fm and hm 2

7/18/2019 fm and hm 2

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Fluid Properties and

Units

Fluid Properties and

UnitsCVEN 311CVEN 311

7/18/2019 fm and hm 2


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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-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


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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'ensity ρ +*#3

pecific 0ei!"tγ +*#

(#

'ynamic iscosity µ +*#1(#1

inematic iscosity ν *(#1

urface tension σ +(

#

2ul mod of elasticity E +*#1(#


'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

7/18/2019 fm and hm 2


=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

7/18/2019 fm and hm 2


'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

=

7/18/2019 fm and hm 2


'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

7/18/2019 fm and hm 2


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

7/18/2019 fm and hm 2


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

7/18/2019 fm and hm 2


Caitation 'ama!eCaitation 'ama!e

7/18/2019 fm and hm 2

http://slidepdf.com/reader/full/fm-and-hm-2 22/25∆ pπ "

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 <

7/18/2019 fm and hm 2


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

7/18/2019 fm and hm 2


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 %

fm and hm 2

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