Tsab xov xwm hais txog Poiseuilles equation
Tus qauv Poiseuille tau tshawb pom los ntawm Jean Louis Marie Poiseuille (1799-1869). Raws li tau piav qhia, txhua cov kua dej tuaj yeem suav tias yog cov kua dej zoo tagnrho. Cov kua dej zoo tagnrho tsis muaj viscosity. Yog tias peb xav tias cov kua dej zoo tagnrho ntws hauv cov yeeb nkab, txhua qhov ntawm cov kua dej txav mus rau tib qhov nrawm (v). Tsis zoo li cov kua dej zoo tagnrho, cov kua dej tiag tiag uas peb ntsib hauv lub neej txhua hnub muaj viscosity. Vim tias nws muaj viscosity, ces thaum ntws hauv cov yeeb nkab, piv txwv li, qhov nrawm ntawm txhua qhov ntawm cov kua dej sib txawv. Cov txheej kua dej uas nyob hauv nruab nrab txav mus sai dua (v tob), ntawm qhov tsis sib xws, cov txheej kua dej txuas rau cov yeeb nkab tsis txav (v = 0). Yog li ntawm nruab nrab mus rau ntug ntawm cov yeeb nkab, txhua qhov ntawm cov kua dej txav mus rau ntau qhov nrawm. Txhawm rau kom koj nkag siab yooj yim, saib daim duab hauv qab no.
R = lub vojvoog ntawm cov yeeb nkab/raj
v 1 = tus nqi ntws ntawm cov kua dej hauv nruab nrab / lub raj xa dej
v 2 = tus nqi ntws ntawm cov kua dej uas yog r 2 los ntawm ntug ntawm lub raj
v 3 = tus nqi ntws ntawm cov kua dej r 3 los ntawm ntug ntawm lub raj
v 4 = tus nqi ntws ntawm cov kua dej r 4 los ntawm ntug ntawm lub raj
r = qhov deb
Yuav kom qhov nrawm ntawm txhua qhov ntawm cov kua dej zoo ib yam, yuav tsum muaj qhov sib txawv ntawm qhov kawg ntawm cov yeeb nkab lossis txhua lub raj uas cov kua dej hla dhau. Lub ntsiab lus ntawm cov kua dej ntawm no yog cov kua dej tiag tiag, piv txwv li, dej lossis roj uas ntws los ntawm cov yeeb nkab, cov ntshav ntws hauv cov hlab ntsha, thiab lwm yam. Ntxiv rau kev pab cov kua dej tiag tiag ntws zoo, qhov sib txawv ntawm qhov siab kuj tseem tuaj yeem ua rau cov kua dej ntws hauv cov yeeb nkab ntawm qhov siab sib txawv.
Jean Louis Marie Poiseuille, ib tug kws tshawb fawb Fabkis yav dhau los uas xav paub txog cov yam ntxwv ntawm tib neeg cov ntshav ncig, tau tshawb nrhiav los tshawb nrhiav seb cov yam ntxwv, xws li qhov sib txawv ntawm lub siab, thaj tsam hla lub raj, thiab qhov loj ntawm lub raj cuam tshuam li cas rau qhov nrawm ntawm cov kua dej tiag tiag. Cov txiaj ntsig tau los ntawm Jean Louis Marie Poiseuille, hu ua Poiseuille's equation.
Tus qauv Poiseuille tuaj yeem tau los ntawm kev siv kev pab ntawm tus qauv viscosity coefficient uas tau suav ua ntej lawm. Peb siv tus qauv viscosity vim tias cov xwm txheej zoo sib xws, txawm tias lawv tsis zoo ib yam. Thaum tau txais tus qauv viscosity coefficient, peb tshuaj xyuas qhov ntws ntawm cov kua dej tiag tiag ntawm 2 lub phaj sib luag, thiab cov kua dej tuaj yeem txav mus los vim yog qhov rub (F). Qhov sib txawv yog tias tus qauv Poiseuille uas peb yuav tau txais hais txog cov yam ntxwv uas cuam tshuam rau qhov ntws ntawm cov kua dej tiag tiag hauv cov yeeb nkab / raj thiab cov kua dej ntws vim yog qhov sib txawv ntawm lub siab. Yog li ntawd, tus qauv viscosity coefficient yuav tsum tau kho dua.
