Areas of Fluid Mechanics

9. 9

10. 10

13. 13
What is a Fluid?
Afluidisasubstancethatdeformscontinuouslyundertheapplicationofashear
(tangential)stressnomatterhowsmalltheshearstressmaybe
Asolidcanresistanappliedshearstressbydeforming.
Afluiddeformscontinuouslyundertheinfluenceofashearstress,nomatterhow
small.
Insolids,stressisproportionaltostrain,butinfluids,stressisproportionaltostrain
rate.
Whenaconstantshearforceisapplied,asolideventuallystopsdeformingatsome
fixedstrainangle,whereasafluidneverstopsdeformingandapproachesaconstant
rateofstrain.

14. 14
What is a Fluid?
The tendency of continuous deformation of substance is fluidity.
A fluid would therefore, flow when subjected to shear force.
Theamount of deformation of solid depends on the solids modulus of rigidity
The rate of deformation of fluid depends on fluid viscosity
We refer to the solid as being elasticand fluid as being viscous
Solid exhibit “springness”
Fluid is “zero memory substance”

15. 15
Fluid and non-fluid
There are two states of matter: Fluidand Non-Fluid
The Fluid State refers to liquid, vapor orgas andnon-fluid state means
only solid phase of matter
Very Strong Intermolecular attractive forces exist in a solid
Weakerin liquid
Extremelyweakin vaporand gas

16. 16
Is Asphalt a Fluid?
Itappearsandbehaveasasolidsinceitresistsshearstressforshortperiod
oftime
Whentheforcesareexertedoverextendedperiodsoftime,theasphalt
deformsslowly,behavingasafluid
Someplastics,lead,andslurrymixturesexhibitsimilarbehavior

17. 17
The arrangement of atoms in different phases: (a) molecules are at relatively fixed
positionsin a solid, (b) groups of molecules move about each other in the liquid phase,
and(c) individual molecules move about at random in the gas phase.
Intermolecular bonds are strongest in solids and weakest in gases.
Solid:The moleculesin a solid are arranged in a pattern that is repeated throughout.
Liquid:In liquids moleculescan rotate and translate freely.
Gas:In the gas phase, the molecules are far apart from each other, and molecular
ordering is nonexistent.

18. 18
Unlike a liquid, a gas
does not form a
free surface, and it
expands to fill the
entire available
space.
In aliquid, groups of molecules can move relative to each other, but thevolume
remains relatively constant because of the strong cohesive forcesbetween the
molecules.As a result, a liquid takes the shape of the container itis in, and it forms
a free surface in a larger container in a gravitational field.
Agasexpands until it encounters the walls of the containerand fills the entire
available space. This is because the gas molecules arewidely spaced, and the
cohesive forces between them are very small. Unlikeliquids, a gas in an open
container cannot form a free surface.

19. 19
Gas and vapor are often used as synonymous words.
Gas:The vapor phase of asubstance is customarily called a gas when it is above the
critical temperature.
Vapor:Usuallyimplies that the current phase is not far from a state ofcondensation.
Onamicroscopicscale,pressureis
determinedbytheinteractionofindividual
gasmolecules.However,wecanmeasure
thepressureonamacroscopicscalewitha
pressuregage.
Macroscopicor classical approach:Doesnot
require a knowledge of the behavior of individual
molecules andprovides a direct and easy way to
analyze engineering problems.
Microscopicor statistical approach:Basedon
the average behaviorof large groups of individual
molecules.

22. 22
A small shear force is applied on an element and then removed. If the element regains it’s original position,
what kind of an element can it be?
SolidLiquidFluid Gaseous
If a person studies about a fluid which is at rest, what will you call his domain of study?
Fluid MechanicsFluid StaticsFluid KinematicsFluid Dynamics
The value of the compressibility of an ideal fluid is
ZeroUnityInfinityMore than real fluid
The value of the Bulk Modulus of an ideal fluid is
ZeroUnityInfinityLess than real fluid

23. 23
A small shear force is applied on an element and then removed. If the element regains it’s original position,
what kind of an element can it be?
SolidLiquidFluid Gaseous
If a person studies about a fluid which is at rest, what will you call his domain of study?
Fluid MechanicsFluid StaticsFluid KinematicsFluid Dynamics
The value of the compressibility of an ideal fluid is
ZeroUnityInfinityMore than real fluid
The value of the Bulk Modulus of an ideal fluid is
ZeroUnityInfinityLess than real fluid

