fm and hm 2
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fluid,fluis mechanics, hydraulics,hydraulic machinery, FM&HM,FMHMTRANSCRIPT
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Fluid Properties and
Units
Fluid Properties and
UnitsCVEN 311CVEN 311
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ContinuumContinuum
All materials, solid or fluid, are composed
of molecules discretely spread and in
continuous motion.Howeer, in dealin! wit" fluid#flow
relations on a mat"ematical $asis, it is
necessary to replace t"e actual molecularstructure $y a "ypot"etical continuous
medium, called t"e continuum.
All materials, solid or fluid, are composed
of molecules discretely spread and in
continuous motion.Howeer, in dealin! wit" fluid#flow
relations on a mat"ematical $asis, it is
necessary to replace t"e actual molecularstructure $y a "ypot"etical continuous
medium, called t"e continuum.
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ContinuumContinuum
%n a continuum, t"e p"ysical aria$le at a
point in space is t"e aera!ed alue of t"e
aria$le in a small sp"ere.How !ood is t"e assumption&
%n a continuum, t"e p"ysical aria$le at a
point in space is t"e aera!ed alue of t"e
aria$le in a small sp"ere.How !ood is t"e assumption&
10-3cm
3x1010 molecules of air
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'imensions and Units'imensions and Units
("e dimensions "ae to $e t"e same for eac"
term in an e)uation
'imensions of mec"anics are len!t"
time
mass force
temperature
("e dimensions "ae to $e t"e same for eac"
term in an e)uation
'imensions of mec"anics are len!t"
time
mass force
temperature
aF m=
*
(
+
+*(#
Θ
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'imensions and Units'imensions and Units
-uantity ym$ol 'imensions
Velocity V *(#1
Accelerationa *(#
Area A *
Volume ∀ *3
'isc"ar!e Q *3(#1
Pressure p +*#1(#
/raity g *(#
(emperatureT’ Θ+ass concentration C +*#3
-uantity ym$ol 'imensions
Velocity V *(#1
Accelerationa *(#
Area A *
Volume ∀ *3
'isc"ar!e Q *3(#1
Pressure p +*#1(#
/raity g *(#
(emperatureT’ Θ+ass concentration C +*#3
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'imensions and Units'imensions and Units
-uantity ym$ol 'imensions
'ensity ρ +*#3
pecific 0ei!"tγ +*#
(#
'ynamic iscosity µ +*#1(#1
inematic iscosity ν *(#1
urface tension σ +(
#
2ul mod of elasticity E +*#1(#
-uantity ym$ol 'imensions
'ensity ρ +*#3
pecific 0ei!"tγ +*#
(#
'ynamic iscosity µ +*#1(#1
inematic iscosity ν *(#1
urface tension σ +(#
2ul mod of elasticity E +*#1(#
("ese are 4444444 properties5fluid
How many independent properties& 44444 6
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'efinition of a Fluid'efinition of a Fluid
7a fluid, suc" as water or air, deforms
continuously w"en acted on $y s"earin!
stresses of any ma!nitude.8# Munson, Young, Okiishi
7a fluid, suc" as water or air, deforms
continuously w"en acted on $y s"earin!
stresses of any ma!nitude.8# Munson, Young, Okiishi
0ater
9il
Air
0"y isn:t steel a fluid&
0ater
9il
Air
0"y isn:t steel a fluid&
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Fluid 'eformation $etween
Parallel Plates
Fluid 'eformation $etween
Parallel Plates
ide iew
Force F causes t"e top plate to "ae elocity U.
0"at ot"er parameters control "ow muc" force is
re)uired to !et a desired elocity&
'istance $etween plates ;b<'istance $etween plates ;b<
Area of plates ; A<Area of plates ; A<
F
b
U
Viscosity5Viscosity5
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"ear tress"ear tress
c"an!e in elocity wit" respect to distance
A F =τ
,m N
b
U µ τ =
b
U
dy
du µ τ =
b
AU F µ = AU
Ft = µ
⋅,
m
s Ndimension of
s
1
(an!ential force per unit area
=ate of an!ular deformation
rate of s"ear
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Fluid classification $y response
to s"ear stress
Fluid classification $y response
to s"ear stress
Newtonian
%deal Fluid
%deal plastic
Newtonian
%deal Fluid
%deal plastic
NewtonianIdeal Fluid
Ideal plastic
"ear stress τ
= a t e o f d e f o r m
a t i o n d y
d u
µ
dy
du µ τ =
1
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Fluid ViscosityFluid Viscosity
E>amples of "i!"ly iscous fluids 4444444444444444444444
Fundamental mec"anisms/ases # transfer of molecular momentum
Viscosity 4444444444 as temperature increases.