Cov kua dej ntws tau vim muaj qhov sib txawv ntawm qhov siab (cov kua dej ntws los ntawm qhov chaw muaj qhov siab mus rau qhov chaw uas qhov siab qis), ces peb hloov F nrog p 1 - p 2 (p 1 > p 2 ).
Thaum peb nrhiav tau tus qauv sib npaug ntawm viscosity, peb yuav tshuaj xyuas qhov ntws ntawm cov kua dej tiag tiag ntawm 2 daim hlau sib luag. Txhua feem ntawm cov kua dej hloov nws qhov ceev mus txog l. Hauv qhov no, qhov nrawm ntawm cov kua dej hloov pauv tas li ntawm txoj kab ntawm lub raj mus rau ntug ntawm lub raj. Cov kua dej hauv txoj kab ntawm lub raj ntws ntawm qhov ceev ntau dua (v). Ntug ntau dua, qhov ceev ntawm cov kua dej me dua. Lub vojvoog ntawm lub raj = qhov deb ntawm txoj kab ntawm lub raj thiab ntug ntawm lub raj = R. Qhov deb ntawm txhua feem ntawm cov kua dej thiab ntug ntawm lub raj = r. Vim tias qhov ntau ntawm txhua feem ntawm cov kua dej yog loj heev thiab qhov deb ntawm ntug ntawm lub raj kuj txawv, ces peb tsuas yog sau li no:
v 1 = qhov ceev ntawm cov kua dej uas nyob ntawm qhov deb r 1 ntawm ntug ntawm lub raj (r 1 = R)
v 2 = qhov ceev ntawm cov kua dej uas nyob ntawm qhov deb r 2 ntawm ntug ntawm lub raj (r 2 < r 1 )
v 3 = qhov ceev ntawm cov kua dej ntawm qhov deb r 3 ntawm ntug ntawm lub raj (r 3 < r 2 < r 1 )
v 4 = qhov ceev ntawm cov kua dej uas nyob ntawm qhov deb r 4 ntawm ntug ntawm lub raj (r 4 < r 3 < r 2 < r 1 )
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v n = tus nqi ntawm cov kua dej ntawm qhov deb rn ntawm ntug ntawm lub raj (rn <…… <r 4 <r 3 <r 2 <r 1 )
Tus nqi ntawm txhua feem ntawm cov kua dej yog loj heev, thiab peb kuj tsis paub meej tias muaj pes tsawg ntawm qhov ntau npaum li cas tiag tiag, yog li nws txaus kom sau nrog lub cim n. Txhua feem ntawm cov kua dej hloov qhov ceev (v) tsis tu ncua, los ntawm lub raj axis (r 1 = R) mus rau ntug ntawm lub raj (rn). Los ntawm lub raj axis (r 1 = R) mus rau ntug ntawm lub raj (rn), tus nqi ntawm txhua feem ntawm cov kua dej yog me dua (v 1 > v 2 > v 3 > v 4 >….> v n ).
Los ntawm cov lus piav qhia saum toj no, peb tuaj yeem muaj daim duab uas los ntawm R mus rau rn, tus nqi kua dej me dua. Qhov ntev ntawm cov yeeb nkab = L. Cov qauv tau txais:
Vim tias qhov peb tab tom tshuaj xyuas yog qhov ceev ntawm cov kua dej ntws, ces kab zauv 2 dhau los ua:
Qhov no yog qhov sib npaug ntawm qhov ceev ntawm cov kua dej ntws hauv qhov deb r ntawm lub yeeb nkab nrog lub vojvoog ntawm R. Yog tias koj tsis meej pem thaum saib daim duab saum toj no ... Thov nco ntsoov tias cov kua dej ntws hauv lub raj, yog li peb yuav tsum tshuaj xyuas qhov nrawm ntawm cov kua dej.