24. Fluid as continuum
Fluidmechanicsissupposedtodescribemotionoffluids&relatedphenomenaat
microscopicscales,whichassumesthatfluidcanberegardedasacontinuous
medium.
Anysmallvolumeelementinthefluidisalwayssupposedsolargethatitstill
containsaverygreatnumberofmolecules.
Whenweconsiderinfinitelysmallelementofvolume,wemeanverysmall
comparedwiththevolumeofbodyunderconsiderationbutlargecomparedwith
distancebetweenmolecules.
Fig. Definition of density at a pointFig. Fluid as molecules flowing
randomly moving in space

25. Fluid as continuum
ifδV=0.001mm3(aboutthesizeofagrainofsand),therewillonaveragebe
2.5×1013moleculespresent
HencewecanconcludethatairatSTP(andothergases,andliquids)canbe
treatedasacontinuousmediumaslongasweconsidera“point”tobeno
smallerthanaboutthissize
Thisissufficientlypreciseformostengineeringapplications
Asaconsequenceofthecontinuumassumption,eachfluidpropertyis
assumedtohaveadefinitevalueateverypointinspace
Thusfluidpropertiessuchasdensity,temperature,velocity,andsoonare
consideredtobecontinuousfunctionsofpositionandtime

26. Knudsen Number
!!=#
$
L is the length scale of the container
!is the mean free path of the molecules
For continuum assumption to be valid "!<0.1
Mol-to-mol collisions > mol-to-vessel collisions

27. NO-SLIP CONDITION
27
The development of a velocity
profile due to the no-slip condition
as a fluid flows over a blunt nose.
A fluid flowing over a stationary
surface comes to a complete stop at
the surface because of the no-slip
condition.
Whenafluidflowisboundedbyasolidsurface,molecularinteractionscause
thefluidincontactwiththesurfacetoseekmomentumandenergy
equilibriumwiththatsurface
Allliquidsessentiallyareinequilibriumwiththesurfacestheycontact

28. NO-SLIP CONDITION
Fig:Theno-slipconditioninwaterflowpastathinfixedplate.Theupper
flowisturbulent;thelowerflowislaminar.Thevelocityprofileismade
visiblebyalineofhydrogenbubblesdischargedfromthewireacrossthe
flow
No-temperature-
jump Condition

29. System Approach Control Volume
•System:A quantity of matter or a region in space chosen
for study.
•Surroundings:The mass or region outside the system
•Boundary:The real or imaginary surface that separates
the system from its surroundings.
•The boundary of a system can be fixedor movable.
•Systems may be considered to be closed or open.
29
•Closed system
(Control mass):
A fixed amount of
mass, and no
mass can cross
its boundary.

30. System Approach Control Volume
Acontrolvolumeisanarbitraryvolumeinspacethroughwhich
fluidflows.Thegeometricboundaryofthecontrolvolumeis
calledthecontrolsurface.Thecontrolsurfacemayberealor
imaginary;itmaybeatrestorinmotion.

31. System Approach CONTROL VOLUME
•Opensystem(controlvolume):
Acontrolvolumeisanarbitraryvolumeinspacethroughwhichfluidflows.It
usuallyenclosesadevicethatinvolvesmassflowsuchasacompressor,
turbine,ornozzle.
•Both mass and energy can cross the boundary of a control volume.
•Control surface:
The geometric boundary of the control volume is called the control surface.
The control surface may be real or imaginary; it may be at rest or in motion.
31
An open system (a
control volume) with one
inlet and one exit.

32. Lagrangian Description
Lagrangiandescriptionoffluidflowtracksthepositionandvelocityof
individualparticles.
Difficulttouseforpracticalflowanalysis.
•Fluidsarecomposedofbillionsofmolecules
•Interactionbetweenmoleculeshardtodescribe/model
However,usefulforspecializedapplications
•Sprays,particles,bubbledynamics,rarefiedgases
NamedafterItalianmathematicianJosephLouisLagrange(1736-1813)

33. Eulerian Description
A flow domainor control volumeis defined by which fluid flows in and out.
We define field variables which are functions of spaceand time.
Pressure field, P=P(x,y,z,t)
Velocity field, V =V (x, y, z,t)
Acceleration field,a = a (x, y, z,t)
These (and other) field variables define the flow field.
Named after Swiss mathematician Leonhard Euler(1707-1783).

