CHAPTER 1 : PROPERTIES OF FLUIDS What is fluid? A fluid is...
Transcript of CHAPTER 1 : PROPERTIES OF FLUIDS What is fluid? A fluid is...
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