Welcome in a Field of Fluid Mechanics & Gas Dynamics

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Jul 18, 2012 (4 years and 11 months ago)

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Welcome
Introduction
–Ashish J. Modi
–B.E. (Mechanical), MSU-Baroda, 2005
ME(JP&GTP)MSU
Baroda2007

M
.
E
.
(JP

&

GTP)
,
MSU
-
Baroda
,
2007
–Research Publications:-

NationalConference
01

National

Conference


01
•International Conference –05
•International Journal

02
–Phone: 02642-222122, 94271010177

Email: ashish
j
modi
@g
mail.com
j@g
–Website: www.ashishjmodi.yolasite.com–Subject thought-

ElementofMechanicalEngg
UG
-Research Interest:

Element

of

Mechanical

Engg
. -
UG
•Fluid Power Engineering -UG
•Fluid Mechanics and Gas Dynamics –UG & PG
•Computational Fluid Dynamics (CFD) -PG
-Computational Heat Transfe
r
-Computational Fluid Dynamics
-Compact Heat Exchanger
AtbilEii
•Conventional & Non Conv. Energy Systems -UG
-
A
u
t
omo
bil
e
E
ng
i
neer
i
ng
AshishJ.ModiAshishJ.Modi
Ashish

J.

ModiAshish

J.

Modi
Department of Mechanical Engineering
SVMIT, Bharuch
References
•FluidMechanics:FundamentalsandApplicationsByYunusA.CengelandJhonM.
Cimbala,McGrawHillPublications
Itdti
t
Flid
Mhi
B
F
&
Dld
Jh
Wil

I
n
t
ro
d
uc
ti
on
t
o
Fl
u
id
M
ec
h
an
i
cs
By
F
ox
&
D
ona
ld
,
J
o
h
n
Wil
e
y
•EngineeringFluidMechanicsByProf.K.L.Kumar
•FluidMechanicsByL.D.Landau&E.M.Lifshitz,PergamonPress
•AdvancedFluidMechanicsB
y
W.
P
.Graebel,AcademicPress

Elsevier
•FluidMechanicsforEngineersByMeinhardT.Schobeiri
•Schaum’sOutline-FluidMechanicsByPotter&Wiggert,McGrawHill
•FluidMechanicsB
y
Rathakrishnan
•EngineeringFluidMechanicsByR.K.Bansal
•EngineeringFluidMechanicsByR.K.Rajput
•EngineeringFluidMechanicsByD.S.Kumar
•FluidMechanicsByCohen&Kundu
•FundamentalsofFluidMechanicsByBruceR.Munson,donaldF.Youngand
TheodoreH.Okiishi
•FluidMechanics,ThermodynamicsofTurbomachineryByS.L.Dixon
•FluidMechanicsbyFrank.M.White,McGrawHillPublishingCompanyLtd.
•MechanicsofFluidsbyShames,McGrawHillPublishingCompanyLtd.
10:10
4
Contents –Cha
p
ter 1
p
•Review of fundamentals;

Typesofflow;

Types

of

flow;

•Generalized continuity equation;

Momentumandenergyequations
Momentum

and

energy

equations
,
•Euler and Navier-Stokes equations,
•Integration of the momentum equation;
•The generalized Bernoulli’s equation;
•Velocity of sound and its importance;
•Physical difference between incompressible,
•Subsonic and supersonic flows;
Thfd

Th
ree re
f
erence spee
d
s;
•Dimensionless velocity;