34. FluiddynamicmeasurementsaresuitedtotheEuleriansystem.For
example,whenapressureprobeisintroducedintoalaboratoryflow,itis
fixedataspecificposition(x,y,z).Itsoutputthuscontributestothe
descriptionoftheEulerianpressurefieldp(x,y,z,t).Tosimulatea
Lagrangianmeasurement,theprobewouldhavetomovedownstreamat
thefluidparticlespeeds;thisissometimesdoneinoceanographic
measurements,whereflowmetersdriftalongwiththeprevailingcurrents.
Eulerian and Lagrangian Descriptions

35. Thetwodifferentdescriptionscanbecontrastedintheanalysisoftrafficflow
alongafreeway.Acertainlengthoffreewaymaybeselectedforstudyand
calledthefieldofflow.Obviously,astimepasses,variouscarswillenterand
leavethefield,andtheidentityofthespecificcarswithinthefieldwill
constantlybechanging.
Thetrafficengineerignoresspecificcarsandconcentratesontheiraveragevelocityasafunctionoftimeandpositionwithinthefield,plustheflowrateor
numberofcarsperhourpassingagivensectionofthefreeway.Thisengineer
isusinganEuleriandescriptionofthetrafficflow.Otherinvestigators,suchas
thepoliceorsocialscientists,maybeinterestedinthepathorspeedor
destinationofspecificcarsinthefield.Byfollowingaspecificcarasa
functionoftime,theyareusingaLagrangiandescriptionoftheflow.

36. Thebasiclawsthatweapplyinourstudyoffluidmechanicscanbeformulatedin
termsofinfinitesimalorfinitesystemsandcontrolvolumes.Asyoumightsuspect,the
equationswilllookdifferentinthetwocases.Bothapproachesareimportantinthe
studyoffluidmechanicsandbothwillbedevelopedinthecourseofourwork.
Inthefirstcasetheresultingequationsaredifferentialequations.Solutionofthe
differentialequationsofmotionprovidesameansofdeterminingthedetailedbehavior
oftheflow.Anexamplemightbethepressuredistributiononawingsurfacethe
informationsoughtdoesnotrequireadetailedknowledgeoftheflow.
Weoftenareinterestedinthegrossbehaviorofadevice;insuchcasesitismore
appropriatetouseintegralformulationsofthebasiclaws.Anexamplemightbetheoverallliftawingproduces.Integralformulations,usingfinitesystemsorcontrol
volumes,usuallyareeasiertotreatanalytically.Thebasiclawsofmechanicsand
thermodynamics,formulatedintermsoffinitesystem.
Differential versus Integral Approach

37. Thedifferentialformmeantodividethecontrolvolumeintoalargenumberof
smallelementsandapplythecontinuity,momentum,energyetc.asinCFD
software.
Theintegralformconsiderthecontrolvolumeasoneelementandapply
themass,momentumandenergyequations.
Integral Approach
Will not give a point by point
description of fluid motion.
Gives only the overall effect of
fluid motion on a structure or
body
Differential Approach
Does give a point by point
description of fluid motion

38. Properties of fluid
•Density or mass density
It is defined as the ratio of the mass of a fluid to it’s volume
'=)*++,--./01
2,./)3,--./01
•Specific weight or weight density
It is the ratio between the weight of a fluid to it’s volume
4=4305ℎ7,--./01
2,./)3,--./01='∗5

39. Properties of fluid
•Specific volume
Volume per unit mass of fluid is called specific volume
+93:0-0:2,./)3=2,./)3,--./01
)*++,--./01=1
'
•Specific gravity
It is defined as the ratio of the weight density (or density) of a fluid to the weight density (or density) of
a standard fluid. For liquids, water & for gases, air is taken as a standard fluid.
!"#$%&%$'()*%+,=.#%'ℎ+0#1!%+,0#1!%+,2&3%45%0(')!)
.#%'ℎ+0#1!%+,0#1!%+,2&8)+#(()%()

40. Calculate the density, specific weight & weight of one liter of petrol of specific
gravity of 0.7.
(700 Kg/m3, 6867 N/m3, 6.867 N)
Calculate the specific weight, density & specific gravity of one liter of a liquid
which weighs 7N.
Numerical

