UEME_2123_Fluid_Mechanics_1_-_Chapter_1.ppt

8/16/2019 UEME_2123_Fluid_Mechanics_1_-_Chapter_1.ppt

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1Ir. Chong Kok Chung UEME 2123 Fluid Mechanics I

Basic Properties of Fluids


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Reference BooksMain textbook : Fundamental of Fluid Mechanics

(7 th Edition SI

!uthor(s : Munson" #kiishi" $oun% and

Rothma&er

Publisher : 'ile& !sia Student Edition

2


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!ssessment est ) : )*+ ('eek 7" )7 th ,ul& -*)." Sunda&"/:0* to 1:0*am

est - : )*+ ( entati2el& 'eek ))

!ssi%nment : )*+ ('eek )0" -- nd !u%ust -*).

3ab Report : )*+

Final Exam : .*+ (4losed book examination


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4on2entional !reas

!erospace!utomoti2ePropulsion

'h& Stud& Fluid Mechanics


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'ind En%ineerin%


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!ir 4ond and 5entilation


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!ero6acoustics


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Biotechnolo%&


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Irri%ation and &droelectric


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Main opicsSome 4haracteristics of Fluids8imensions and 9nits!nal&sis of Fluid Beha2iorsIdeal as 3a;

Fluid Properties4ompressibilit& of Fluids5apor PressureSurface ension


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4haracteristics of Fluids'hat is a Fluid<

'hat is the di=erence bet;een a Solid and a Fluid<


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Fluids comprise the liquid and gas (or apor! phase o" the ph#sical "orms.

$ "luid is a su%stance that de"orms continuousl# under theapplication o" a shear stress no matter ho& small the shear stressma# %e.

$ shearing stress is created &hene er a tangential "orce acts on a

sur"ace.

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8e>nition of Fluid


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'hen a constant shear "orce is applied

)olid de"orms or %ends

Fluid continuousl# de"orms.

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Fluid and Solid


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*ague idea

Fluid is so"t and easil# de"ormed.)olid is hard and not easil# de"ormed.

Molecular structure)olid has densel# spaced molecules &ith large intermolecularcohesi e "orce allo&ed to maintain its shape.

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Fluid and Solid


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)ome materials+ such as slurries+ tar+ putt#+ toothpaste+ and so on+

are not easil# classi"ied since the# &ill %eha e as solid i" theapplied shearing stress is small+ %ut i" the stress e,ceeds somecritical alue+ the su%stance &ill "lo&. -he stud# o" such materialsis called rheology .

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Fluid and Solid

h


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ualitati e aspect

uantitati e aspect

'hat is ualitati e and 'hat is uantitati e/'hat is ualitati e and 'hat is uantitati e/

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4haracteristic 8escription" 8imensionand 9nits


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ualitati e aspect ser es to identi"# the nature+ or t#pe+ o" thecharacteristics ( such as length+ time+ stress+ and elocit#! .

ualitati e description is gi en in terms o" certain primaryquantities, such as Length, L, time, T, mass, M, andtemperature, θ . -he primar# quantities are also re"erred to as

%asic dimensions .

-hese primar# quantities can then used to pro ide a qualitati edescription o" an# other secondary quantity : "or e,ample+ area 0

2+ elocit# 0 - 1 +densit# 0 M 3.

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?ualitati2e !spect


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ro ide a numerical measure o" the characteristics.

4equire %oth a num%er and a standard.

$ standard "or length might %e a meter or "oot+ "or time an houror second+ and "or mass a slug or kilogram.

)uch standards are called units.

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?uantitati2e !spect

d d


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rimar# quantities also re"erred as %asic dimensions

)uch as ength+ + time+ -+ mass+ M+ and temperature+ 5.

Used to pro ide a qualitati e description o" an# othersecondar# quantit#.

)econdar# quantitiesFor e,ample+ area 0 2+ elocit# 0 - 1 +densit# 0 M 3.

