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8/8/2019 Microsoft Power Point - Fluids -Senatorlibya [Compatibility Mode]
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Introduction and FundamentalsIntroduction and Fundamentals
The concept of a Fluid Continuum Approximations
Dimensions and Units
Thermod namic ro erties of a fluid
ME395 Lecture2 Fluid Mechanics EPN Duque
Viscosity and other properties
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The concept of a FluidThe concept of a Fluid
For a fluid the moleculesnot fixed to a latticestructure
Solid can resist a shearstress b a static
ME395 Lecture2 Fluid Mechanics EPN Duque
deformation; a fluidcannot
A fluid at rest must be ina state of zero shearstress
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The concept of a Fluid,The concept of a Fluid, 22
Liquids - Closelypacked molecules
Strong cohesive forces
Tend to retain its volume
Forms a free surface ingravitational field atunsupported surface
ME395 Lecture2 Fluid Mechanics EPN Duque
Gases - Widely spacedmolecules
Negligable cohesive force
Cannot for a free surface
8/8/2019 Microsoft Power Point - Fluids -Senatorlibya [Compatibility Mode]
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Density of Fluid definedas:
Too large volume givesnoticable variations inparticles
Continuum ApproximationsContinuum Approximations
Fluid Properties vary smoothly or continuously in space
V
m
V
0
lim
=
ME395 Lecture2 Fluid Mechanics EPN Duque
molecular variations Limiting volume ~10e-09
mm3 - Most engineeringproblems
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Dimensions and UnitsDimensions and Units
Dimensions - measure of a physical variable
Unit - value of the quantitative dimension
Mass {M} Kilogram (kg) Slug
Length {L} Meter (m) Foot (ft)
ME395 Lecture2 Fluid Mechanics EPN Duque
Time {T} Second (s) Second (s)
Temperature {} Kelvin (K) Rankine (oR)
8/8/2019 Microsoft Power Point - Fluids -Senatorlibya [Compatibility Mode]
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Dimensions and Units (Dimensions and Units (22))
ME395 Lecture2 Fluid Mechanics EPN Duque
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Dimensions and Units (Dimensions and Units (33))
Equations should be dimensionally consistent
gZVPPo ++=2
2
1
}{PressureStagnation 21 == TMLPo
PressureStatic 21 == TLP
ME395 Lecture2 Fluid Mechanics EPN Duque
}{}{}{Velocity)anddensityf(2
1 212232 === TMLTLMLV
}{}}{}{{altitude)gravity,f(density, 2123 === TMLLLTMLgZ
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Thermodynamic Properties of FluidsThermodynamic Properties of Fluids -- 11
Current statePressure - P
Density - Temperature - T
Capacity to do work or the availability to dowork
A quantity which describes a fluid's
ME395 Lecture2 Fluid Mechanics EPN Duque
Internal Energy - e
Enthalpy - h = u + P/
Entropy - s
Specific Heats - Cp and Cv
Diffusion of momentum or energy (TransportProperties)
Dynamic or Absolute Viscosity -
Thermal Conductivity - k
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Thermodynamic Properties of FluidsThermodynamic Properties of Fluids -- 22
Pressure -pScalar Property
Seen as a compression stress ( force per unit area )
Gradients in Pressure drive fluid flow
Density - A fluids mass per unit volume
ME395 Lecture2 Fluid Mechanics EPN Duque
Temperature - TMeasure of internal energy
Absolute Temperature Scales
16.273
69.459
+=
+=
CK
FRo
oo
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Thermodynamic Properties of FluidsThermodynamic Properties of Fluids -- 33
EnergyInternal - stored energy from molecular activity and
bonding forces
ue ====
2V
1++++ gz++++
ME395 Lecture2 Fluid Mechanics EPN Duque
-
zero to a velocity V (give mathematical definition)
Potential - the work to move a mass against a gravityfield
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Thermodynamic Properties of FluidsThermodynamic Properties of Fluids -- 44
State Relations for a Gas
Perfect or Ideal Gas - P =RT
Gas Constant -R = Cp- Cv
Universal Gas Constant - Rgas= /MgasSpecific Heats
Cv = du/dTat constant density -> du = Cv(T)dT
= du/dTat constant ressure -> dh = C T dT
ME395 Lecture2 Fluid Mechanics EPN Duque
Ratio of Specific Heat = Cv/Cp
Air Considered A perfect gas
R= 287 J/kg-K
= 1.4
Cv= 718 m2 / (s2-K)
Cp= 1,004 J/kg-K
