v intro to dimensional analysis · 2016. 8. 4. · axisymmetric heated jet of fluid a (sewage...
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Introtodimensionalanalysis
THURSDAYLAB#3
1.Diffusion
a)Itisdesiredtoevaluatechangesinsaltconcentration(salinity)inaquiescenttankofwater10mdeepinwhichasalinitygradienthasbeenestablishedintheverticaldirection.Thetankisnotstirredandiscompletelysealedfromitssurroundings(nowaterorsaltisaddedortakenaway).Estimatethetimerequiredforthegradienttobesmoothedbymoleculardiffusion(moleculardiffusivityforsaltinwateris10-9cm2/s).Doesthemagnitudeoftheinitialgradientmakeanydifference?
b)Whatifwearelookingatheatdiffusionthruthesametank?Thethermaldiffusivityforwateris10-7m2/s.Howlongdoesittakenow?
c)Ifturbulenceispresent,whatwillbethetimeforthegradienttobesmoothedout?Assumeaturbulentdiffusivityof10-5m2/s.
2.Diffusionversusturbulence
Qualitativelyshowtheradialprofilesofvelocity,temperature,andconcentrationforanaxisymmetricheatedjetoffluidA(sewagedischargeinawellmixedbayforexample),introducedintoquiescentambientfluidB.AssumeD>α>ν,whereDandαaremassandthermaldiffusioncoefficients,respectively,andνisthekinematicviscosity.Make2separateplotsatx/d=0.5andx/d=30.
1. The impulse is conserved and And therefore the velocity Also, and therefore And
2. We talked about that today in class: drag coefficient, lift coefficient, aspect ratio, roughness ratio, Re, dimensionless spin
3. Pure diffusion process so
The time it takes is then 1011s. No effect of initial gradient.
4.
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L = Dt
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3.Momentumversusbuoyancy
Usingabeaker,wewillcreateaverticaljet(withasyringe)andaverticalplume(differentdensityfluid)andlookatthedifferenceinspatialspreadingandspeedinbothcases.Alosnoticethedifferenceineddystructureastheflowmovesdownstream.
Demonstratethrudimensionalanalysistherelationshipbetweenwidth/spreadandcenterlinevelocityasafunctionoftimeanddownstreamdistanceforjetsversusplumes.
AlbumofFluidMotion,VanDyke oceanography101.wikispaces.com
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