8/2/2019 Chapter 01 Lee

1/3

Whatisafluid?

Afluidisasu

bstanceinthegaseousorliquidform

Distinctionb

etweensolidandfluid?

Solid:canresistanappliedshearbydeforming.Stressis

proportiona

ltostrain

Fluid:defor

mscontinuouslyunderapplie

dshear.Stressis

proportiona

ltostrainrate(m1)

FA

=

F

V

A

h

=

Solid

Fluid

Whatisafluid?

Stressisdefinedasthe

forceperunitarea.

Normalcom

ponent:

normalstres

s

Inafluidat

rest,the

normalstre

ssiscalled

pressure

Tangentialcomponent:

shearstress

Wh

atisafluid?Liquidvs.

Gas

Aliquidt

akestheshapeof

thecontaineritisinand

formsaf

reesurfaceinthe

presence

ofgravity

Agasexp

andsuntilit

encounte

rsthewallsofthe

containerandfillstheentire

available

space.Gasescannot

formafreesurface

Gasandvaporareoftenused

assynonymouswords

Whatisafluid?

solid

liqu

id

gas

(a)moleculesareatrelative

lyfixedpositionsina

solid,(b)groupsofmoleculesmoveabouteach

otherintheliquidphase,and(c)moleculesmove

aboutatrandominthegas

phase.

No-slipcondition

No-slipcond

ition:Afluidin

directconta

ctwithasolid

``sticks'tothesurfacedueto

viscouseffects(m1,m2)

Responsible

forgenerationof

wallshearstresstw,surface

dragD=twdA,andthe

developmen

toftheboundary

layer

Thefluidpropertyresponsible

fortheno-slipconditionis

viscosity(m

3)

Importantb

oundarycondition

informulatinginitialboundary

valueproble

m(IBVP)for

analyticalan

dcomputational

fluiddynam

icsanalysis

Cla

ssificationofFlows

Weclassifyflowsasatoolinmakingsimplifying

assumptionstot

hegoverningpartial-diffe

rential

equations,which

areknownastheNavier

-Stokes

equations

ConservationofMass

ConservationofMomentum

8/2/2019 Chapter 01 Lee

2/3

Viscou

svs.InviscidRegionsofFlow

Regionswhere

frictional

effectsaresign

ificantare

calledviscousr

egions.

Theyareusuallycloseto

solidsurfaces.

Regionswhere

frictional

forcesaresmallcompared

toinertialorpressure

forcesarecalle

dinviscid

Thedevelopmentofviscousandinviscid

regionsofflowasaresultofinsertinga

flatplateparallelintoafluidstream

of

uniformvelocity.

Inter

nalvs.ExternalFlow

Internalflowsare

dominatedbythe

influenceofviscosity

throughoutthe

flowfield

Forexternalflows,

viscouseffectsare

limitedtothe

boundary

layerandwake.

Compre

ssiblevs.IncompressibleFlow

Aflowisclassified

as

incompressibleifthedensity

remainsnearlycon

stant.

Liquidflowsaretypically

incompressible.

Gasflowsareoftencompressible,

especiallyforhigh

speeds.

Machnumber,Ma

=V/cisagood

indicatorofwheth

erornot

compressibilityeffectsare

important.

Ma>1:Hyper

sonic

Lamin

arvs.TurbulentFlow

Laminar:highlyord

eredfluid

motionwithsmooth

streamlines.(m1)

Turbulent:highlydisordered

fluidmotioncharacterizedby

velocityfluctuationsand

eddies.

Transitional:aflow

that

containsbothlamin

arand

turbulentregions

Reynoldsnumber,R

e=UL/

isthekeyparamete

rin

determiningwhetherornota

flowislaminarortu

rbulent.

(m2)

Steadyvs.UnsteadyFlo

w

Steadyimpliesn

ochangeata

pointwithtime.Transient

termsinN-Sequationsarezero

Unsteadyisthe

oppositeof

steady.

Transientusuallydescribesa

starting,ord

evelopingflow.

Periodicrefe

rstoaflow

whichoscilla

tesabouta

mean.

Unsteadyflows

mayappear

steadyiftime-averaged

One-,Two-,a

ndThree-DimensionalFlows

N-Sequationsare3Dvectorequations.

Velocityvector,U(x,y,z,t)=[U

x(x,y,z,t),Uy(x,y,z,t),Uz(x,y,z,t)]

Lowerdimensionalflowsreducecomplexityofanalyticalan

d

computationalsolution

Changeincoordinatesystem(cylindrical,spherical,etc.)mayfacilitate

reductioninorder.

Example:forfully-developedpipeflow,velocityV(r)isafun

ctionofradius

randpressurep(z)isafunctionofdistancezalongthepipe.

8/2/2019 Chapter 01 Lee

3/3

SystemandControlVolu

me

Asystemis

definedasa

quantityof

matterora

regioninspacechosenfor

study.

Aclosedsy

stemconsistsof

afixedamountofmass.

Anopensy

stem,orcontrol

volume,is

aproperly

selectedre

gioninspace.

We'lldiscusscontrol

volumesin

moredetailin

Chapter6.

Dim

ensionsandUnits

Anyphysicalquantitycanbecharacterizedbydim

ensions.

Themagnitudesassignedtodimensionsarecalledunits.

Primarydimensions

include:massm,lengthL,tim

et,and

temperatureT.

Secondarydimensio

nscanbeexpressedinterms

ofprimary

dimensionsandinclude:velocityV,energyE,and

volumeV.

UnitsystemsincludeEnglishsystemandthemetr

icSI

(InternationalSystem).We'lluseboth.

Dimensionalhomog

eneityisavaluabletoolinch

eckingfor

errors.Makesuree

veryterminanequationhas

thesame

units.

Accuracy,Precision,andSignific

antDigits

Engineersmustbe

awareofthreeprincipalstha

tgovernthe

properuseofnum

bers.

1.Accuracyerror:V

alueofonereadingminusthetrue

value.Closenessof

theaveragereadin

gtothetruevalue.Generallyassoc

iatedwith

repeatable,fixede

rrors.

2.Precisionerror:V

alueofonereadingminustheaverageofreadings.Isa

measureofthefin

enessofresolutionandrepeatabilityoftheinstrument.

Generallyassociatedwithrandomerrors.

3.Significantdigits:

Digitsthatarerelevantandmeaningful.When

performingcalculations,thefinalresultisonlyaspreciseastheleast

preciseparameter

intheproblem.Whenthenumber

ofsignificantdigits

isunknown,theacceptedstandardis3.Use3inallhomeworkand

exams.