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Thermodynamic Properties of FluidsThermodynamic Properties of Fluids -- 55
Equation of State for a Liquid= constant
Cp~ Cv~ const
dh = CpdT
ME395 Lecture2 Fluid Mechanics EPN Duque
ee a es or ermo ynam c roper es
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Viscosity and other propertiesViscosity and other properties
When a fluid is sheared, it moves at a strainrate inversely proportional to the coefficientof Viscosity -
t
ME395 Lecture2 Fluid Mechanics EPN Duque
y =)tan(
anglessmallassuming;dy
du
dt
d=
dy
du
dt
d
==
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Shear Velocity ProfilesShear Velocity Profiles
Example of a velocityprofile near a wall
Velocity changes with y
Gradient at wall causes
ME395 Lecture2 Fluid Mechanics EPN Duque
r ct on
Shear stress varieslinearly with strain rate =Newtonian Fluid
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NonNon--Newtonian FluidsNewtonian Fluids
Shear stress is notproportional to strain rate
Bingham - linear after a yieldstress
Dilatant - strain harding
pseudoplastic - shear
ME395 Lecture2 Fluid Mechanics EPN Duque
nn ng
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Temperature Variation of ViscosityTemperature Variation of Viscosity
Gas
( ) ( )
+
+
LawsSutherland
lawPower2/3
ST
STTT
T
T
oo
n
o
o
KS
n
o199or110
7.0
:Air
ME395 Lecture2 Fluid Mechanics EPN Duque
Liquid
2
ln
+
+
T
TcT
Tba oo
o
74684941
s)-kg/(m001792.016.273
:
., c.-, b.-a
KT
Water
o
o
===
=
=
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The Reynolds NumberThe Reynolds Number
A dimensionlessquantity
Use dimensionless
ConvecttoTime
DiffusetoTimeRe ===
VLVL
Re = 15,000
ME395 Lecture2 Fluid Mechanics EPN Duque
quantities tocharacterize a flow.
By stating the Reynoldsnumber we have someidea on flows behavior
Re = 30,000
ViscosityKinematic==
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Example ProblemExample Problem
ME395 Lecture2 Fluid Mechanics EPN Duque
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Surface TensionSurface Tension
Liquids that expand freely will form interfacewith 2nd liquid or Gas
At interface a Mechanical tension occurs
- Coefficient of Surface Tension{Force/Length}
ME395 Lecture2 Fluid Mechanics EPN Duque
P dA
= 0Fr
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Force Balance on Idealized ShapesForce Balance on Idealized Shapes
ME395 Lecture2 Fluid Mechanics EPN Duque
= 0.0050 lbf/ft = 0.073 N/m (air-water)= 0.033 lbf/ft = 0.48 N/m (air-mercury)
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Contact SurfaceContact Surface
Contact Angle - Angle at which interfaceintersects a surface
ME395 Lecture2 Fluid Mechanics EPN Duque
Depends on the physical-chemical conditions
of solid-liquid interface
Finish on a Newly waxed car vs. dirty old car
Clean Hg- glass =130o
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Surface Tension ExampleSurface Tension Example
ME395 Lecture2 Fluid Mechanics EPN Duque
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Flow TypesFlow Types
Compressible and IncompressibleCompressible and Incompressible
For static fluidsIncompressible if density undergoes small changes
For dynamic fluids (flowing)Fluid velocit a roaches or exceeds S eed of Sound
ME395 Lecture2 Fluid Mechanics EPN Duque
Defn: Mach Number =Ma= Fluid velocity / Speed of Sound
Speed of Sound = RTa =gasideal
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Flow TypesFlow Types
Inviscid vs ViscousInviscid vs Viscous
For high Reynolds number can be consideredinviscid flow
Viscosity important in certain regions of the
ME395 Lecture2 Fluid Mechanics EPN Duque
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Flow TypesFlow Types
Steady and Unsteady FlowSteady and Unsteady Flow
Steady - the flow field
does not change in time
ME395 Lecture2 Fluid Mechanics EPN Duque
Unsteady - the flow fieldchanges in time
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InIn--Class ProblemClass Problem
Couete flow related
ME395 Lecture2 Fluid Mechanics EPN Duque
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SummarySummary
The Concept of Fluid
Continuum Approximations Dimensions and Units Thermodynamic properties of a fluid
Viscosity and other properties
ME395 Lecture2 Fluid Mechanics EPN Duque
Couet Flow
Surface Tension Flow types
Compressible, Incompressible
Viscous, Inviscid