Conceptsofstaticandstagnationparameters
Concepts

of

static

and

stagnation

parameters
.
10:10
5
Review of fundamentals
BasicConcepts
Basic

Concepts
In
t
r
oduct
i
o
n
toducto
•Mechanicsistheoldestphysical
sciencethatdealswithboth
tti
d
i
bdi
s
t
a
ti
onaryan
d
mov
i
ng
b
o
di
es
undertheinfluenceofforces.
•Thebranchofmechanicsthat
deals
with
bodies
at
rest
is
called
deals
with
bodies
at
rest
is
called
statics,whilethebranchthatdeals
withbodiesinmotioniscalled
d
y
namics.
y
•Thesubcategoryfluidmechanics
isdefinedasthesciencethatdeals
withthebehavioroffluidsatrest
(
flid
tti
)
i
ti
(
flid
(
fl
u
id
s
t
a
ti
cs
)
o
r
i
nmo
ti
on
(
fl
u
id
dynamics),andtheinteractionof
fluidswithsolidsorotherfluidsat
the
boundaries
.
the
boundaries
.
•Fluidmechanicsisalsoreferredto
asfluiddynamicsbyconsidering
fluidsatrestasaspecialcaseof
FIGURE 1–1 Fluid mechanics deals
with liquids and gases in motion or at
10:10
7
motionwithzerovelocity(Fig.1

1).
rest. © Vol. 16/Photo Disc
.
In
t
r
oduct
i
o
n
toducto
Fluid mechanics itself is also divided into several categories.
The study of
•Hydrodynamics:themotionoffluidsthatarepractically
incompressible(suchasliquids,especiallywater,andgasesatlow
speeds)
is
usually
referred
to
as
speeds)
is
usually
referred
to
as
.
•Asubcategoryofhydrodynamicsishydraulics,whichdealswith
liquidflowsinpipesandopenchannels.
Gas
dynamics
deals
with
the
flow
of
fluids
that
undergo
significant

Gas
dynamics
deals
with
the
flow
of
fluids
that
undergo
significant
densitychanges,suchastheflowofgasesthroughnozzlesathigh
speeds.

Aerodynamics
deals
with
the
flow
of
gases
(especially
air)
over

Aerodynamics
deals
with
the
flow
of
gases
(especially
air)
over
bodiessuchasaircraft,rockets,andautomobilesathighorlow
speeds.

So
m
e
o
th
er
spec
i
a
liz
ed
ca
t
ego
ri
es
suc
h
as
m
eteo
r
o
l
ogy,
Soe
oe
specaed
caegoes
suc
as
eteooogy,
oceanography,andhydrologydealwithnaturallyoccurringflows.
10:10
8
Wh
at
i
s

a
fl
u
i
d
?
atsaud
•A substance in the liquid or gas phase is referred to as a
flid
fl
u
id
.
•Distinction between a solid and a fluid is made on the
basisofthesubstance

sabilitytoresistanappliedshear
basis

of

the

substances

ability

to

resist

an

applied

shear

(or tangential) stress that tends to change its shape.

A
solid can resist an a
pp
lied shear stress b
y
deformin
g,

ppyg,
whereas a fluid deforms continuously under the influence
of shear stress, no matter how small.
Ilidtitilt
ti
btiflid

I
n so
lid
s s
t
ress
i
s propor
ti
ona
l

t
o s
t
ra
i
n,
b
u
t

i
n
fl
u
id
s
stress is proportional to strain rate. When a constant
shear force is a
pp
lied
,
a solid eventuall
y
sto
p
s deformin
g,

pp,ypg,
at some fixed strain angle, whereas a fluid never stops
deforming and approaches a certain rate of strain.
10:10
9
What is a fluid?
•Distinction between solid and fluid?
Sliditlidhbdfi

S
o
lid
: can res
i
s
t
an app
li
e
d
s
h
ear
b
y
d
e
f
orm
i
ng.
Stress is proportional to strain
Fluid:deformscontinuouslyunderappliedshear

Fluid:

deforms

continuously

under

applied

shear
.
Stress is proportional to strain rate
Solid
Fluid
F
FV
Solid
Fluid
F
A
τ
α
=∝
A
h
τ
μ
=

10:10
10
What is a fluid?
•Stress is defined as the
force per unit area.