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Primar& and Secondar&?uantities


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Mass6M7+ ength6 7+ time6-7+ and -emperature6Mass6M7+ ength6 7+ time6-7+ and -emperature6 θ 77

MLT systemMLT system

Force6F7+ ength6 7+ time6-7+ and -emperature6Force6F7+ ength6 7+ time6-7+ and -emperature6 θ 77FLT systemFLT system

Force6F7+ Mass6M7+ ength6 7+ time6t7+ and -emperature6Force6F7+ Mass6M7+ ength6 7+ time6t7+ and -emperature6θ 77FMLTFMLTθ systemsystem

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S&stem of 8imensions

8imensions !ssociated ;ith 4ommon Ph&sical


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8imensions !ssociated ;ith 4ommon Ph&sical?uantities

8i i ll&


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2

2 gt d =

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$ll theoreticall# deri ed equations are dimensionally

homogeneous 8 that is+ the dimensions o" the le"t side o" theequation must %e the same as those on the right side+ and alladditi e separate terms ha e the same dimensions.

9eneral homogeneous equation alid in an# s#stem o" units.

4estricted homogeneous equation restricted to a particulars#stem o" units.

21.1: t d =

Valid only for the system ofValid only for the system of

units using feet and secondsunits using feet and seconds

8imensionall&omo%eneous


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In addition to the qualitati e description o" the arious quantities

o" interest+ it is generall# necessar# to ha e a quantitati e measureo" an# gi en quantit#.

For e,ample+ i" &e measure the &idth o" this page in the %ook and sa#that it is 1; units &ide+ the statement has no meaning until the unit o"

length is de"ined.

I" &e indicate that the units o" length is a meter+ and de"ine themeter as some standard length+ a unit s#stem "or length has %een

esta%lished.$ unit must %e esta%lished "or each o" the remaining %asic quantities.

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S&stems of 9nits


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ength "t

-ime secondForce l%-emperature oF or o4 o4 0 oF=>?@.:AMass slug 1 l% 1 slug B 1 "t sec 2

9ra it# g 32.1A> "t sec2 'eight ' (l%! 0 m (slug!B g ("t sec 2!

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British ra2itationalS&stem


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ength m

-ime secondMass Kg-emperature o K o K o C=2A3.1?Force De&ton 1 D 1 KgB1 m sec 2

'ork oule ( ! 1 DBmo&er 'att ('! ' sec DBm sec

9ra it# g 0 @.G;A m sec2 'eight ' (D! 0 m (Kg! B g (m sec 2 ! 1 kg mass &eights @.G1D

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International S&stem (SI

En%lish En%ineerin% (EE


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Mass l%m

Force l%"

ength "t

-ime second

-emperatureo

4 (a%solute temperature!

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En%lish En%ineerin% (EES&stem


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Ma@or En%ineerin% Blunders 4aused b& Fault&


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Ma@or En%ineerin% Blunders 4aused b& Fault&Measurement

4on2ersion Factor


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4on2ersion Factor

4on2ersion Factor


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4on2ersion Factor

S& f 9 i


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M -t

International )#stem (kg+ m+ s+ oK!

F -t


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)I (kg+ m+ s+oK!

1D 0 1kgm s 2


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$ tank o" liquid ha ing a total mass o" 3: kg rests on a support in theequipment %a# o" the )pace )huttle. Hetermine the "orce (in ne&tons! thatthe tank e,erts on the support shortl# a"ter li"t o"" &hen the shuttle isaccelerating up&ards as sho&n in the "igure at 1?"t s 2 .

Example )A) B and SI9nits

Example )A) B and SI


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$ tank o" liquid ha ing a total mass o" 3: kg rests on a support in theequipment %a# o" the )pace )huttle. Hetermine the "orce (in ne&tons! thatthe tank e,erts on the support shortl# a"ter li"t o"" &hen the shuttle isaccelerating up&ards as sho&n in the "igure at 1?"t s 2 .

Example )A) B and SI9nits

N

a g m F

maW F or am F

f

f

?1G

7!3;>G.;61?G1.@(3:

!(

=

+=

+=

=−=∑

! l& i f Fl id B h 2i


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$nal#sis o" an# pro%lem in "luid mechanics necessaril# includesstatement o" the %asic la&s go erning the "luid motion. -he %asicla&s+ &hich applica%le to an# "luid+ are

Conser ation o" mass

De&ton s second la& o" motion

-he "irst la& o" thermod#namics

-he second la& o" thermod#namics

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!nal&sis of Fluid Beha2iors

Measurement of Fluid Mass and


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Hensit#

)peci"ic &eight

)peci"ic 9ra it#

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Measurement of Fluid Mass and'ei%ht

8ensit&


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-he densit# o" a "luid+ designated %# the 9reek s#m%ol ρ (rho! + isde"ined as its mass per unit olume .