Viscosity 4444444444 as pressure increases.*i)uids # co"esion and momentum transfer
Viscosity decreases as temperature increases.
=elatiely independent of pressure ;incompressi$le<
E>amples of "i!"ly iscous fluids 4444444444444444444444
Fundamental mec"anisms/ases # transfer of molecular momentum
Viscosity 4444444444 as temperature increases.
Viscosity 4444444444 as pressure increases.*i)uids # co"esion and momentum transfer
Viscosity decreases as temperature increases.
=elatiely independent of pressure ;incompressi$le<
molasses, tar, ?w#@? oil
increases
4444444 increases
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E>ample +easure t"e iscosity
of water
E>ample +easure t"e iscosity
of water
("e inner cylinder is 1?cm in diameter and rotates
at 1? rpm. ("e fluid layeris mm t"ic and 1? cm"i!". ("e power re)uiredto turn t"e inner cylinder
is @?>1?#B watts. 0"at ist"e dynamic iscosity oft"e fluid&
("e inner cylinder is 1?cm in diameter and rotates
at 1? rpm. ("e fluid layeris mm t"ic and 1? cm"i!". ("e power re)uiredto turn t"e inner cylinder
is @?>1?#B watts. 0"at ist"e dynamic iscosity oft"e fluid&
9uter
cylinder
("in layer of water
%nner
cylinder
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olution c"emeolution c"eme
=estate t"e !oal %dentify t"e !ien parameters and represent t"e
parameters usin! sym$ols 9utline your solution includin! t"e e)uations
descri$in! t"e p"ysical constraints and anysimplifyin! assumptions
ole for t"e unnown sym$olically u$stitute numerical alues wit" units and do t"e
arit"metic C"ec your units5
C"ec t"e reasona$leness of your answer
=estate t"e !oal %dentify t"e !ien parameters and represent t"e
parameters usin! sym$ols 9utline your solution includin! t"e e)uations
descri$in! t"e p"ysical constraints and anysimplifyin! assumptions
ole for t"e unnown sym$olically u$stitute numerical alues wit" units and do t"e
arit"metic C"ec your units5
C"ec t"e reasona$leness of your answer Solution
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=ole of Viscosity=ole of Viscosity
taticsFluids at rest "ae no relatie motion $etween
layers of fluid and t"us dud y D ?("erefore t"e s"ear stress is 44444 and is
independent of t"e fluid iscosity
FlowsFluid iscosity is ery important w"en t"e fluid
is moin!
taticsFluids at rest "ae no relatie motion $etween
layers of fluid and t"us dud y D ?("erefore t"e s"ear stress is 44444 and is
independent of t"e fluid iscosity
FlowsFluid iscosity is ery important w"en t"e fluid
is moin!
eroero
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'ynamic and inematic
Viscosity
'ynamic and inematic
Viscosity
inematic iscosity ;44< is a fluid property
o$tained $y diidin! t"e dynamic iscosity
;44< $y t"e fluid density
inematic iscosity ;44< is a fluid property
o$tained $y diidin! t"e dynamic iscosity
;44< $y t"e fluid density
ρ
µ ν =
⋅=
3m
3!
sm
3 g
ν
⋅
⇒m
s N µ [ ]
⋅
=,s
m! N
msG
Connection to Reynolds number!
n
=eVDr
m
=
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'ensity and pecific 0ei!"t'ensity and pecific 0ei!"t
'ensity ;massunit
olume< ρ ___________density of water
density of air at
atmosp"eric pressure and
1@ °Cpecific 0ei!"t ;wei!"t
per unit olume< γ 444444444444444444
'ensity ;massunit
olume< ρ ___________density of waterdensity of air at
atmosp"eric pressure and
1@ °Cpecific 0ei!"t ;wei!"t
per unit olume< γ 444444444444444444
@?