Normalcomponent:
Normal

component:

normal stress

Inafluidatrestthe

In

a

fluid

at

rest
,
the

normal stress is called
p
ressure
p
•Tangential component:
shearstress
shear

stress
10:10
11
What is a fluid?
•A liquid takes the shape of
the container it is in and
forms a free surface in the
fit
presence o
f
grav
it
y
•A gas expands until it
encountersthewallsofthe
encounters

the

walls

of

the

container and fills the entire
available s
p
ace. Gases
p
cannot form a free surface
•Gas and vapor are often
used as synonymous
words
10:10
12
What is a fluid?
On a microscopic scale,
pressure is determined
by

t
h
e
in
te
r
act
i
o
n
of
byteteactoo
individual gas
molecules.
solidliquidgas
Intermolecular bonds are strongest in solids and
weakest in gases. One reason is that molecules in
solidsarecloselypackedtogether,whereasin
solids

are

closely

packed

together,

whereas

in
gases they are separated by relatively large
distances
10:10
13
Application Areas of Fluid Mechanics
&GasDynamics
&

Gas

Dynamics
10:10
14
No-slip condition

No
slip
condition
:
A
fluid
in

No
-
slip
condition
:
A
fluid
in
directcontactwithasolid
``sticks'‘tothesurfacedueto
viscouseffects
•Responsibleforgenerationof
wallshearstressτw,surface
dragD=∫τw
dA,andthe
dlt
f
th
bd
d
eve
l
opmen
t
o
f
th
e
b
oun
d
ary
layer
•Thefluidpropertyresponsible
for
the
no
slip
condition
is
for
the
no
-
slip
condition
is
viscosity
•Importantboundarycondition
in
formulating
initial
boundary
in
formulating
initial
boundary
valueproblem(IBVP)for
analyticalandcomputational
fluiddynamicsanalysis
10:10
15
No-sli
p
condition
p
Wh
e
n
a
fl
u
i
d
i
s
f
o
r
ced
to
fl
o
w
o
v
er
a
cu
rv
ed
su
rf
ace,
t
h
e
When
a
fluid
is
forced
to
flow
over
a
curved
surface,
the
boundarylayercannolongerremainattachedtothe
surface,andatsomepointitseparatesfromthesurface—a
processcalledflowseparation.
10:10
16
A BRIEF HISTORY OF FLUID MECHANICS
Please refer to section 1-3 in the text book
From283to133BC
,
the
y
,
y
builtaseriesofpressurized
leadandclaypipelines,upto
45kmlongthatoperatedat
pressuresexceeding1.7
MPa
(
180
m
of
head)
Done
MPa
(
180
m
of
head)
Done
attheHellenisticcityof
Per
g
amonin
p
resent-da
y
g
p
y
Turkey
.
10:10
17
Hi
sto
r
y
Faces of Fluid Mechanics
stoy
Archimedes
(C. 287-212 BC)
Newton
(1642-1727)
Leibniz
(1646-1716)
Euler
(1707-1783)
Bernoulli
(1667-1748)
NavierStokesReynoldsPrandtl
Taylor
(1785-1836)(1819-1903)(1842-1912)(1875-1953)(1886-1975)
Classification of Flows
•Weclassifyflowsasatoolinmakingsimplifying
assumptions
to
the
governing
partial
differential
assumptions
to
the
governing
partial
-
differential
equations,whichareknownastheNavier-
Stokes
equations
Stokes
equations
–Conservation of Mass
(RefSection37inKLKumar)
(Ref
.
Section

3
.
7

in

K
.
L
.
Kumar)
Conservation of Momentum
10:10
19
Viscous vs. Inviscid Regions of Flow
•Regionswherefrictional
effects
are
significant
are
effects
are
significant
are
calledviscousregions.
They
are
usually
close
to
They
are
usually
close
to
solidsurfaces.
•Re
g
ionswherefrictional
g
forcesaresmall
comparedtoinertialor
f
lld
pressure
f
orcesareca
ll
e
d
inviscid
10:10
20
Internal vs. External Flow
•Internalflowsare
dominatedbythe
influenceo
f
viscosity
throughouttheflow
field
•Fo
r
externalflows,
viscouseffectsare
limitedtothe
boundarylayerand
wake.
10:10
21
Com
p
ressible vs. Incom
p
ressible Flow
pp
•Aflowisclassifiedas
incom
p
ressibleifthedensit
y
p
y
remainsnearlyconstant.
•Liquidflowsaretypically
incompressible.
•Gasflowsareoften
compressible,especiallyfor
highspeeds.
Mh
b
M
V/
i

M
ac
h
num
b
er,
M
=
V/
c
i
sa
goodindicatorofwhetheror
notcompressibilityeffectsare
important
important
.
–M<0.3:Incompressible
–M<1:Subsonic

M
=
1
:
Sonic
M
1
:
Sonic
–M>1:Supersonic
–M>>1:Hypersonic

0.7<M<1.2:Transonic
10:10
22
Laminar vs. Turbulent Flow

Laminar
:
highly
ordered
Laminar
:
highly
ordered
fluidmotionwithsmooth
streamlines.

