Ibizwa ngokuthi i-Poiseuille equation ngoba yatholakala nguJean Louis Marie Poiseuille (1799-1869) ongasekho. Njengoba kuchaziwe, lonke uketshezi lungabhekwa njengoketshezi olufanele. Uketshezi olufanele alunawo uketshezi oluqinile. Uma sicabanga ngoketshezi olufanele olugeleza epayipini, yonke ingxenye yoketshezi ihamba ngesivinini esifanayo (v). Ngokungafani noketshezi olufanele, uketshezi lwangempela, noma uketshezi esihlangana nalo ekuphileni kwansuku zonke, lunoketshezi oluqinile. Ngoba lunoketshezi oluqinile, uma lugeleza epayipini, isibonelo, isivinini sengxenye ngayinye yoketshezi siyahlukahluka. Ungqimba loketshezi oluphakathi luhamba ngokushesha (v lukhulu), kuyilapho ungqimba loketshezi olunamathele epayipini lungahambi, noma lunganyakazi (v = 0). Ngakho-ke, kusukela maphakathi kuya emaphethelweni epayipini, yonke ingxenye yoketshezi ihamba ngesivinini esihlukile. Ukuze kube lula ngawe ukuqonda, bheka isithombe esingezansi…
Imininingwane:
R = irediyasi yepayipi/ithubhu
v 1 = izinga lokugeleza koketshezi enkabeni/e-axis yepayipi
v 2 = izinga lokugeleza koketshezi ebangeni r 2 ukusuka emaphethelweni epayipi
v 3 = izinga lokugeleza koketshezi ebangeni r 3 kusukela emaphethelweni epayipi
v 4 = izinga lokugeleza koketshezi ebangeni r 4 kusukela emaphethelweni epayipi
r = ibanga
Ukuqinisekisa ukuthi izinga lokugeleza koketshezi ngalunye liyafana, kumele kube nomehluko wokucindezela kuzo zombili iziphetho zanoma yiliphi ipayipi noma ithubhu lapho uketshezi lugeleza khona. Ngoketshezi lapha, sisho uketshezi lwangempela, njengamanzi noma uwoyela ogeleza ngepayipi, igazi eligeleza ngemithambo yegazi, njll. Ngaphandle kokusiza uketshezi lwangempela lugeleze kahle, umehluko wokucindezela ungavumela noketshezi ukuthi lugeleze emapayipini aphakeme ngendlela ehlukene.
UJean Louis Marie Poiseuille, owayengusosayensi waseFrance owayenesithakazelo ezicini zomzimba zokujikeleza kwegazi lomuntu, wenza ucwaningo ukuze ahlole ukuthi izici ezifana nokwehluka kwengcindezi, indawo enqamula ipayipi, kanye nosayizi wepayipi kuthinta kanjani ijubane loketshezi lwangempela. Imiphumela etholwe nguJean Louis Marie Poiseuille yaziwa ngokuthi i-Poiseuille equation.
I-Poiseuille equation ingatholakala kusetshenziswa i-viscosity coefficient equation etholakale ngaphambilini. Sisebenzisa i-viscosity equation ngoba icala liyafana, nakuba lingafani. Lapho sithola i-viscosity coefficient equation, sicabangela ukugeleza kwengqimba yoketshezi lwangempela phakathi kwamapuleti amabili ahambisanayo, futhi uketshezi luyakwazi ukuhamba ngenxa yamandla okudonsa (F). Umehluko uwukuthi i-Poiseuille equation esizoyithola empeleni isho izici ezithonya ukugeleza koketshezi lwangempela epayipini/epayipini, kanye nokugeleza koketshezi ngenxa yokwehluka kwengcindezi. Ngakho-ke, i-viscosity coefficient equation idinga ukulungiswa futhi.
Uketshezi lungageleza ngenxa yokwehluka kokucindezela (uketshezi lugeleza lusuka ezindaweni ezinengcindezi ephezulu luye ezindaweni ezinengcindezi ephansi), ngakho-ke sithatha indawo ka-F nge-p 1 – p 2 (p 1 > p 2 ).
Uma sithola i-equation ye-viscosity coefficient, sicabangela ukugeleza kwengqimba yangempela yoketshezi phakathi kwamapuleti amabili ahambisanayo. Ingxenye ngayinye yoketshezi ibhekana noshintsho olujwayelekile lwejubane ngebanga l. Kulesi simo, izinga lokugeleza koketshezi lishintsha njalo kusukela ku-axis yepayipi kuya emaphethelweni epayipi. Uketshezi oluku-axis yepayipi lugeleza ngesivinini esikhulu (v). Uma luqhubekela phambili emaphethelweni, isivinini soketshezi siyancipha. I-radius yepayipi = ibanga eliphakathi kwe-axis yepayipi kanye nomphetho wepayipi = R. Ibanga eliphakathi kwengxenye ngayinye yoketshezi nomphetho wepayipi = r. Njengoba inani lengxenye ngayinye yoketshezi likhulu kakhulu futhi ibanga lazo ukusuka emaphethelweni epayipi nalo liyahlukahluka, simane silibhale kanje:
v 1 = isivinini soketshezi ebangeni r1 kusukela emaphethelweni epayipi (r1 = R)
v 2 = isivinini soketshezi ebangeni r2 ukusuka emaphethelweni epayipi (r2 < r1)
v 3 = isivinini soketshezi ebangeni r3 ukusuka emaphethelweni epayipi (r3 < r2 < r1)
v 4 = isivinini soketshezi kude r4 kusukela emaphethelweni epayipi (r4 < r3 < r2 < r1)
……………………………………………..
