Isihloko mayelana ne-Poiseuilles equation
Isibalo sikaPoiseuille satholakala nguJean Louis Marie Poiseuille (1799-1869). Njengoba kuchaziwe, uketshezi ngalunye lungabhekwa njengoketshezi olufanele. Uketshezi olufanele alunawo umswakama. Uma sicabanga ukuthi uketshezi olufanele lugeleza epayipini, ingxenye ngayinye yoketshezi ihamba ngesivinini esifanayo (v). Ngokungafani noketshezi olufanele, uketshezi lwangempela esiluthola ekuphileni kwansuku zonke lunomswakama. Ngoba lunomswakama, khona-ke uma lugeleza epayipini, isibonelo, izinga lengxenye ngayinye yoketshezi liyahlukahluka. Ungqimba loketshezi oluphakathi luhamba ngokushesha (v ejulile), ngokuphambene nalokho, ungqimba loketshezi olunamathele epayipini aluhambi (v = 0). Ngakho-ke kusukela maphakathi kuya emaphethelweni epayipi, yonke ingxenye yoketshezi ihamba ngesivinini esihlukile. Ukuze kube lula ukuqonda kwakho, bheka isithombe esingezansi.
R = irediyasi yepayipi/ithubhu
v 1 = izinga lokugeleza koketshezi ku-axis ephakathi / yeshubhu
v 2 = izinga lokugeleza koketshezi okungu-r 2 kusukela emaphethelweni epayipi
v 3 = izinga lokugeleza koketshezi r 3 kusukela emaphethelweni epayipi
v 4 = izinga lokugeleza koketshezi r 4 kusukela emaphethelweni epayipi
r = ibanga
Ukuze izinga lokugeleza kwengxenye ngayinye yoketshezi lifane, kudingeka kube nomehluko wokucindezela kunoma yiliphi ipayipi noma kunoma yiliphi ipayipi uketshezi oludlula kulo. Okushiwo uketshezi lapha uketshezi lwangempela, isibonelo, amanzi noma uwoyela ogeleza ngepayipi, igazi eligeleza emthanjeni wegazi, njll. Ngaphezu kokusiza uketshezi lwangempela ukuthi lugeleze kahle, umehluko wokucindezela ungenza noketshezi lugeleze emapayipini anobude obuhlukene.
UJean Louis Marie Poiseuille, owayengusosayensi waseFrance owayenesithakazelo ezicini zomzimba zokujikeleza kwegazi lomuntu, wacwaninga ukuze ahlole ukuthi izici, njengokwehluka kwengcindezi, indawo ewela amashubhu, kanye nosayizi wamashubhu kuthinta kanjani izinga langempela loketshezi. Imiphumela etholwe nguJean Louis Marie Poiseuille, owaziwa ngokuthi i-Poiseuille's equation.
I-Poiseuille's equation ingatholakala kusetshenziswa usizo lwe-viscosity coefficient equation ebalwe ngaphambilini. Sisebenzisa i-viscosity equation ngoba amacala afana, yize engafani. Lapho sithola i-viscosity coefficient equation, sibuyekeza ukugeleza kwengqimba yoketshezi lwangempela phakathi kwamapuleti amabili ahambisanayo, futhi uketshezi lungahamba ngenxa yokukhanga (F). Umehluko ukuthi i-Poiseuille's equation esizoyithola isho izici ezithonya ukugeleza koketshezi lwangempela epayipini/epayipini kanye noketshezi olugeleza ngenxa yomehluko wokucindezela. Ngakho-ke, i-viscosity coefficient equation idinga ukulungiswa futhi.
Uketshezi lungageleza ngenxa yomehluko wokucindezela (uketshezi lugeleza lusuka endaweni enomfutho ophezulu luye endaweni lapho umfutho uphansi khona), bese sishintsha u-F nge-p 1 – p 2 (p 1 > p 2 ).
Uma sithola i-viscosity coefficient equation, sibuyekeza ukugeleza kwengqimba yoketshezi yangempela phakathi kwamapuleti amabili ahambisanayo. Ingxenye ngayinye yoketshezi ishintsha isivinini sayo esivamile kuze kufike ku-l. Kulesi simo, izinga lokugeleza koketshezi lishintsha njalo kusukela ku-axis yeshubhu kuya emaphethelweni eshubhu. Uketshezi oluku-axis yeshubhu lugeleza ngesivinini esikhulu (v). Uma unqenqema luningi, isivinini soketshezi siba sincane. I-Tube radius = ibanga phakathi kwe-axis yeshubhu kanye nonqenqema lweshubhu = R. Ibanga phakathi kwengxenye ngayinye yoketshezi kanye nonqenqema lweshubhu = r. Ngoba inani lengxenye ngayinye yoketshezi likhulu futhi ibanga elivela emaphethelweni eshubhu nalo lihlukile, bese sibhala kanje:
v 1 = isivinini soketshezi esisebangeni r 1 kusukela emaphethelweni epayipi (r 1 = R)
v 2 = isivinini soketshezi olusebangeni r 2 ukusuka emaphethelweni epayipi (r 2 < r 1 )
v 3 = isivinini soketshezi ebangeni r 3 kusukela emaphethelweni epayipi (r 3 < r 2 < r 1 )
v 4 = isivinini soketshezi esisebangeni r 4 ukusuka emaphethelweni epayipi (r 4 < r 3 < r 2 < r 1 )
……………………………………………..