Turbulent
:
highly

Turbulent
:
highly
disorderedfluidmotion
characterizedbyvelocity
fluctuations
and
eddies
fluctuations
and
eddies
.
•Transitional:aflowthat
containsbothlaminarand
tblt
i
t
ur
b
u
l
en
t
reg
i
ons
•Reynoldsnumber,
is
the
key
parameter
in
Re
UL
ρ
μ
=
is
the
key
parameter
in
determiningwhetheror
notaflowislaminaror
turbulent
10:10
23
turbulent
.
Natural (or Unforced) versus Forced
Flow
Flow
•Afluidflowissaidtobenatural
fd
ddi
h
h
o
r
f
orce
d
,
d
epen
di
ngon
h
owt
h
e
fluidmotionisinitiated.

In
forced
flow
a
fluid
is
forced

In
forced
flow
,
a
fluid
is
forced
toflowoverasurfaceorina
pipebyexternalmeanssuchas
f
apumpo
r
a
f
an.
•Innaturalflows,anyfluid
motion
is
due
to
natural
means
motion
is
due
to
natural
means
suchasthebuoyancyeffect,
whichmanifestsitselfastherise
ofthewarme
r
(andthuslighter)
fluidandthefallofcooler(and
thus
denser)
fluid
10:10
24
thus
denser)
fluid
Stead
y
vs. Unstead
y
Flow
yy

Steady
im
p
li
es
n
o
c
h
a
n
ge
at
Steady
implies
no
change
at
apointwithtime.Transient
termsinN-Sequationsare
zero
•Unsteadyistheoppositeof
td
s
t
ea
d
y.
–Transientusuallydescribesa
starting,
or
developing
flow
.
starting,
or
developing
flow
.
–Periodicreferstoaflowwhich
oscillatesaboutamean.
•Unsteadyflowsmayappea
r
steadyif“time-averaged”
10:10
25
One-, Two-, and Three-Dimensional
Flows
Flows
•N-Sequationsare3Dvectorequations.
•Velocityvector,U(x,y,z,t)=[U
x(x,y,z,t),Uy(x,y,z,t),Uz(x,y,z,t)
]
•Lowerdimensionalflowsreducecomplexityofanalyticaland
computationalsolution
•Changeincoordinatesystem(cylindrical,spherical,etc.)may
facilitatereductioninorder.
•Example:forfully-developedpipeflow,velocityV(r)isafunctionof
radius
r
and
pressure
p(z)
is
a
function
of
distance
z
along
the
pipe
radius
r
and
pressure
p(z)
is
a
function
of
distance
z
along
the
pipe
.
10:10
26
One-, Two-, and Three-Dimensional
Flows
Flows
Aflowmaybeapproximatedastwo-dimensionalwhentheaspectratiois
l
d
h
fl
d
h
ibl
l
h
l
dii
l
argean
d
t
h
e
fl
ow
d
oesnotc
h
angeapprec
i
a
bl
ya
l
ongt
h
e
l
onge
r
di
mens
i
on.
Forexample,theflowofairoveracarantennacanbeconsideredtwo-
dimensionalexceptnearitsendssincetheantenna’slengthismuch
greaterthanitsdiameter,andtheairflowhittingtheantennaisfairlyuniform
10:10
27
S
y
stem and Control Volume
y
•Asystemisdefinedasa
quantity
of
matter
or
a
region
in
quantity
of
matter
or
a
region
in
spacechosenforstudy.
•Aclosedsystem(knownasa
tl
)
it
f
con
t
ro
l
mass
)
cons
i
s
t
so
f
a
fixedamountofmass.
•Anopensystem,orcontrol
l
i
l
ltd
vo
l
ume,
i
saproper
l
yse
l
ec
t
e
d
regioninspace.
Itusually
enclosesadevicethat
involvesmassflowsuch
asacompressor,turbine,
or
nozzle
or
nozzle
.
10:10
28
System and Control Volume
•Ingeneral,an
y
arbitrar
y
regioninspace
canbeselectedasacontrolvolume.
Therearenoconcreterulesforthe
selection
of
control
volumes
but
the
selection
of
control
volumes
,
but
the
properchoicecertainlymakestheanalysis
much
easier
much
easier
.
10:10
29
Dimensions and Units
Any
physical
quantity
can