vn = ijubane loketshezi ebangeni rn kusukela emaphethelweni epayipi (rn < …… < r4 < r3 < r2 < r1 )
Inombolo yengxenye ngayinye yoketshezi inkulu kakhulu futhi asazi kahle ukuthi ingakanani ngempela, ngakho kwanele ukuyibhala ngophawu n. Ingxenye ngayinye yoketshezi ibhekana noshintsho lwesilinganiso (v) njalo, kusukela ku-axis yepayipi (r1 = R) kuya emaphethelweni epayipi (rn). Kusukela ku-axis yepayipi (r1 = R) kuya emaphethelweni epayipi (rn), izinga lengxenye ngayinye yoketshezi liya lincipha (v1 > v2 > v3 > v4 > …. > vn).
Kusukela encazelweni engenhla, singathola umbono wokuthi kusukela ku-R kuya ku-rn, izinga loketshezi liyancipha. Ubude bepayipi = L. Isibalo esitholiwe yilesi:
Ngoba lokho esikucabangayo yisilinganiso (v) sokugeleza koketshezi, isibalo 2 siba:
Lesi yisibalo sezinga lokugeleza koketshezi ebangeni elingu-r ukusuka epayipini elinobubanzi buka-R. Uma udidekile ngenkathi ubheka isithombe esingenhla.... Sicela uqaphele ukuthi uketshezi lugeleza epayipini noma epayipini, ngakho-ke sidinga ukubuyekeza izinga lokugeleza koketshezi.
Ngaphakathi kwepayipi kukhona uketshezi. Isibonelo, sihlukanisa uketshezi lube yizicucu ezincane kakhulu, lapho ucezu ngalunye lunendawo yeyunithi dA, luqhelelene ne-axis yepayipi futhi lunezinga lokugeleza v. Ngokwezibalo, lokhu kungabhalwa kanje:
dA1 = isigaba soketshezi 1, okuyibanga elingu-1 ukusuka ku-axis yeshubhu
dA2 = isigaba soketshezi 2, okuyibanga elingu-2 ukusuka ku-axis yeshubhu
dA3 = isigaba soketshezi 3, okuyibanga elingu-3 ukusuka ku-axis yeshubhu
…………………………….
dA n = isigaba soketshezi n, okuyibanga dA n ukusuka ku-axis yeshubhu
Kunezingcezu eziningi kakhulu zoketshezi kangangokuthi kulula ukuzibhala nje ngophawu n. Izinga lokugeleza kwevolumu yengcezu ngayinye yoketshezi lingabhalwa ngokwezibalo kanje:
Ingxenye ngayinye yoketshezi isebangeni lika-r = 0 kuya ku-r = R (R = irediyasi yethubhu). Ngamanye amazwi, ibanga lengxenye ngayinye yoketshezi liyahlukahluka uma lilinganiswa kusukela ku-axis yethubhu. Uma sishintsha i-calculus (ukuhlanganiswa), sizothola i-equation yesilinganiso sokugeleza komthamo woketshezi ethubhu:
Imininingwane:
Q = Idebithi
R = Irediyasi yangaphakathi yepayipi noma ithubhu
η = i-coefficient ye-viscosity
P 1 – p 2 = Umehluko wokucindezela phakathi kwezinhlangothi ezimbili zepayipi
L = Ubude bepayipi
p 1 -p 2 /L = Ukwehla komfutho (ukugeleza koketshezi kuhlala kuhamba ngendlela yokunciphisa umfutho)
Ngokusekelwe ku-Poiseuille equation engenhla, kubonakala sengathi izinga lokugeleza komthamo woketshezi, okubizwa nangokuthi ukukhishwa (Q), lilingana namandla wesine erediyasi yeshubhu (R 4 ), i-gradient yokucindezela (p 2 – p 1 /L) futhi lilingana ngokuphambene ne-viscosity. Uma irediyasi yeshubhu ikhuphukile (i-viscosity coefficient kanye ne-pressure gradient zihlala zingaguquguquki), khona-ke izinga lokugeleza koketshezi liyanda ngesilinganiso esingu-16.
Umqondo oyisisekelo wokuklama amapayipi, amasirinji, nezinye izinto usebenzisa lesi sibalo. Izinga lokugeleza koketshezi lilingana no-R 4 (R = irediyasi yethubhu). Irediyasi yesirinji noma irediyasi yepayipi idinga ukubalwa ngokucophelela. Isibonelo, uma siphinda kabili irediyasi yenaliti (r x 2), khona-ke izinga lokugeleza koketshezi olufafazayo = landisa amandla okucindezela kwesithupha ngezikhathi eziyi-16.
Isibalo sikaPoiseuille sibonisa nokuthi amandla esine erediyasi (r 4 ) alingana ngokuphambene nomehluko wokucindezela phakathi kwezinhlangothi ezimbili zombhobho. Isibonelo, ekuqaleni igazi ligeleza emthanjeni wegazi onerediyasi yangaphakathi engu-r. Uma kukhona ukuncishiswa komthambo wegazi (isibonelo, r / 2 = irediyasi yangaphakathi yomthambo wegazi incishiswa izikhathi ezi-2), khona-ke umehluko wokucindezela wezikhathi eziyi-16 uyadingeka ukuze kwenziwe ukugeleza kwegazi njengakuqala (ukuze izinga lokuphuma noma izinga lokugeleza kwegazi lihlale lingaguquki).