Sab hauv lub raj, muaj kua dej. Piv txwv li, peb faib cov kua dej ua tej daim me me, qhov twg txhua daim muaj ib cheeb tsam ntawm dA, sib nrug ntawm lub raj axis thiab muaj qhov ceev ntws v. Hauv lej, peb sau tau raws li nram no:
dA 1 = kua dej ntu 1, uas yog qhov deb ntawm dr 1 ntawm lub raj axis
dA 2 = kua dej ntu 2, uas yog qhov deb ntawm dr 2 ntawm lub raj axis
dA 3 = cov kua dej seem 3, uas yog qhov deb ntawm dr 3 ntawm lub raj axis
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dAn = kua dej ib feem n, uas yog qhov deb ntawm dn ntawm lub raj axis
Cov kua dej muaj ntau heev, yog li nws tsuas yog sau nrog lub cim n xwb, yog li nws siv tau zoo dua. Qhov ntim ntws ntawm txhua feem ntawm cov kua dej tuaj yeem sau ua lej raws li hauv qab no:
Txhua feem ntawm cov kua dej nyob ntawm qhov deb ntawm r = 0 txog r = R (R = lub raj vojvoog). Hauv lwm lo lus, qhov deb ntawm txhua feem ntawm cov kua dej sib txawv thaum ntsuas los ntawm lub raj txoj kab. Peb yuav tau txais cov qauv ntsuas ntws ntawm cov kua dej hauv lub raj:
Q = Kev Tawm, R = lub vojvoog ntawm cov yeeb nkab lossis lub raj, η = tus lej ntawm viscosity, P 1 – p 2 = Qhov sib txawv ntawm lub siab ntawm ob qho kawg ntawm cov yeeb nkab, L = qhov ntev ntawm cov yeeb nkab, p 1 -p 2 / L = Qhov sib txawv ntawm lub siab (cov kua ntws ib txwm nyob rau hauv qhov kev taw qhia ntawm qhov siab poob)
Raws li Poiseuille equation saum toj no, nws zoo li qhov ntws ntawm cov kua dej (Q) yog proportional rau lub raj radius (R4 ) , qhov siab gradient (p2 - p1 / L) thiab inversely proportional rau viscosity. Yog tias lub raj radius ntxiv (viscosity coefficient thiab fixed pressure gradient), ces qhov ceev ntws ntawm cov kua dej nce ntxiv los ntawm ib qho ntawm 16.
Hauv lub tswv yim yooj yim ntawm kev tsim cov yeeb nkab, siv cov qauv no. Cov kua dej tawm yog proportional rau R 4 (R = lub raj radius). Lub radius ntawm lub koob txhaj tshuaj lossis cov ntiv tes yeeb nkab yuav tsum tau xam kom zoo zoo. Piv txwv li, yog tias peb ob npaug ntawm lub radius ntawm koob (rx 2), cov kua dej tawm uas txau = ua rau lub zog nias ntiv tes xoo nce 16 zaug.
Tus qauv Poiseuille kuj qhia tau tias lub vojvoog (r4 ) yog sib piv rau qhov sib txawv ntawm qhov siab ntawm ob sab kawg ntawm lub yeeb nkab. Piv txwv li, cov ntshav ntws thawj zaug hauv cov hlab ntsha uas muaj lub vojvoog sab hauv ntawm r. Yog tias muaj kev nqaim ntawm cov hlab ntsha (piv txwv li, r/2 = lub vojvoog ntawm cov hlab ntsha raug txo ob zaug),
ces yuav tsum muaj qhov sib txawv ntawm lub siab ntawm 16 npaug kom ua rau cov ntshav ntws zoo li ua ntej (kom qhov ceev ntawm cov ntshav ntws tas li).