41. 31
VISCOSITY
Viscosity: Viscosity is quantitative measure of a fluid’s resistance to flow. It
is defined as the property of a fluid which offers resistance to the movement
of one layer of fluid over another adjacent layer of fluid.
Theviscosityofafluidisa
measureofits“resistanceto
deformation.”
Viscosityisduetotheinternal
frictionalforcethatdevelops
betweendifferentlayersof
fluidsastheyareforcedto
moverelativetoeachother.
It determines the fluid strain rate
that is generated by a given
applied shear stress.
Newton law of viscosity states
that the shear stress on a fluid
element layer is directly
proportional to the rate of shear
strain
;=<1/
1=(?/)")

42. 32
The behavior of a fluid in laminar flow between
two parallel plates when theupper plate moves
with a constantvelocity.
Newtonian fluids: Fluids for which the rate of
deformation is proportional to the shear stress.
Shear
stress
Shearforce
µcoefficientofviscosity
Dynamic (absolute)viscosity
kg/m ×sorN ×s/m2orPa×s
1 poise = 0.1 Pa ×s
du
dy=v
ld)≈tan.)=./
0=1.2
0=.3
.4.2
.)
.2=.3
.4
The rate of shear strain is equal to velocity gradient

43. 33
Therateofdeformation(velocity
gradient)ofaNewtonianfluidis
proportionaltoshearstress,andthe
constantofproportionalityisthe
viscosity.
Variation of shear stress withthe rate
of deformation for Newtonian and
non-Newtonian fluids (the slope of a
curve at a point is the apparent
viscosity of the fluid at thatpoint).

44. Rheological Behavior of Fluids
Itisastudyofrelationshipbetweenforceanddeformation
incontinuousmedium.
Non-Newtonianfluidsarecommonlyclassifiedashaving
timedependentandortimeindependentbehavior.
For,engineeringpurposestheyaremodelledas
;56=B1/
1=
7
Here,nisflowbehaviorindexandktheconsistencyindex
Theexpressioncanalsobeexpressedas
;56=B1/
1=
7891/
1==C1/
1=
HereCisreferredasapparentviscosity

45. Rheological Behavior of Fluids
;56=B1/
1=
7891/
1==C1/
1=
HereCand<aresimilar,differenceis<isconstantwhile
Cdependsonshearrate
n<1:Pseudoplasticfluids(apparentviscositydecreases
withincreasingdeformationrate)E.g.Polymersolutions
n>1:Dilatantfluids(Apparentviscosityincreaseswith
increasingdeformationrate)E.g.starch
Binghamplasticsaremodelas
;56=;5+<:1/
1=

46. Kinematic Viscosity-It is defined as the ratio of dynamic viscosity and density
of fluid.
"0E3)*70:20+:,+07=(2)=F0+:,+07=
13E+07=
What is physical significance of kinematic viscosity?
It can be thought of as a “viscosity density”,i.e., how much momentum a fluid
can transfer per volume
The higher thekinematic viscosity, the more a fluid is able to transport
momentum. Highly viscous fluids and liquids of low density are good
candidates for excellent momentum transport properties.

47. Variation of viscosity
Generallyspeaking,theviscosityofafluidincreasesweaklywithpressure.
Increasingpressurefrom1to50atm.Willincrease!ofaironlyby10percent
Temperaturehoweverhasastrongeffect,with!increasingwithTforgases&decreasingforliquid.
SI unit of viscosity= Ns/m2= Pa.s
The unit of viscosity in CGS is Poise
One poise = 1/10 Ns/m2
One centipoise = 1/100 Poise

48. Numerical
Aplate0.025mmdistantfromafixedplates,movesat60cm/sandrequiresa
forceof2Nperunitareai.e.2N/m2tomaintainthisspeed.Determinethe
fluidviscositybetweentheplates.
(8.33*10-4Poise)
Aplatehavinganareaof0.6m2isslidingdowntheinclinedplaneat30otothe
horizontalwithavelocityof0.36m/s.Thereisacushionoffluid1.8mmthick
betweentheplaneandtheplate.Findtheviscosityoffluidiftheweightofthe
plateis280N.
(11.66Poise)

