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8/20/2019 Materi Medflu

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Chapter 1: Basic Concepts

Eric G. PatersonDepartment of Mechanical and Nuclear Engineering

The Pennsylania !tate "niersity

!pring #$$%


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( #

Note to )nstructorsThese slides (ere deeloped1 during the spring semester #$$%* as a teaching aid for the

undergraduate 'luid Mechanics course +ME&&: 'luid 'lo(, in the Department of Mechanicaland Nuclear Engineering at Penn !tate "niersity. This course had t(o sections* one taught-y myself and one taught -y Prof. ohn Cim-ala. /hile (e gae common home(or0 andeams* (e independently deeloped lecture notes. This (as also the first semester thatFluid Mechanics: Fundamentals and Applications (as used at P!". My section had 2&students and (as held in a classroom (ith a computer* pro3ector* and -lac0-oard. /hileslides hae -een deeloped for each chapter of Fluid Mechanics: Fundamentals and

Applications, ) used a com-ination of -lac0-oard and electronic presentation. )n the studentealuations of my course* there (ere -oth positie and negatie comments on the use ofelectronic presentation. Therefore* these slides should only -e integrated into your lectures(ith careful consideration of your teaching style and course o-3ecties.

Eric Paterson

Penn !tate* "niersity Par0 4ugust #$$%

1 These slides (ere originally prepared using the 5aTe6 typesetting system +http:77(((.tug.org7, and the -eamer class +http:77late8-eamer.sourceforge.net7,* -ut (ere translated to Po(erPoint for(ider dissemination -y McGra(89ill.

http://www.tug.org/http://latex-beamer.sourceforge.net/http://latex-beamer.sourceforge.net/http://www.tug.org/


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( &

/hat is a fluid

4 fluid is a su-stance in the gaseous or li;uidformDistinction -et(een solid and fluid

!olid: can resist an applied shear -y deforming.

!tress is proportional to strain'luid: deforms continuously under applied shear.!tress is proportional to strain rate

F

Aτ α = µ

F V

A hτ µ = µ

!olid 'luid


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( <

/hat is a fluid

!tress is defined as theforce per unit area.

Normal component:normal stress

)n a fluid at rest* thenormal stress is calledpressure

Tangential component:shear stress


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( %

/hat is a fluid

4 li;uid ta0es the shape ofthe container it is in andforms a free surface in thepresence of graity

4 gas epands until itencounters the (alls of thecontainer and fills the entireaaila-le space. Gasescannot form a free surface

Gas and apor are oftenused as synonymous(ords


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( =

/hat is a fluid

solid li;uid gas


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( >

4pplications of fluid mechanic


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( ?

No8slip condition

No8slip condition: 4 fluid indirect contact (ith a solid@@stic0sA to the surface due toiscous effectsesponsi-le for generation of(all shear stress τ(* surfacedrag D τ( d4* and thedeelopment of the -oundarylayer The fluid property responsi-lefor the no8slip condition isviscosity

)mportant -oundary conditionin formulating initial -oundaryalue pro-lem +)BFP, foranalytical and computationalfluid dynamics analysis


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 2

Classification of 'lo(s

/e classify flo(s as a tool in ma0ing simplifyingassumptions to the goerning partial8differentiale;uations* (hich are 0no(n as the Naier8!to0es e;uations

Conseration of Mass

Conseration of Momentum


10/18

Chapter 1: Basic ConceptsME&& : 'luid 'lo( 1$

Fiscous s. )niscid egions of 'lo(

egions (here frictionaleffects are significant arecalled iscous regions.They are usually close tosolid surfaces.

egions (here frictionalforces are smallcompared to inertial orpressure forces are called

iniscid


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 11

)nternal s. Eternal 'lo(

)nternal flo(s aredominated -y theinfluence of iscositythroughout the

flo(field'or eternal flo(s*iscous effects arelimited to the

-oundary layer and(a0e.


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 1#

Compressi-le s. )ncompressi-le 'lo(

4 flo( is classified asincompressi-le if the densityremains nearly constant.5i;uid flo(s are typicallyincompressi-le.Gas flo(s are often

compressi-le* especially forhigh speeds.Mach num-er* Ma F7c is agood indicator of (hether ornot compressi-ility effects areimportant.

Ma $.& : )ncompressi-leMa 1 : !u-sonicMa 1 : !onicMa H 1 : !upersonicMa HH 1 : 9ypersonic


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 1&

5aminar s. Tur-ulent 'lo(

5aminar: highly orderedfluid motion (ith smoothstreamlines.Tur-ulent: highlydisordered fluid motion

characteriIed -y elocityfluctuations and eddies.Transitional: a flo( thatcontains -oth laminar andtur-ulent regions

eynolds num-er* eρ"57µ is the 0eyparameter in determining(hether or not a flo( islaminar or tur-ulent.


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 1<

!teady s. "nsteady 'lo(

!teady implies no change ata point (ith time. Transientterms in N8! e;uations areIero

"nsteady is the opposite ofsteady.Transient usually descri-es astarting* or deeloping flo(.

Periodic refers to a flo( (hich

oscillates a-out a mean."nsteady flo(s may appearsteady if Jtime8aeragedK


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 1%

Lne8* T(o8* and Three8Dimensional 'lo(s

N8! e;uations are &D ector e;uations.Felocity ector* U (x,y,z,t)= [U x (x,y,z,t),U y (x,y,z,t),U z (x,y,z,t)] 5o(er dimensional flo(s reduce compleity of analytical andcomputational solutionChange in coordinate system +cylindrical* spherical* etc., mayfacilitate reduction in order.

Eample: for fully8deeloped pipe flo(* elocity V(r) is a function ofradius r and pressure p(z) is a function of distance z along the pipe.


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 1=

!ystem and Control Folume

4 system is defined as a;uantity of matter or aregion in space chosenfor study.

4 closed system consists

of a fied amount ofmass.

4n open system* orcontrol olume* is aproperly selected regionin space./eAll discuss contrololumes in more detail inChapter =.


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 1>

Dimensions and "nits

4ny physical ;uantity can -e characteriIed -y dimensions.The magnitudes assigned to dimensions are called units.Primary dimensions include: mass m* length L* time t * andtemperature T .!econdary dimensions can -e epressed in terms of

primary dimensions and include: elocity V * energy E * andolume V ."nit systems include English system and the metric !)+)nternational !ystem,. /eAll use -oth.Dimensional homogeneity is a alua-le tool in chec0ing

for errors. Ma0e sure eery term in an e;uation has thesame units.Unity conversion ratios are helpful in conerting units."se them.


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Chapter 1: Basic ConceptsME&& : 'luid 'lo( 1?

4ccuracy* Precision* and !ignificant Digits

Engineers must -e a(are of three principals that goern the proper useof num-ers.

1. Accuracy error : Falue of one reading minus the true alue.Closeness of the aerage reading to the true alue. Generallyassociated (ith repeata-le* fied errors.

2. Precision error : Falue of one reading minus the aerage ofreadings. )s a measure of the fineness of resolution andrepeata-ility of the instrument. Generally associated (ith randomerrors.

3. Significant digits : Digits that are releant and meaningful. /hen

performing calculations* the final result is only as precise as theleast precise parameter in the pro-lem. /hen the num-er ofsignificant digits is un0no(n* the accepted standard is &. "se & inall home(or0 and eams.

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