v n = izinga loketshezi ebangeni rn kusukela emaphethelweni epayipi (rn <…… <r 4 <r 3 <r 2 <r 1 )
Inani lengxenye ngayinye yoketshezi likhulu, futhi asazi kahle ukuthi lingakanani inani empeleni, ngakho-ke kwanele ukubhalwa ngophawu n. Ingxenye ngayinye yoketshezi ishintsha isivinini (v) njalo, kusukela ku-axis yeshubhu (r 1 = R) kuya emaphethelweni eshubhu (rn). Kusukela ku-axis yeshubhu (r 1 = R) kuya emaphethelweni eshubhu (rn), izinga lengxenye ngayinye yoketshezi lincane (v 1 > v 2 > v 3 > v 4 > ….> v n ).
Kusukela encazelweni engenhla, singaba nesibalo sokuthi kusukela ku-R kuya ku-rn, izinga loketshezi liya ngokuya lincipha. Ubude bepayipi = L. Isibalo esitholiwe:
Ngoba esikubuyekezayo ijubane lokugeleza koketshezi , khona-ke i-equation 2 iba:
Lesi yisilinganiso sejubane lokugeleza koketshezi ebangeni elingu-r ukusuka epayipini elinobubanzi buka-R. Uma udidekile ngenkathi ubheka isithombe esingenhla… Sicela uqaphele ukuthi uketshezi lugeleza epayipini, ngakho-ke sidinga ukubuyekeza izinga lokugeleza komthamo woketshezi.
Ngaphakathi kwepayipi, kukhona uketshezi. Isibonelo, sihlukanisa uketshezi lube izingxenye ezincane, lapho ingxenye ngayinye inendawo yeyunithi engu-dA, ehlukaniswe ne-axis yepayipi futhi inejubane lokugeleza v. Ngokwezibalo kungabhalwa kanje:
dA 1 = ingxenye yoketshezi 1, okuyibanga lika-dr 1 ukusuka ku-axis yeshubhu
dA 2 = ingxenye yoketshezi 2, okuyibanga lika-dr 2 ukusuka ku-axis yeshubhu
dA 3 = ingxenye yoketshezi 3, okuyibanga lika-dr 3 ukusuka ku-axis yeshubhu
…………………………….
dAn = ingxenye yoketshezi n, okuyibanga le-dn ukusuka ku-axis yeshubhu
Ingxenye yoketshezi iningi kakhulu, ngakho-ke ibhalwe ngophawu u-n, ngakho-ke iyasebenza kakhulu. Izinga lokugeleza kwevolumu yengxenye ngayinye yoketshezi lingabhalwa ngokwezibalo kanje:
Ingxenye ngayinye yoketshezi isebangeni lika-r = 0 kuya ku-r = R (R = irediyasi yeshubhu). Ngamanye amazwi, ibanga lengxenye ngayinye yoketshezi liyahlukahluka uma lilinganiswa kusukela ku-axis yeshubhu. Sizothola i-equation yesilinganiso sokugeleza komthamo woketshezi eshubhu:
Q = Ukukhishwa, R = irediyasi yepayipi noma ithubhu, η = i-coefficient of viscosity, P 1 – p 2 = Umehluko wokucindezela phakathi kwezinhlangothi ezimbili zepayipi, L = ubude bepayipi, p 1 -p 2 / L = I-gradient yokucindezela (ukugeleza koketshezi kuhlala kuqonde ekwehleni kokucindezela)
Ngokusekelwe ku-Poiseuille equation engenhla, kubonakala sengathi izinga lokugeleza kwevolumu yoketshezi (Q) lilingana nerediyasi yeshubhu (R 4 ), i-gradient yokucindezela (p 2 – p 1 / L) futhi lilingana ngokuphambene ne-viscosity. Uma irediyasi yeshubhu yengezwa (i-viscosity coefficient kanye ne-gradient yokucindezela engaguquki), khona-ke ijubane lokugeleza koketshezi liyanda ngesilinganiso esingu-16.
Emqondweni oyisisekelo womklamo wepayipi, sebenzisa lesi sibalo. Ukukhishwa koketshezi kuhambelana no-R 4 (R = irediyasi yepayipi). Irediyasi yesirinji noma iminwe yepayipi idinga ukubalwa ngokucophelela. Isibonelo, uma siphinda kabili irediyasi yenaliti (rx 2), ukukhishwa koketshezi okufuthwayo = kwandisa amandla okucindezela isithupha izikhathi ezingu-16.
I-Poiseuille equation ikhombisa nokuthi i-radius (r 4 ) ilingana ngokuphambene nomehluko wokucindezela phakathi kwezinhlangothi ezimbili zombhobho. Isibonelo, igazi liqala ligeleze emthanjeni wegazi one-radius yangaphakathi engu-r. Uma kukhona ukuncishiswa kwemithambo yegazi (isb., r/2 = i-radius yemithambo yegazi incishisiwe kabili),
bese kudingeka umehluko wokucindezela izikhathi ezingu-16 ukuze igazi ligeleze njengakuqala (ukuze ijubane lokugeleza lihlale linjalo).
