Maqaal ku saabsan isla'egta Poiseuilles
Isle'egta Poiseuille waxaa ogaaday Jean Louis Marie Poiseuille (1799-1869). Sida la sharraxay, dareere kasta waxaa loo tixgelin karaa dareere ku habboon. Dareeraha ku habboon ma laha viscosity. Haddii aan u qaadanno dareere ku habboon inuu ku qulqulo tuubo, qayb kasta oo dareere ah waxay ku socotaa isla heerka (v). Si ka duwan dareeraha ku habboon, dareeraha dhabta ah ee aan la kulanno nolol maalmeedka wuxuu leeyahay viscosity. Sababtoo ah wuxuu leeyahay viscosity, markaa marka uu ku qulqulayo tuubo, tusaale ahaan, heerka qayb kasta oo dareere ah wuu kala duwan yahay. Lakabka dareeraha ah ee ku jira bartamaha ayaa si dhakhso leh u dhaqaaqa (v qoto dheer), lidkeeda, lakabka dareeraha ah ee ku xiran tuubada ma dhaqaaqo (v = 0). Markaa laga bilaabo bartamaha ilaa geeska tuubada, qayb kasta oo dareere ah ayaa ku dhaqaaqda heerar kala duwan. Si aad u fududeyso fahamkaaga, fiiri sawirka hoose.
R = gacanka tuubada/tuubada
v 1 = heerka socodka dareeraha ee dhidibka dhexe / tuubada
v 2 = heerka socodka dareeraha oo ah r 2 laga bilaabo geeska tuubada
v 3 = heerka socodka dareeraha r 3 laga bilaabo geeska tuubada
v 4 = heerka socodka dareeraha r 4 laga bilaabo geeska tuubada
r = masaafada
Si heerka socodka qayb kasta oo ka mid ah dareeraha uu isku mid noqdo, waxaa loo baahan yahay in farqi cadaadis uu ka jiro labada dhinac ee tuubada ama tuubo kasta oo dareeruhu dhex maro. Waxa halkan looga jeedo dareere waa dareere dhab ah, tusaale ahaan, biyo ama saliid ka soo daadata tuubo, dhiig ku socda xidid dhiig, iwm. Marka laga soo tago caawinta dareere dhab ah inuu si habsami leh u socdo, farqiga cadaadiska ayaa sidoo kale ka dhigi kara dareerayaashu inay ku socdaan tuubooyinka dhererkoodu kala duwan yahay.
Jean Louis Marie Poiseuille, oo ah saynisyahan hore oo Faransiis ah oo xiisaynayay dhinacyada jirka ee wareegga dhiigga aadanaha, ayaa cilmi baaris ku sameeyay sida arrimaha, sida kala duwanaanshaha cadaadiska, aagga isgoyska tuubada, iyo cabbirka tuubada ay u saameeyaan heerka dareeraha dhabta ah. Natiijooyinka waxaa helay Jean Louis Marie Poiseuille, oo loo yaqaan isla'egta Poiseuille.
Isle'egta Poiseuille waxaa laga heli karaa iyadoo la adeegsanayo isle'egta isku-dhafka viscosity oo hore loo xisaabiyay. Waxaan isticmaalnaa isle'egta viscosity sababtoo ah kiisaska waa isku mid, inkastoo aysan isku mid ahayn. Marka aan soo saareyno isle'egta isku-dhafka viscosity, waxaan dib u eegeynaa socodka lakabka dareeraha dhabta ah ee u dhexeeya 2 saxan oo is barbar socda, dareeruhuna wuu dhaqaaqi karaa sababtoo ah soo jiidashada (F). Farqiga ayaa ah in isle'egta Poiseuille ee aan soo saari doonno ay sheegayso arrimaha saameeya socodka dareeraha dhabta ah ee ku jira tuubada/tuubada iyo dareeraha socda ee ay ugu wacan tahay farqiga cadaadiska. Sidaa darteed, isle'egta isku-dhafka viscosity waxay u baahan tahay in mar kale la hagaajiyo.
Dareeraha ayaa ku qulquli kara farqiga cadaadiska (dareeraha wuxuu ka socdaa meel cadaadis sare leh ilaa meel cadaadisku hooseeyo), ka dibna waxaan ku beddelnaa F p 1 - p 2 (p 1 > p 2 ).
Marka aan soo saarno isle'egta isku-dhafka viscosity, waxaan dib u eegeynaa socodka lakabka dareeraha dhabta ah ee u dhexeeya 2 saxan oo is barbar socda. Qayb kasta oo ka mid ah dareeraha waxay beddeshaa xawaaraheeda caadiga ah ilaa l. Xaaladdan, heerka socodka dareeraha si joogto ah ayuu isu beddelaa laga bilaabo dhidibka tuubada ilaa cidhifka tuubada. Dareeraha ku jira dhidibka tuubada wuxuu ku socdaa xawaare weyn (v). Cidhifka badan, xawaaraha dareeraha ayaa yar. Radiuska tuubada = masaafada u dhaxaysa dhidibka tuubada iyo cidhifka tuubada = R. Masaafada u dhaxaysa qayb kasta oo ka mid ah dareeraha iyo cidhifka tuubada = r. Sababtoo ah xaddiga qayb kasta oo ka mid ah dareeraha waa weyn yahay masaafada u dhaxaysa cidhifka tuubadana sidoo kale way ka duwan tahay, markaa waxaan u qornaa sidan:
v 1 = xawaaraha dareeraha ee masaafada r 1 u jirta geeska tuubada (r 1 = R)
v 2 = xawaaraha dareeraha ee masaafada u jirta r 2 geeska tuubada (r 2 < r 1 )
v 3 = xawaaraha dareeraha masaafada r 3 ee u jirta geeska tuubada (r 3 < r 2 < r 1 )
v 4 = xawaaraha dareeraha ee masaafada r 4 u jirta geeska tuubada (r 4 < r 3 < r 2 < r 1 )
……………………………………… ..
