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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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3
!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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10
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.
12
8e>nition of Fluid
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'hen a constant shear "orce is applied
)olid de"orms or %ends
Fluid continuousl# de"orms.
13
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.
14
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 .
15
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/
16
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.
18
?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.
19
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
20
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 =
22
$ll theoreticall# deri ed equations are dimensionally
homogeneous 8 that is+ the dimensions o" the le"t side o" theequation must %e the same as those on the right side+ and alladditi e separate terms ha e the same dimensions.
9eneral homogeneous equation alid in an# s#stem o" units.
4estricted homogeneous equation restricted to a particulars#stem o" units.
21.1: t d =
Valid only for the system ofValid only for the system of
units using feet and secondsunits using feet and seconds
8imensionall&omo%eneous
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In addition to the qualitati e description o" the arious quantities
o" interest+ it is generall# necessar# to ha e a quantitati e measureo" an# gi en quantit#.
For e,ample+ i" &e measure the &idth o" this page in the %ook and sa#that it is 1; units &ide+ the statement has no meaning until the unit o"
length is de"ined.
I" &e indicate that the units o" length is a meter+ and de"ine themeter as some standard length+ a unit s#stem "or length has %een
esta%lished.$ unit must %e esta%lished "or each o" the remaining %asic quantities.
23
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!
25
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
26
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!
27
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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34
$ 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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35
$ 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
36
!nal&sis of Fluid Beha2iors
Measurement of Fluid Mass and
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Hensit#
)peci"ic &eight
)peci"ic 9ra it#
37
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!.
41
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
45
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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5iscosit& and emperature
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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
49
5iscosit& and emperature
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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.
$s the temperature increases+ the random molecular acti it#increases &ith a corresponding increase in iscosit#.
-he )utherland equation & CT )#* # (T+S50
De;tonian and Don6De;tonianl id
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Fluids "or &hich the shearing stress is linearl# related to the rate
o" shearing strain are designated as De&tonian "luids a"ter I. De&ton (1:>2 1A2A!.
Most common "luids such as &ater+ air+ and gasoline are
De&tonian "luid under normal conditions.
Fluids "or &hich the shearing stress is not linearl# related to therate o" shearing strain are designated as non De&tonian "luids .
51
Fluid
De;tonian and Don6De;tonianFl id
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)hear thinning "luids.
)hear thickening "luids.
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)hear thinning "luids -he iscosit#
decreases &ith increasing shear rate 8 the harder the "luid is sheared+ theless iscous it %ecomes. Man#colloidal suspensions and pol#mersolutions are shear thinning. ate,
paint is e,ample.
53
Fluid
De;tonian and Don6De;tonianFl id
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)hear thickening "luids -he iscosit#increases &ith increasing shear rate 8 theharder the "luid is sheared+ the more iscous it
%ecomes. 'ater corn starch mi,ture &atersand mi,ture are e,amples.
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He"ining kinematic iscosit# ,= ρ
-he dimensions o" kinematic iscosit# are 2
-.
-he units o" kinematic iscosit# in
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ρ ρ CC d dp
- - d dp
. v =−=
57
iquids are usuall# considered to %e incompressi%le+&hereas gases are generall# consideredcompressi%le.Compressible of the fluid?$ 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
58
'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
/ ==
59
-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!"##$!", p v .
60
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Surface ension
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$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.
62
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 .
63
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,.
65
Measurement of Surface ension
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# L%&
Liquid'
l
# #l
Measurement of Surface ension
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