Hensit# is used to characteriJe the mass o" a "luid s#stem.In the


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-he speci"ic &eight o" a "luid+ designated %# the 9reek s#m%ol γ

(gamma! + is de"ined as its &eight per unit olume.

Under conditions o" standard gra it# (g0 @.G;Am s 2 0 32.1A> "t s2!+ &ater at :;LF has a speci"ic &eight o" :2.>l% "t 3 and

@.G;kD m3.

-he densit# o" &ater is 1.@> slug "t 3 or @@@ kg m3.

Speci>c 'ei%ht

g ρ γ =


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Ideal as 3a;


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9ases are highl# compressi%le in comparison to "luids+ &ith changes ingas densit# directl# related to changes in pressure and temperaturethrough the equation p=ρRT .

-he ideal gas equation o" state p=ρRT is a model that relates densit#to pressure and temperature "or man# gases under normal conditions.

-he pressure in the ideal gas la& must %e e,pressed as an a%solute pressure &hich is measured relati e to a%solute Jero pressure.

-he standard sea le el atmospheric pressure is 1>.:@@: psi (a%s! or1;1.33k a (a%s!.

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Ideal as 3a;

5iscosit&


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-he properties o" densit# and speci"ic &eight are measures o" the

Nhea inessO o" a "luid.

It is clear+ ho&e er+ that these properties are not su""icient touniquel# characteriJe ho& "luids %eha e since t&o "luids can ha e

appro,imatel# the same alue o" densit# %ut %eha e quitedi""erentl# &hen "lo&ing.

-here is apparentl# some additional propert# that is needed to

descri%e the N"luidit#Oo" the "luid.

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5iscosit&

Fluidit& of Fluid


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Po& to descri%e the N"luidit#O o" the "luid/-he %ottom plate is rigid "i,ed+ %ut the upper plate is "ree tomo e.I" a solid+ such as steel+ &ere placed %et&een the t&o platesand loaded &ith the "orce P + the top plate &ould %e displacedthrough some small distance+ δa.-he ertical line $< &ould %e rotated through the small angle+δβ+ to the ne& position $< .

A p τ =

Fluidit& of Fluid


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'hat happens i" the solid is replaced &ith a "luid such as&ater/

'hen the "orce is applied to the upper plate+ it &ill mo econtinuousl# &ith a elocit# U.-he "luid NsticksO to the solid %oundaries and is re"erred toas the no slip conditions.

-he "luid %et&een the t&o plates mo es &ith elocit#u=u(y that &ould %eassumed to ar# linearl#+u="y#$ . In such case+ the

elocit# gradient is du # dy " # $%

Fluidit& of Fluid


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γ ∝τ

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In a small time increment+ Qt+ an imaginar# ertical line $< &ouldrotate through an angle+ QR + so that

tan QR QR≒ Qa %)inceQa U Qt it "ollo&s that QR0 U Qt %QR / SQR QR + t

He"ining the rate o" shearing strain+ γ + as

-he shearing stress is increased %# + the rate o" shearing strain isincreased in direct proportion+ or

d#duµ=τ

d#

du

%

U

tlim

;t

==δ

δβ=γ →δ

d#Cdu∝τ

-he common "luids such as &ater+ oil+ gasoline+ and air. -he shearing-he common "luids such as &ater+ oil+ gasoline+ and air. -he shearingstress and rate o" shearing strain can %e related &ith a relationshipstress and rate o" shearing strain can %e related &ith a relationship


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5iscosit& and emperature


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For "luids+ the iscosit#decreases &ith an increasein temperature.For gases+ an increase intemperature causes anincrease in iscosit#.

'P /'P /molecular structuremolecular structure

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-he liquid molecules are closel# spaced+ &ith strong cohesi e"orces %et&een molecules+ and the resistance to relati e motion

%et&een adVacent la#ers is related to these intermolecular "orce.

$s the temperature increases+ these cohesi e "orce are reduced&ith a corresponding reduction in resistance to motion. )ince

iscosit# is an inde, o" this resistance+ it "ollo&s that iscosit# isreduced %# an increase in temperature.

-he $ndrade s equation & 'e (#T

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In gases+ the molecules are &idel# spaced and intermolecular

"orce negligi%le.

-he resistance to relati e motion mainl# arises due to thee,change o" momentum o" gas molecules %et&een adVacent

la#ers.

$s the temperature increases+ the random molecular acti it#increases &ith a corresponding increase in iscosit#.

