Wor k i ngpr i nc i pl eofVor t exflowmet er Whenaflui dmoveswi t hhi ghReynol dsnumberpastast at i onar yobj ect( a“bl uffbody”) ,t her ei sat endency f ort heflui dt of or mv or t i c esone i t he rs i deoft heobj e ct .Ea chv or t e xwi l lf or m,t he nde t a chf r om t heobj e ct a ndc ont i nuet omo vewi wi t ht heflowi ngga sorl i qui d,onesi deatat i mei na l t e r na t i ngf a shi on.Thi s phenomenoni sknown wnasvor t exsheddi ng,andt hepat t er nofmovi ngvor t i cescar r i eddownst r eam oft he s t a t i ona r yobj e cti sk nowna sav or t e xs t r e et . I ti scommonpl acet oseet heeffect sofvor t exsheddi ngonawi wi ndydaybyobser vi ngt hemo mot i onof fla gpol e s,l i ghtpol e s,a ndt a l ls mok mo es t a ck s.Ea choft he seobj e ct sha sat e nde nc yt oos ci l l a t epe r p endi c ul a r t ot hedi r e ct i onoft hewi nd,owi ngt ot hepr e ss ur ev ar i a t i onsc aus edbyt hev or t i c esa st he ya l t e r n at e l yf or m andbr eakawa wayf r om t heobj ect :
Thi sa l t e r n at i ngs er i e sofv or t i c eswa ss t udi e dbyVi nc encSt r ouha li nt hel a t eni ne t e ent hc ent ur ya ndl a t e r b yThe odor ev onK´ a r m´ a ni nt hee ar l yt we nt i e t hc ent ur y .I twa sde t e r mi ne dt ha tt hedi s t a nc ebe t we e n s uc ce ss i v ev or t i c esdowns t r e am oft hest a t i ona r yobj e cti sr e l a t i v el yconst a nt ,a nddi r e ct l ypr opor t i ona lt o t hewi wi dt hoft heobj e c t ,f orawi wi der a n geofRe y nol dsnumbe rv a l ue s.I fwev i e wt he sev or t i c esascr e st sofa cont i nuouswave,t hedi st ancebet weenvor t i cesma mayber epr esent edbyt hesymb mbolcust omar i l yr eser ved f orwa v el e ngt h:t heGr Gr e ekl e t t e r“ l a mbda mb ”( λ) .
Thepr opor t i ona l i t ybe t we enobj e ctwi dt h( d)a ndv or t e xs t r e etwa v el e ngt h( λ)i sca l l e dt he St r ouha lnumbe r( S) ,a ppr o xi ma t e l ye qua lt o0 . 1 7 : λS=d
λ≈d/ 0. 17
I fadi ffe r e nt i a lpr e ss ur ese ns ori si ns t a l l e di mme di a t e l ydowns t r e am oft hest a t i ona r yobj e cti ns uc ha n or i ent a t i ont ha ti tde t e ct st hepas si ngv or t i c esaspr e ss ur ev ar i a t i ons ,a na l t e r na t i ngs i gna lwi l lbede t e ct ed:
Thef r eque nc yoft hi sa l t e r na t i ngpr e ss ur es i gna li sdi r e ct l ypr opor t i ona lt oflui dv el oc i t ypa stt heobj e ct , s i nc et hewa v el e ngt hi scons t a nt .Thi sf ol l owst hecl a ss i cf r e que nc yv e l oc i t y wa v e l e ngt hf or mul acommon t oa l lt r a v el i ngwa v e s( λf=v ) .Si nc eweknow t hewa v el e ngt hwi l lbeequa lt ot hebl uffbody ’ swi dt hdi v i de d byt heSt r ouha lnumbe r( a ppr ox i ma t e l y0. 1 7) ,wema ysubs t i t ut et hi si nt ot hef r e que nc yv el oc i t y wa v el e ngt h f or mul at os ol v ef orflui dv el oc i t y( v )i nt e r msofs i gna lf r e que nc y( f )a ndbl uffbodywi dt h( d) . v=λf v=d/ 0 . 1 7* f v=df / 0. 17 Thus ,ast a t i ona r yobj e cta ndpr e ss ur ese ns ori ns t a l l e di nt hemi ddl eofapi pese ct i onc ons t i t ut eaf or m of flowme t e rc al l e davor t e xflowme t e r .Li k eat ur bi neflowme t e rwi t ha ne l e ct r oni c“pi c kup”sens ort ode t e ct t hepa ss ageofr ot a t i ngt ur bi nebl a de s,t heout putf r e que nc yofav or t e xflowme t e ri sl i ne ar l ypr opor t i ona lt o v ol ume t r i cflo wr a t e . Thepr e s sur ese ns or sus e di nv or t e xflowme t e r sar enots t a nda r ddi ffe r e nt i a lpr e ss ur et r a ns mi t t e r s ,s i nc e t hev or t e xf r e que nc yi st oohi ght obesuc ce ss f ul l yde t e ct e dbysuc hbul k yi ns t r ume nt s .I ns t e ad,t he s ens or sa r et y pi c al l ypi e z oe l e ct r i cc r y s t a l s .The sepr e ss ur es ens or sne ednotbec al i br a t e d,s i nc et he a mpl i t udeoft hepr e ss ur ewa v esde t e ct e di si r r e l e v ant .Onl yt hef r e que nc yoft hewa v esma t t e rf or measur i ngflow r at e,andsonear l yanypr essur esensorwi t haf astenoughr esponset i mewi l lsuffice.
