Welcome
Introduction
–Ashish J. Modi
–B.E. (Mechanical), MSUBaroda, 2005
ME(JP>P)MSU
Baroda2007
–
M
.
E
.
(JP
&
GTP)
,
MSU

Baroda
,
2007
–Research Publications:
•
NationalConference
01
•
National
Conference
–
01
•International Conference –05
•International Journal
–
02
–Phone: 02642222122, 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’sOutlineFluidMechanicsByPotter&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 NavierStokes 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
Noslip 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
Nosli
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 13 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
resentda
y
g
p
y
Turkey
.
10:10
17
Hi
sto
r
y
Faces of Fluid Mechanics
stoy
Archimedes
(C. 287212 BC)
Newton
(16421727)
Leibniz
(16461716)
Euler
(17071783)
Bernoulli
(16671748)
NavierStokesReynoldsPrandtl
Taylor
(17851836)(18191903)(18421912)(18751953)(18861975)
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
termsinNSequationsare
zero
•Unsteadyistheoppositeof
td
s
t
ea
d
y.
–Transientusuallydescribesa
starting,
or
developing
flow
.
starting,
or
developing
flow
.
–Periodicreferstoaflowwhich
oscillatesaboutamean.
•Unsteadyflowsmayappea
r
steadyif“timeaveraged”
10:10
25
One, Two, and ThreeDimensional
Flows
Flows
•NSequationsare3Dvectorequations.
•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:forfullydevelopedpipeflow,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 ThreeDimensional
Flows
Flows
Aflowmaybeapproximatedastwodimensionalwhentheaspectratiois
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
楳
摥瑥牭楮敤
晲潭
捡汬敤
瑨t
specific
weight
γ
慮a
楳
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“newtonmeter
(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.
•Allnonprimaryunits(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, timeconsuming, 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
PROBLEMSOLVING TECHNIQUE
•using a stepbystep
approach, an
engineer can reduce
the solution of a
complicated problem
into the solution of a
series of simple
problems.
10:10
42
PROBLEMSOLVING 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
widelyusedforflowmodelingapplications.
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; problemsolving
technique; and accuracy, precision, and significant digits will be
used throughout the entire text.
10:10
48
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