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ScaZemodeling
Scalemodelingutilizesthelawofnature，inanartificialreplicaoftheequipmentwhichis smalerthantherealsystemhavethekeyproperties.Thescalingupordownprocesiscaried outbysimilaritycriteriawhichconecttogetherthephysicalproperty，characteristicsofthef1uid f10wandthedimensionsoftherealsystemandlaboratorymode.lFirstofal，itisindispensable toobserveanddiscernthephenomenaoftherealobjectcarefuly，toselectthephysicallaw whichgovemingphenomena.Thegoverningequationsselectedbykeyphenomenaforthescale modelingisasfolows[8].
尺=ρf2U2
FJ=μZu (2) ζ=ρgZ3 (3)
F:=(J-f (4) Threenon-dimensionalnumberswhichcaledπ-numbersisderivedbyequation(1)through
equation(4)formomentumbalance.
lnertiaforceofwaterandair
Viscosityofwaterandair
Gravityforceofwaterandair
(1)
Surfacetensionofwater
22
-，F; ρZ'U ρlu
yrl=一一一一一=一一 (Reynoldsnumber) (5) F;， j.ilu μ
F OZ2U2 u2
π _1_=こー， 1
ι ζ p gf' gZ
222 F; ρZ'U ρlu
一 (Froudenumber) (6)
7r3=-:;-一=一 (Webernumber) (7)
F: Theπ1toπ3arenon-dimensionalnumbersforsimilaritylawsofairandwaterf1ow，whichshows
(jZ σ
theReynoldsnumber，theFroudenumber，andtheWebernumber，respectively.lnreality，itis imposibletosetupthelawofsimilaritywhichitissimultaneouslysatisfiedwithalofπ- numbersinamodelexperiment.Then，therelaxationofthesimilaritylawisaprocedureby eliminationofsecondphysicslaw，employingtheanalyticalmethodandseparationaphenomena.
π，二円 =ρlu F;， μ
Ip=p'l~三司
↓ Lh=IUI 日
(8)
TheReynoldsnumberoftherealmodelisinaturbulentf10wrange.lntheturbulencerange， sincetheefectofaninertiaforceisoveridingly，itisnotnecesarytotaketheefectofviscous forceintoconsideration.Therefore，theequalizationoftheReynoldsnumberbetweenareal modelandascalemodelisnotrequired.
π1=F7r1' (Relaxed) (9)
