CHAPTER 1 : PROPERTIES OF FLUIDS What is fluid? A fluid is …syahruls/resources/MKMM-1313/1-Lecture... · 2018. 9. 15. · CHAPTER 1 : PROPERTIES OF FLUIDS What is fluid? A fluid

CHAPTER1:PROPERTIESOFFLUIDSWhatisfluid?Afluidisdefinedasasubstancethatdeformscontinuouslywhenactedonbyashearingstressatanymagnitude. Ina fluidatrest,normalstress iscalled“pressure”.Unit:Pleaserememberalltheunitthatyouuseinyourcalculation.Therearenomarksforcorrectanswerwithoutunit.Pleasebecarefulaboutthis.

DENSITYDesignatedbytheGreeksymbol 𝜌 (rho).Definedasitsmassperunitvolume.

𝜌 =𝑚𝑎𝑠𝑠𝑣𝑜𝑙𝑢𝑚𝑒

=𝑘𝑔𝑚_

Specific volume, 𝜈 is the volume per unit mass. This property is notcommonlyusedinfluidmechanicsbutisusedwidelyinthermodynamics.

𝜈 =𝑣𝑜𝑙𝑢𝑚𝑒𝑚𝑎𝑠𝑠

=1𝜌=𝑚_

𝑘𝑔

“Pleaserememberallthebasicpropertiesofcommonfluids”

Densityalsochangewithtemperature!

SPECIFICWEIGHTDesignatedbytheGreeksymbol 𝛾 (gamma).Definedasitsweightperunitvolume.

𝛾 =𝑤𝑒𝑖𝑔ℎ𝑡𝑣𝑜𝑙𝑢𝑚𝑒

=𝑚𝑎𝑠𝑠 𝑔𝑟𝑎𝑣𝑖𝑡𝑦

𝑣𝑜𝑙𝑢𝑚𝑒=𝑘𝑔 ∙ 𝑔𝑚_ = 𝜌𝑔

Unit:jklmnm

atau olp

SPECIFICGRAVITYDesignatedasSG.Definedastheratioofthedensityofthefluidtothedensityofwateratsomespecifiedtemperature.Usuallythespecifiedtemperatureistakenas4°C.

𝑆𝐺 =𝜌vwxyz

𝜌{|}~�|}�∘�

Unit:Dimensionless

THEPERFECTGASAll the commongases followwith reasonable accuracy, at least in somefiniteregion,theso-calledidealorperfectgaslaw:

𝑝 = 𝜌𝑅𝑇𝑅iscalledthegasconstantwhichistheratioofBoltzmann’sconstanttothemassofasinglemolecule:

𝑅 =𝐾𝑚

alternatively,𝑅maybewrittenintermsofthemolecularweight,𝑀ofthegases:

𝑅k|n =𝑅�𝑀k|n

=8314(J/kg∙mol∙K)

𝑀k|n(mol)

Unit: J

kg∙K

VISCOSITYViscosityisameasureofafluid'sresistancetoflow.Itdescribestheinternalfrictionofamovingfluid.Afluidwithlargeviscosityresistsmotionbecauseitsmolecularmakeup gives it a lot of internal friction. A fluidwith lowviscosity flowseasilybecause itsmolecularmakeupresults invery littlefrictionwhenitisinmotion.Gasesalsohaveviscosity,althoughitisalittlehardertonoticeitinordinarycircumstances.

Noslipcondition:Particlesclosetoasurfacedonotmovealongwithaflowwhenadhesionisstrongerthancohesion.Atthefluid-solidinterface,theforceofattractionbetweenthefluidparticlesandsolidparticles(Adhesiveforces)isgreaterthan that between the fluid particles (Cohesive forces). This forceimbalancebringsdownthefluidvelocitytozero.For a givenmotion 𝑉 of theupperplate, 𝜏�� is constant, hence

zxz� is

constant,sothattheresultingvelocityprofileislinearacrosstheplate.

𝜏�� = 𝜇𝑑𝑢𝑑𝑦

Thequantity𝜇,calledthecoefficientofviscosityofaNewtonianfluid.Alsocalledasdynamicviscosity.Unit:𝑁 ∙ 𝑠/𝑚�or𝑘𝑔/𝑚 ∙ 𝑠Example:water,commonoils,commongases

Ifthecoefficient𝜇nonlinear,thefluidissaidtobenon-Newtonian.Example:toothpaste,shampoo,paintorblood.

Pseudoplasticfluidorshear-thinningfluid:Itslocalviscositydecreaseswithincreasingstress.Dilatantfluidorshear-thickeningfluid:Itslocalviscosityincreaseswithincreasingstress.Inthissituation,thereisonlyasinglefinitestrainrateinthisflow.

𝜖�� =12𝜕𝑢𝜕𝑦

+𝜕𝑣𝜕𝑥

=12𝜕𝑢𝜕𝑦

=12𝑑𝑢𝑑𝑦

𝜏�� = 2𝜇𝜖�� = 𝜇𝑑𝑢𝑑𝑦

Asimplebutofteneffectiveanalyticapproachtonon-Newtonianbehavioristhepower-lawapproximationofOstwaldanddeWaele:

𝜏�� ≈ 2𝐾𝜖��£ where𝐾 and𝑛arematerial parameters which in general vary with thepressureandtemperature(andcompositioninthecaseofmixture).Theexponent𝑛delineatesthreecases. 𝑛 < 1 Pseudoplastic 𝑛 = 1 Newtonian 𝐾 = 𝜇 𝑛 > 1 Dilatant

COMMONDIMENSIONLESSPARAMETERSConsiderarelativelygeneralrelationshipbetweenthepressuredrop∆𝑝,alength L, a characteristic velocity V, the density𝜌 , the viscosity𝜇 , thegravity g, the surface tension𝜎 , the sound of speed c and an angularfrequency𝜔,writtenas:The pi-theorem applied to this problem, with L, V and 𝜌 as repeatingvariables,resultsin:

∆𝑝𝜌𝑉�

= 𝑓𝜌𝑉𝐿𝜇

,𝑉�

𝑔𝐿,𝑉𝑐,𝐿𝜔𝑉,𝑉�𝜌𝐿𝜎

Eulernumber:

𝐸𝑢 =∆𝑝𝜌𝑉�

Reynoldsnumber:

𝑅𝑒 =𝜌𝑉𝐿𝜇

Froudenumber:

𝐹𝑟 =𝑉�

𝑔𝐿

Machnumber:

𝑀 =𝑉𝑐

Strouhalnumber:

𝑆𝑡 =𝐿𝜔𝑉

Webernumber:

𝑊𝑒 =𝑉�𝜌𝐿𝜎