Any
physical
quantity
can
becharacterizedby
dimensions.
•Themagnitudesassigned
todimensionsarecalled
units.
•Primarydimensions(or
fundamentaldimensions)
include
:
mass
m
length
include
:
mass
m
,
length
L,timet,andtemperature
T,etc.
B
GlCffWihtd
B
y
G
enera
l

C
on
f
erence o
f

W
e
i
g
ht
s an
d

Measures
10:10
30
Dimensions and Units
•Secondarydimensions(deriveddimensions)canbe
expressed
in
terms
of
primary
dimensions
and
include
:
expressed
in
terms
of
primary
dimensions
and
include
:
velocityV,energyE,andvolumeV.
•Units
y
stemsincludeEn
g
lishs
y
stemandthemetricSI
y
g
y
(InternationalSystem).We'lluseboth.
10:10
31
Dimensions and Units
Basedonthenotationalschemeintroducedin1967,

The
degree
symbol
was
officially
dropped
from
the
absolute

The
degree
symbol
was
officially
dropped
from
the
absolute
temperatureunit,
•Allunitnamesweretobewrittenwithoutcapitalizationevenifthey
were
derived
from
proper
names
(Table
1

1
)
were
derived
from
proper
names
(Table
1
1
)
.
•However,theabbreviationofaunitwastobecapitalizediftheunit
wasderivedfromapropername.Forexample,theSIunitofforce,
whichisnamedafte
r
Si
r
IsaacNewton
(
1647

1723
),
isnewton
(
not
(
),
(
Newton),anditisabbreviatedasN.
•Also,thefullnameofaunitmaybepluralized,butitsabbreviation
cannot.Forexample,thelengthofanobjectcanbe5mor5meters,
t
5
5
t
no
t
5
mso
r
5
me
t
e
r
.
•Finally,noperiodistobeusedinunitabbreviationsunlessthey
appearattheendofasentence.Forexample,theproperabbreviation
of
meter
is
m
(not
m
)
of
meter
is
m
(not
m
.
)
.
10:10
32
Dimensions and Units
S
SI
d
Elih
Uit
S
ome
SI
an
d
E
ng
li
s
h
U
n
it
s
•InSI,theunitsofmass,length,andtimearethekilogram(kg),
meter(m),andsecond(s),respectively.Therespectiveunitsin
th
Elih
t
th
d
(lb)
ft
(ft)
d
th
e
E
ng
li
s
h
sys
t
emare
th
epoun
d
-mass
(lb
m
)
,
f
oo
t
(ft)
,an
d
second(s).
10:10
33
Dimensions and Units
FUi
F
orce
U
n
i
ts
We call a mass of 32.174 lbm 1 slug
10:10
34
Dimensions and Units

Weight
W
is
a
force
It
is
the
gravitational
force

Weight
W
is
a
force
.
It
is
the
gravitational
force
appliedtoabody,anditsmagnitudeisdetermined
fromNewton’ssecondlaw,
()
WN
wheremisthemassofthebody,andgisthelocal
ittil
lti
(
i
9
807
/
2
32
174
()
W
mg
N
=
grav
it
a
ti
ona
l
acce
l
era
ti
on
(
g
i
s
9
.
807
m
/
s
2
o
r
32
.
174
ft/s2atsealeveland45°latitude).
Theweightofaunitvolumeofasubstanceis
called
the
specific
weight
γ
慮a