-he )utherland equation & CT )#* # (T+S50

De;tonian and Don6De;tonianl id


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Fluids "or &hich the shearing stress is linearl# related to the rate

o" shearing strain are designated as De&tonian "luids a"ter I. De&ton (1:>2 1A2A!.

Most common "luids such as &ater+ air+ and gasoline are

De&tonian "luid under normal conditions.

Fluids "or &hich the shearing stress is not linearl# related to therate o" shearing strain are designated as non De&tonian "luids .

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Fluid

De;tonian and Don6De;tonianFl id


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)hear thinning "luids.

)hear thickening "luids.


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)hear thinning "luids -he iscosit#

decreases &ith increasing shear rate 8 the harder the "luid is sheared+ theless iscous it %ecomes. Man#colloidal suspensions and pol#mersolutions are shear thinning. ate,

paint is e,ample.

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Fluid

De;tonian and Don6De;tonianFl id


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)hear thickening "luids -he iscosit#increases &ith increasing shear rate 8 theharder the "luid is sheared+ the more iscous it

%ecomes. 'ater corn starch mi,ture &atersand mi,ture are e,amples.


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He"ining kinematic iscosit# ,= ρ

-he dimensions o" kinematic iscosit# are 2

-.

-he units o" kinematic iscosit# in


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ρ ρ CC d dp

- - d dp

. v =−=

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iquids are usuall# considered to %e incompressi%le+&hereas gases are generall# consideredcompressi%le.Compressible of the fluid?$ propert#+ bulk modulus E v+ is used to characteriJecompressi%ilit# o" "luid.

-he %ulk modulus has dimensions o" pressure. F 2.

4ompression and Expansion


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t /o0s p

tan= ρ

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'hen gases are compressed or e,panded+ the relationship %et&een pressure and densit# depends on the nature o" the process.

For isothermal process

For isentropic process t /o0s pk tan= ρ

, 'here k is the ratio o" the speci"ic heat at constant pressure+ c p+ to the speci"ic

heat at constant olume+ c ., / p 1 / v 0 R 0 gas constant

. . vv=p=p

. . vv=kp=kp

Speed of Sound


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ρ ρ v .

d dp

/ ==

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-he elocit# at &hich small distur%ances propagate in a "luid iscalled the speed of sound .

-he speed o" sound is related to change in pressure and densit# o"the "luid medium through

For isentropic process

For ideal gas

ρ kP

/ =

kRT / =

5apor Pressure and Boilin%


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I" liquids are simpl# placed in a container open to theatmosphere+ some liquid molecules &ill o ercome theintermolecular cohesi e "orces and escape into theatmosphere.

I" the container is closed &ith small air space le"t a%o e the

sur"ace+ and this space e acuated to "orm a acuum+ a pressure &ill de elop in the space as a result o" the apor thatis "ormed %# the escaping molecules.

'hen an equili%rium condition is reached+ the apor is said to %e saturated and the pressure that the apor e,erts on theliquid sur"ace is termed the VAP ! P!"##$!", p v .

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Surface ension


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$t the inter"ace %et&een a liquid and a gas+ or %et&een t&oimmisci%le liquids+ "orces de elop in the liquid sur"ace &hichcause the sur"ace to %eha e as i" it &ere a NskinO or Nmem%raneOstretched o er the "luid mass.

$lthough such a skin is not actuall# present+ this conceptualanalog# allo&s us to e,plain se eral commonl# o%ser ed

phenomena.

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Surface ension


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)ur"ace tension the intensit#o" the molecular attraction perunit length along an# line inthe sur"ace and is designated

%# the 9reek s#m%ol σ .

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R p p p

R p R

e2 σ

π σ π

2

2 2

=−=∆

∆='here'here p p 22 is the internal pressureis the internal pressure

andand

p p

ee is the e,ternal pressureis the e,ternal pressure

The force due tosurface tension The force due topressure difference=


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Surface ension E=ects


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)ur"ace tension e""ects pla# a role in man# "luid mechanics pro%lems including the mo ement o" liquids through soil andother porous media+ "lo& o" thin "ilm+ "ormation o" drops and

%u%%les+ and the %reakup o" liquid Vets.

)ur"ace phenomena associated &ith liquid gas+ liquid liquid orliquid gas solid inter"aces are e,ceedingl# comple,.

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Measurement of Surface ension


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# L%&

Liquid'

l

# #l

Measurement of Surface ension


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UEME_2123_Fluid_Mechanics_1_-_Chapter_1.ppt