Li k et ur bi neme t e r s ,t her e l a t i ons hi pbe t we e ns ens orf r e que nc y( f )a ndv ol ume t r i cflo wr a t e( Q)ma ybe e xpr es se dasapr opor t i ona l i t y ,wi t ht hel e t t e rkus edt or epr es entt hecons t a ntofpr opor t i ona l i t yf ora ny pa r t i c ul a rfl owme t e r f=k Q Wher e, f=F r e que nc yofout puts i gna l( Hz ) Q =Vol ume t r i cflow r a t e( e . g.ga l l onspe rs ec ond) k=“ K”f a ct oroft hev or t e xs he ddi ngflowt ube( e . g.pul s espe rga l l on) Thi sme ansv or t e xflowme t e r s ,l i k ee l e ct r oni ct ur bi neme t e r s ,e ac hha v eapa r t i c ul a r“ kf a ct or ”r e l a t i ngt he numberofpul sesgener at edperuni tvol umepassedt hr ought hemet er .Count i ngt het ot alnumberofpul ses o ve racer t a i nt i mespa ny i e l dst ot a lflui dvol umepa ss e dt hr ought heme t e ro ve rt ha ts amet i mespa n, ma ki ngt hev or t e xflowme t e rr e adi l yada pt a bl ef or“ t ot a l i z i ng”flui dv ol umej us tl i k et ur bi neme t e r s .The di r ectpr opor t i onbet weenvor t exf r equencyandvol umet r i cflow r at eal someansvor t exflowmet er sar e l i ne ar r e spondi ngi ns t r ume nt s .Unl i k eor i fic epl a t e swhi c he xhi bi taqua dr a t i cr e spons e,t ur bi nea ndv or t e x flowmet er sal i keenj oyawi derr ange( t ur ndown)offlow measur ementanddonotr equi r especi alsi gnal c har a ct er i z at i ont of unct i onpr ope r l y . Si ncevor t exflowmet er shavenomovi ngpar t s,t heydonotsuffert hepr obl emsofwearandl ubr i cat i on f aci ngt ur bi nemet er s.Ther ei snomovi ngel ementt o“coast ”asi nat ur bi neflowmet eri fflui dflow suddenl y st ops,whi chmeansvor t exflowmet er sar ebet t ersui t edt omeasur i nger r at i cflows. Asi gni ficantdi sadvant ageofvor t exmet er si sabehavi orknownasl ow flow cut off,wher et heflowmet er s i mpl yst opswor k i ngbe l ow ace r t a i nflow r a t e .Ther e as onf ort hi si sl a mi na rflow:a tl ow flow r a t e s( i . e .l ow Reynol dsnumberval ues)flui dvi scosi t ybecomessuffici entt opr eventvor t i cesf r om f or mi ng,causi ngt he vor t exflowmet ert or egi st erzer oflow evenwhent her emaybesome( l ami nar )flow t hr ought hepi pe.Athi gh flow r at es( i . e.hi ghReynol dsnumberval ues) ,flui dmoment um i senought oover comevi scosi t yand pr oducevor t i ces,andt hevor t exflowmet erwor ksj ustfine. Thephenomenonofl owflow cut offf oravor t exflowmet eratfir stseemsanal ogoust ot hemi ni mum l i near flow l i mi t a t i onofat ur bi neflo wme t e r .Howe v er ,v or t e xflo wme t e rl o wflow c ut offi sact ua l l yaf a rmor esev e r e pr obl e m.I ft hevol ume t r i cflow r a t et hr oughat ur bi neflowme t e rf a l l sbe l ow t hemi ni mum l i ne arv a l ue ,t he t ur bi necont i nue st os pi n,a l be i ts l owe rt ha ni ts houl d.I ft hev ol ume t r i cflow r a t et hr oughavor t e xflowme t e r f a l l sbe l ow t hel owflow c ut offv a l ue ,ho we v e r ,t heflo wme t e r ’ ssi gna lgoe sc ompl e t e l yt oz e r o,i ndi c a t i ngno flow a ta l l . Thef ol l owi ngphot ogr aphshowsaRosemountmodel8800Cvor t exflow t r ansmi t t er :
Thene x tt wophot ogr a phssho wc l os e upv i e wsoft heflo wt ubeas se mbl y ,f r ont( l e f t )a ndr e ar( r i ght ) :