摥瑥牭楮敤
晲潭
捡汬敤
瑨t
specific
weight
γ
慮a

摥瑥牭楮敤
晲潭
γ=ρg,whereρisdensity.
10:10
35
Dimensions and Units

Work
,
which
is
a
form
of
energy,
can
simply
be
defined
as
Work
,
which
is
a
form
of
energy,
can
simply
be
defined
as
forcetimesdistance;therefore,ithastheunit“newton-meter
(N.m),”whichiscalledajoule(J).Thatis,
11
JN
AmorecommonunitforenergyinSIisthekilojoule(1kJ=
10
3
J)
In
the
English
system
the
energy
unit
is
the
Btu
11
JN
m
=
i
10
3
J)
.
In
the
English
system
,
the
energy
unit
is
the
Btu
(Britishthermalunit),whichisdefinedastheenergyrequired
toraisethetemperatureof1lbmofwaterat68°Fby1°F.
Inthemetricsystem,theamountofenergyneededtoraise
thetemperatureof1gofwaterat14.5°Cby1°Cisdefined
as1calorie(cal),and1cal=4.1868J.Themagnitudesof
thekilojouleandBtuarealmostidentical(1Btu=1.0551kJ).
10:10
36
Dimensions and Units
•Dimensional homogeneityis a valuable tool in checking for errors. Make
sureeveryterminanequationhasthesameunits
sure

every

term

in

an

equation

has

the

same

units
.
10:10
37
Dimensions and Units
•Unityconversionratiosarehelpfulinconvertingunits.Usethem.
•Allnon-primaryunits(secondaryunits)canbeformedby
combinationsofprimaryunits.Forceunits,forexample,canbe
ex
p
ressedas
p
10:10
38
MATHEMATICAL MODELING
OFENGINEERINGPROBLEMS
OF

ENGINEERING

PROBLEMS
•An engineering device or process can be studied either
itll
(ttidtkit)

exper
i
men
t
a
ll
y
(t
es
ti
ng an
d

t
a
ki
ng measuremen
t
s
)
Advantage : deal with the actual physical system, and the desired
quantity is determined by measurement, within the limits of
experimentalerror
experimental

error
.
Drawback: approach is expensive, time-consuming, and often
impractical. Besides, the system we are studying may not even
exist
exist
.
–analytically (by analysis or calculations).
Advantage : fast and inexpensive
Drawback:theresultsobtainedaresubjecttotheaccuracyofthe
Drawback:

the

results

obtained

are

subject

to

the

accuracy

of

the

assumptions, approximations, and idealizations made in the
analysis.

Inengineeringstudiesoftenagoodcompromiseis

In

engineering

studies
,
often

a

good

compromise

is

reached by reducing the choices to just a few by analysis,
and then verifying the findings experimentally.
10:10
39
MATHEMATICAL MODELING OF
ENGINEERINGPROBLEMS
ENGINEERING

PROBLEMS
10:10
40
MATHEMATICAL MODELING OF
ENGINEERINGPROBLEMS
ENGINEERING

PROBLEMS
•The stud
y
of
p
h
y
sical
p
henomena involves two
ypyp
important steps.
–In the first step, all the variables that affect the
hidtifidblti
p
h
enomena are
id
en
tifi
e
d
, reasona
bl
e assump
ti
ons
and approximations are made, and the
interdependenceofthesevariablesisstudied.The
interdependence

of

these

variables

is

studied.

The

relevant physical laws and principles are invoked, and
the problem is formulated mathematically. The
equationitselfisveryinstructiveasitshowsthe
equation

itselfis

very

instructive

as

it

shows

the

degree of dependence of some variables on others,
and the relative importance of various terms.
–In the second step the problem is solved using an
appropriate approach, and the results are interpreted.
10:10
41
PROBLEM-SOLVING TECHNIQUE
•using a step-by-step
approach, an
engineer can reduce
the solution of a
complicated problem
into the solution of a
series of simple
problems.
10:10
42
PROBLEM-SOLVING TECHNIQUE
St1PblSttt

St
ep
1
:
P
ro
bl
em
St
a
t
emen
t
•Ste
p
2: Schematic
p
•Step 3: Assumptions and
Approximations
Approximations
•Step 4: Physical Laws
S

