UNIVERSITA¨TDUISBURG-ESSEN

INSTITUTFU¨RVERBRENNUNGUNDGASDYNAMIK

Prof.Dr.-Ing.D.H¨anel

Problem1: FluidDynamics

d

u

h

SEMESTERKLAUSURFU¨R

“MECHANICALENGINEERING”–FLUIDMECHANICS–

Theactingonabridgepillarinwaterflowisdeterminedinawind

tunnelexperimentusingair.Theoriginalpillar(index“2”)anditswindtunnelmodel(index“1”)aregeometricallysimilar(h1=d1).

TagderPru¨fung: 17.2.2004

Bearbeitungszeit: 120Minuten

Hilfsmit: licheMitschriftenundScripte

Known:

ρ1=1.25kg/m3, η1=1.875·10?5Ns/m2

ρ2=1000kg/m3, η2=1.0·10?3Ns/m2

h2 d2

F

Calculatetheratioofdrag sF1actingonthemodel(1)andthe

2

original(2)pillarassumingReynoldssimilarity.

s

Thesizeofoneoriginalpillarisd2=1m,h2=4matwaterspeedu2=5m.TheairtemperatureinthewindtunnelisT=300Kandthemodelscaleis1:2.

Known:

d2=2d1=1m,h2=2h1=4m

u2=5m, T=300K, R=287J, γ=1.4

s kgK

Determinetheairspeedinthewindtunnel.Istheassumptionofpressibilitywarrantableinthemodelexperiment?Givereasons

foryouranswer!

Problem2: FluidDynamics

Themathematicalmodelofatornasarigidbodyrotationfortheinnercoreandapotentialvortexfortheouterregion.

Problem3: FluidDynamics

Twonetesinarowareholdinparallelflowwithvelocityu.Forthe

calculationofthedragcoefficienttheBlasiussolutionfortheboundarylayerataneteisused.

Θ

v(r)=(ωr r≤rm

;vr=0

L1

L2

F1

F2

ωr2

r

mr>rm u L

Thepressuremeasuredinthetornadowas

p0 =p(r=0) =0.8barp1 =p(r=50m)=0.85barp∞=p(r=∞) =1.0bar

m3

attheconstantdensityρ=1.25kg.

Calculatethepressuredistributionp(r)fortherigidbodyrotation.

Calculatethepressuredistributionp(r)ofthepotentialvortex.

Known:

L=L1+L2=0.36m, B=1m,

Sketchthequalitativevelocityv(r)andpressuredistributionp(r)of

u=1m, ρ=1000kg, ν=1·10?6m2

Θ

thetornanadiagram.

Calculatetheumvelocityvmandthecorrespondingpressure

pminsidethetornado.

Calculatethepositionrmofthehighestvelocity.

s m3 s

CalculatethesF1andF2forL1=L2.

CalculatethelengthL1andL2forF1=F2.

Hint:

?p v2

=ρ

?r r

Problem4: FluidDynamics

1

*

2

3

Airofstate“1”flowsthroughalavalnozzleintoatestsection.Abluntbodyiscedinthetestsection,wherebyadetachedcompressionshockisgeneratedinfrontofit.Theflowisstationary,one-dimensional,adiabaticandexcepttheshock,isentropic.Betweenstates“2”and“3”theshockisassumedtobenormal.

Known:

p1=6.5bar, T1=440K, M1=0.5, A1=0.016m2,

kgK

p2=1bar, R=287J, γ=1.4

CalculatetheMachnumberM2beforetheshockinthemeasuringsection.

CalculatethecrosssectionsA?andA2.

Calculatethemassfluxm˙throughthemeasuringsection.

Calculatetheconditionsafterthenormalshock(M3,p3,T3)andthestagnationties(p03,T03)atthebluntbody.

Hint:

Youcanusethediagramsbelowtosolvetheproblem.Pleasem