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

3.Momentumversusbuoyancy

Usingabeaker,wewillcreateaverticaljet(withasyringe)andaverticalplume(differentdensityfluid)andlookatthedifferenceinspatialspreadingandspeedinbothcases.Alosnoticethedifferenceineddystructureastheflowmovesdownstream.

Demonstratethrudimensionalanalysistherelationshipbetweenwidth/spreadandcenterlinevelocityasafunctionoftimeanddownstreamdistanceforjetsversusplumes.

AlbumofFluidMotion,VanDyke oceanography101.wikispaces.com