S
tep 5: Properties
•Ste
p
6: Calculations
p
•Step 7: Reasoning, Verification, and
Discussion
10:10
43
Discussion
Reasoning, Verification, and
Discussion
Discussion
10:10
44
ENGINEERING SOFTWARE
PACKAGES
PACKAGES

Engineering
Equation
Solver
(EES)
is
a

Engineering
Equation
Solver
(EES)
is
a
programthatsolvessystemsoflinearor
li
lbi
difftil
non
li
nea
r
a
l
ge
b
ra
i
co
r
diff
eren
ti
a
l
equationsnumerically.
•ANSYSCFX/ANSYSFLUENTare
computational
fluid
dynamics
(CFD)
code
computational
fluid
dynamics
(CFD)
code
widelyusedforflow-modelingapplications.
10:10
45
Accuracy, Precision, and Significant
Digits
Digits
Engineers must be aware of three principals that govern the proper use
ofnmbers
of

n
u
mbers
.
1.Accuracy error : Value of one reading minus the true value.
ClosenessoftheaveragereadingtothetruevalueGenerally
Closeness

of

the

average

reading

to

the

true

value
.
Generally

associated with repeatable, fixed errors.
2.Precision error:Value of one reading minus the average of
diIfthfifltid
rea
di
ngs.
I
s a measure o
f

th
e
fi
neness o
f
reso
l
u
ti
on an
d

repeatability of the instrument. Generally associated with random
errors.
Sf
f
3.
S
igni
f
icant digits :Digits that are relevant and meaning
f
ul. When
performing calculations, the final result is only as precise as the
least precise parameter in the problem. When the number of
iifitdiitikthtdtddi3U3i
s
i
gn
ifi
can
t

di
g
it
s
i
s un
k
nown,
th
e accep
t
e
d
s
t
an
d
ar
d

i
s
3
.
U
se
3

i
n
all homework and exams.
10:10
46
Summary
In this chapter some basic concepts of fluid mechanics are introduced
and discussed.
•A substance in the liquid or gas phase is referred to as a fluid. Fluid
mechanics is the science that deals with the behavior of fluids at rest
or in motion and the interaction of fluids with solids or other fluids at
thbdi
th
e
b
oun
d
ar
i
es.
•The flow of an unbounded fluid over a surface is external flow, and
the flow in a pipe or duct is internal flow if the fluid is completely
boundedbysolidsurfaces
bounded

by

solid

surfaces
.
•A fluid flow is classified as being compressible or incompressible,
depending on the density variation of the fluid during flow. The
densitiesofliquidsareessentiallyconstantandthustheflowof
densities

of

liquids

are

essentially

constant
,
and

thus

the

flow

of

liquids is typically incompressible.
•The term steady implies no change with time. The opposite of
stead
y
is unstead
y,
or transient.
y
y,
•The term uniform implies no change with location over a specified
region.
•A flow is said to be one
-
dimensional when the velocit
y
chan
g
es in
10:10
47
yg
one dimension only.
Summary
•A fluid in direct contact with a solid surface sticks to the surface and
thereisnoslipThisisknownasthe
no
-
slipcondition
whichleads
there

is

no

slip
.
This

is

known

as

the

no
-
slip

condition
,
which

leads

to the formation of boundary layers along solid surfaces.
•A system of fixed mass is called a closed system, and a system that
involves mass transfer across its boundaries is called an o
p
en
p
system or control volume. A large number of engineering problems
involve mass flow in and out of a system and are therefore modeled
as control volumes.
Iiilltiitiittttilttti

I
n eng
i
neer
i
ng ca
l
cu
l
a
ti
ons,
it

i
s
i
mpor
t
an
t

t
o pay par
ti
cu
l
ar a
tt
en
ti
on
to the units of the quantities to avoid errors caused by inconsistent
units, and to follow a systematic approach.

Itisalsoimportanttorecognizethattheinformationgivenisnot

It

is

also

important

to

recognize

that

the

information

given

is

not

known to more than a certain number of significant digits,and the
results obtained cannot possibly be accurate to more significant
di
g
its.
g
The information given on dimensions and units; problem-solving
technique; and accuracy, precision, and significant digits will be
used throughout the entire text.
10:10
48