microsoft power point - fluids -senatorlibya [compatibility mode]

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


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


Gases - Widely spacedmolecules

Negligable cohesive force

Cannot for a free surface


4/27

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

=


molecular variations Limiting volume ~10e-09

mm3 - Most engineeringproblems


5/27

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)


Time {T} Second (s) Second (s)

Temperature {} Kelvin (K) Rankine (oR)


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Dimensions and Units (Dimensions and Units (22))



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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


}{}{}{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


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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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


Temperature - TMeasure of internal energy

Absolute Temperature Scales

16.273

69.459

+=

+=

CK

FRo

oo


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EnergyInternal - stored energy from molecular activity and

bonding forces

ue ====

2V

1++++ gz++++


-

zero to a velocity V (give mathematical definition)

Potential - the work to move a mass against a gravityfield


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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


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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Equation of State for a Liquid= constant

Cp~ Cv~ const

dh = CpdT


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


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


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


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


Liquid

2

ln

+

+

T

TcT

Tba oo

o

74684941

s)-kg/(m001792.016.273

:

., c.-, b.-a

KT

Water

o

o

===

=

=


17/27

The Reynolds NumberThe Reynolds Number

A dimensionlessquantity

Use dimensionless

ConvecttoTime

DiffusetoTimeRe ===

VLVL

Re = 15,000


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



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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}


P dA

= 0Fr


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Force Balance on Idealized ShapesForce Balance on Idealized Shapes


= 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


Depends on the physical-chemical conditions

of solid-liquid interface

Finish on a Newly waxed car vs. dirty old car

Clean Hg- glass =130o


22/27

Surface Tension ExampleSurface Tension Example



23/27

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


Defn: Mach Number =Ma= Fluid velocity / Speed of Sound

Speed of Sound = RTa =gasideal


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Inviscid vs ViscousInviscid vs Viscous

For high Reynolds number can be consideredinviscid flow

Viscosity important in certain regions of the



25/27


Steady and Unsteady FlowSteady and Unsteady Flow

Steady - the flow field

does not change in time


Unsteady - the flow fieldchanges in time


26/27

InIn--Class ProblemClass Problem

Couete flow related



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SummarySummary

The Concept of Fluid

Continuum Approximations Dimensions and Units Thermodynamic properties of a fluid

Viscosity and other properties


Couet Flow

Surface Tension Flow types

Compressible, Incompressible

Viscous, Inviscid

microsoft power point - fluids -senatorlibya [compatibility mode]

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