B?
I?
J?
?
1???
? @? 1??(emperature ;C<
' e n s i t y ; ! C m 3 <
I
J
1???
? 1? ?
(emperature ;C<
' e n s i t y ;
! C m 3 <
1??? !m3
1. !m3
γ D ρ ! D J?B Nm3
pecific mass
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Perfect /as *awPerfect /as *aw
V ! n"T " is t"e uniersal !as constant
T is in elin
V ! n"T " is t"e uniersal !as constant
T is in elin
Note deiation from t"e te>t5
"
J316. N m
mol
Use a$solute pressure for and a$solute
temperature for T
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2ul +odulus of Elasticity2ul +odulus of Elasticity
=elates t"e c"an!e in
olume to a c"an!e in
pressurec"an!es in density at
"i!" pressure
pressure waes 444444444
444444 4444444444
=elates t"e c"an!e in
olume to a c"an!e in
pressurec"an!es in density at
"i!" pressure
pressure waes 444444444
444444 4444444444 .??
.?@
.1?
.1@
.?
.@
.3?
.3@
? ? 6? B? J? 1??
(emperature ;C<
2 u l + o d u l u
s o f e l a s t i c i t y ; / P a <
soundsound
water hammerwater hammer
E dp
d #
E
dp
dV V #
Water
-
ρ
# E a =
speed of soundspeed of sound
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Vapor PressureVapor Pressure
?
1???
???
3???
6???
@???
B???
I???
J???
? 1? ? 3? 6?
(emperature ;C<
V a p o r p r e s s
u r e ; P a <
liuid
What is apor pressure of water at 100"C#1?1 Pa
Connection forward to caitation!
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CaitationCaitation
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Caitation 'ama!eCaitation 'ama!e
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D π "σ
urface (ensionurface (ension
Pressure
increase in a
sp"erical droplet
Pressure
increase in a
sp"erical droplet
"
p σ ,
=∆
∆ pπ "
π "σ
Surface moleculeSurface molecule
?.?@?
?.?@@
?.?B?
?.?B@
?.?I?
?.?I@
?.?J?
? ? 6? B? J? 1??
(emperature ;C<
. u r f a c e t e n s
i o n ; N C m <
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E>ample urface (ensionE>ample urface (ension
Estimate t"e difference in pressure ;in Pa<
$etween t"e inside and outside of a $u$$le
of air in ?KC water. ("e air $u$$le is ?.3mm in diameter.
Estimate t"e difference in pressure ;in Pa<
$etween t"e inside and outside of a $u$$le
of air in ?KC water. ("e air $u$$le is ?.3mm in diameter.
" p
σ ,=
R = 0$1% x 10-3 mR = 0$1% x 10-3 m
σ = 0$0&3 '(mσ = 0$0&3 '(m
( )
m1?1@.?
NCm?I3.?,
3−×= p
HI? Pa p =
What is the di)erence between
pressure in a water droplet and in an
h p γ = water m1.?J?B
I63===
m $
a ph
γ Statics!
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9utline t"e solution9utline t"e solution
=estate t"e !oal
%dentify t"e !ien parameters and represent
t"e parameters usin! sym$ols
9utline your solution includin! t"e
e)uations descri$in! t"e p"ysical
constraints and any simplifyin!assumptions
=estate t"e !oal
%dentify t"e !ien parameters and represent
t"e parameters usin! sym$ols9utline your solution includin! t"e
e)uations descri$in! t"e p"ysical
constraints and any simplifyin!assumptions
,3# sm N1.1B>1? ⋅= µ
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Viscosity +easurement olutionViscosity +easurement olution
h% t
3,,πω
µ =
,3#
3,
B#
sm N1.1B>1?
m<;? 1m<;? ?@;1 ?6Is<
m<;?.??0<1?;@?⋅==
π
µ &
t
AU F µ = =U = A
t h% F
πω µ =
=
t
h% 3πω µ =
9uter
cylinder
("in layer of water
%nner
cylinder
r = % cm
t = * mmh = 10 cmP = %0 x 10-+ W10 rpm
ω % π%h
F ω %