49. Numerical
1. A large plate is pulled at a constant speed of 4 m/s over a fixed plate. The
space between the plates is filled with engine oil. The shear stress developed
on the upper plate and its direction are to be determined for parabolic and
linear velocity profile cases. Viscosity =0.8374 Pa.s
(------N/m2 , 670 N/m2)
2. The viscosity of a fluid is to be measured by a viscometer constructed of two
40 cm long concentric cylinders. The outer diameter of the inner cylinder is 12
cm, and the gap between the two cylinder is 0.15 cm. The inner cylinder is
rotated at 300 rpm, and the torque is measured to be 1.8 Nm. Determine the
viscosity of the fluid
(0.158 Ns/m2)

50. Question
When the force P is applied to the plate, the velocity profile for a
Newtonian fluid that is confined under the plate is approximated by
u=(4.23 y^1/3) mm/s, where y is in mm. Determine the shear stress
within the fluid at y=5mm and minimum shear stress. Take viscosity=
0.630 *10^-3 N.s/m^2.

51. Question
The Newtonian fluid is confined between a plate and a fixed surface.
If its velocity profile is defined by U= (8y-0.3y^2) mm/s, where y is
in mm, determine the shear stress that the fluid exerts on the plate
and on the fixed surface and the force P that must be applied to the
plate to cause this motion.The plate has a surface area of 15(10^3)
mm^2 in contact with the fluid. Take viscosity = 0.482 N.s/m^2

52. Question
If a force of P = 2 N causes the 30-mm-diameter
shaft to slide along the lubricated bearing with a
constant speed of 0.5 m/s, determine the viscosity
of the lubricant and the constant speed of the shaft
when P = 8 N. Assume the lubricant is a Newtonian
fluid and the velocity profile between the shaft and
the bearing is linear. The gap between the bearing
and the shaft is 1 mm.
Viscosity: 0.8498, V= 2 m/s

53. Question
A plastic strip having a width of 0.2 m and a mass of 150
g passes between two layers A and B of paint having a
viscosity of 5.24 N.s/m2 . Determine the force P
required to overcome the viscous friction on each side if
the strip moves upwards at a constant speed of 4 mm/s.
Neglect any friction at the top and bottom openings, and
assume the velocity profile through each layer is linear.
Ans: 1.84 N

54. Question
Determine the torque T required to rotate the disk with a constant angular velocity w= 30 rad/s. The oil has a thickness of 0.15 mm. Assume the velocity profile is linear, and viscosity= 0.428 N.s/m2.
Ans: 68.1 N.m

55. Liquidshavecohesionandadhesion,bothofwhich
areformsofmolecularattraction.Cohesionenablesa
liquidtoresisttensilestress,whileadhesionenablesit
toadheretoanotherbody.Attheinterfacebetweena
liquidandagas,i.e.,attheliquidsurface,andatthe
interfacebetweentwoimmiscible(notmixable)
liquids,theout-of-balanceattractionforcebetween
moleculesformsanimaginarysurfacefilmwhich
exertsatensionforceinthesurface.Thisliquid
propertyisknownassurfacetension
Surface Tension

56. Ideal fluid and Real fluid
Ideal fluid:Real fluid:
Viscositynoyes
Surface Tensionyesyes
Compressibilitynoyes
Densityyesyes
12/19/22 56

57. Vapor Pressure and Cavitation
Achangefromtheliquidstatetothegaseousstateisknownasvaporization
Thevaporpressureofaliquidistheequilibriumpressureofavaporaboveits
liquid
Cavitationistheformation,growth,andsubsequentcollapseofthebubblesin
water

58. 1. The weightper unit volume of a liquid at a STP is called
a. Specific Weightb. Mass Densityc. SpecificGravityd. Noneof these
2. The specific gravity of an oil whose specific weight is 7.85 kN/m3
a. 0.8b. 1c. 1.2d. 1.6
3. Kinematic viscosity is theproduct of dynamic viscosity and the density of the liquid
a.Yes b. No
4. The mercury does not wet the glass.This is due to the property of the liquid known as
a.Cohesionb. Adhesionc. Viscosityd. Surface Tension

59. Aninfiniteplateismovedoverasecondplateonalayerofliquidasshown.For
smallgapwidth,d,weassumealinearvelocitydistributionintheliquid.The
liquidviscosityis0.65centipoiseanditsspecificgravityis0.88.Determine
i)Thekinematicviscosityoftheliquid
ii)Theshearstressontheupperplate
iii)Theshearstressonthelowerplate
iv)Thedirectionofeachshearcalculatedabove

60. Thank You