v n = heerka dareeraha masaafada rn ee ka fog cidhifka tuubada (rn <…… <r 4 <r 3 <r 2 <r 1 )
Qaddarka qayb kasta oo dareere ah waa mid aad u weyn, sidoo kale ma naqaanno inta ay le'eg tahay qaddarka dhabta ah, sidaa darteed waxaa ku filan in lagu qoro calaamadda n. Qayb kasta oo dareere ah ayaa si joogto ah u beddesha xawaaraha (v), laga bilaabo dhidibka tuubada (r 1 = R) ilaa geeska tuubada (rn). Laga bilaabo dhidibka tuubada (r 1 = R) ilaa geeska tuubada (rn), heerka qayb kasta oo dareere ah waa yar yahay (v 1 > v 2 > v 3 > v 4 > ….> v n ).
Sharaxaadda kor ku xusan, waxaan ka heli karnaa jaantus muujinaya in laga bilaabo R ilaa rn, heerka dareeruhu uu yaraanayo. Dhererka tuubada = L. Isle'egta la helay:
Sababtoo ah waxa aan dib u eegeyno waa xawaaraha socodka dareeraha , ka dibna isle'egta 2aad waxay noqoneysaa:
Kani waa isle'egta xawaaraha socodka dareeraha ee masaafada r ee ka fog tuubada oo leh gacan R ah. Haddii aad wareerto inta aad fiirineyso sawirka kore… Fadlan ogow in dareeruhu uu ku socdo tuubo, markaa waxaan u baahanahay inaan dib u eegno heerka socodka mugga dareeraha.
Gudaha tuubada, waxaa ku jira dareere. Tusaale ahaan, waxaan dareeraha u qaybinnaa qaybo yaryar, halkaas oo qayb kastaa ay leedahay bedka halbeegga ee dA, oo u dhexeeya dhidibka tuubada oo leh xawaare socod v. Xisaab ahaan waxaa loo qori karaa sidan soo socota:
dA 1 = qaybta dareeraha 1, taas oo ah masaafada dr 1 ee u jirta dhidibka tuubada
dA 2 = qaybta dareeraha 2, taas oo ah masaafada dr 2 ee u jirta dhidibka tuubada
dA 3 = qaybta dareeraha ah ee 3, taas oo ah masaafada dr 3 ee u jirta dhidibka tuubada
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dAn = qaybta dareeraha ah n, taas oo ah masaafada dn laga bilaabo dhidibka tuubada
Qaybta dareeruhu aad bay u badan tahay, markaa waxaa lagu qoray calaamadda n, markaa waa mid aad u macquul ah. Heerka socodka mugga ee qayb kasta oo dareeruhu ka mid yahay waxaa loo qori karaa xisaab ahaan sidan soo socota:
Qayb kasta oo dareere ah waxay ku jirtaa masaafada r = 0 ilaa r = R (R = radius tuubada). Si kale haddii loo dhigo, masaafada qayb kasta oo dareere ah way kala duwan tahay marka laga cabbiro dhidibka tuubada. Waxaan heli doonnaa isle'egta heerka socodka mugga dareeraha ee tuubada:
Q = Soo daadinta, R = gacanka tuubbo ama tuubo, η = isku-darka viscosity, P 1 – p 2 = Farqiga cadaadiska ee u dhexeeya labada daraf ee tuubada, L = dhererka tuubada, p 1 -p 2 / L = Jaangoynta cadaadiska (socodka dareeraha had iyo jeer wuxuu ku socdaa jihada hoos u dhaca cadaadiska)
Iyada oo lagu saleynayo isleegga Poiseuille ee kor ku xusan, waxay u muuqataa in heerka socodka mugga dareeraha (Q) uu la mid yahay radius-ka tuubada (R 4 ), radius-ka cadaadiska (p 2 – p 1 / L) iyo si liddi ku ah viscosity-ga. Haddii radius-ka tuubada lagu daro (isku-dhafka viscosity-ga iyo radius-ka cadaadiska go'an), markaa xawaaraha socodka dareeraha wuxuu kordhaa 16.
Fikradda aasaasiga ah ee naqshadeynta tuubooyinka, isticmaal isla'egtan. Daadinta dareeraha waxay la mid tahay R 4 (R = radius tuubada). Gacanka sirinjiga ama faraha tuubada waa in si taxaddar leh loo xisaabiyaa. Tusaale ahaan, haddii aan labanlaabno radiuska irbadda (rx 2), daadinta dareeraha ah ee la buufiyo = waxay kordhisaa xoogga cadaadiska suulka 16 jeer.
Isleegga Poiseuille wuxuu sidoo kale muujinayaa in gacanka (r4 ) uu si liddi ku ah ugu dhigmayo farqiga cadaadiska u dhexeeya labada daraf ee tuubada. Tusaale ahaan, dhiiggu marka hore wuxuu ku socdaa xidid dhiig oo leh gacanka gudaha ee r. Haddii uu jiro cidhiidhi xididada (tusaale ahaan, r/2 = gacanka xididdada dhiigga ayaa laba jeer la dhimay),
markaa waxaa loo baahan yahay farqi cadaadis oo 16 jeer ah si loo sameeyo socodka dhiigga sidii hore (si xawaaraha socodka uu u ahaado mid joogto ah).
