Chinyorwa pamusoro pePoiseuilles equation
Equation yaPoiseuille yakawanikwa naJean Louis Marie Poiseuille (1799-1869). Sezvakatsanangurwa, mvura yega yega inogona kutorwa semvura yakakwana. Mvura yakakodzera haina viscosity. Kana tikafungidzira kuti mvura yakakwana inoyerera mupombi, chikamu chimwe nechimwe chemvura chinofamba nemwero wakafanana (v). Kusiyana nemvura yakakodzera, mvura chaiyo yatinosangana nayo muhupenyu hwezuva nezuva ine viscosity. Nekuti ine viscosity, saka kana ichiyerera mupombi, semuenzaniso, mwero wechikamu chimwe nechimwe chemvura unosiyana. Rutivi rwemvura ruri pakati runofamba nekukurumidza (deep v), pane zvinopesana, rutivi rwemvura rwakabatana nepombi harufambi (v = 0). Saka kubva pakati kusvika kumucheto wepombi, chikamu chimwe nechimwe chemvura chinofamba nemwero wakasiyana. Kuti unzwisise zviri nyore, tarisa mufananidzo uri pazasi.
R = nharaunda yepombi/chubhu
v 1 = mwero wekuyerera kwemvura muchikamu chepakati / chechubhu
v 2 = mwero wekuyerera kwemvura uri r 2 kubva kumucheto kwechubhu
v 3 = mwero wekuyerera kwemvura r 3 kubva kumucheto kwechubhu
v 4 = mwero wekuyerera kwemvura r 4 kubva kumucheto kwechubhu
r = daro
Kuti mwero wekuyerera kwechikamu chimwe nechimwe chemvura ufanane, panofanira kuva nemusiyano wekumanikidzwa pamucheto wepombi kana chero chubhu iyo mvura inopfuura nayo. Chinorehwa nemvura pano mvura chaiyo, semuenzaniso, mvura kana mafuta anoyerera nemupombi, ropa rinoyerera mutsinga yeropa, nezvimwewo. Pamusoro pekubatsira mvura chaiyo kuti ifambe zvakanaka, musiyano wekumanikidzwa unogonawo kuita kuti mvura ifambe mumapombi akareba zvakasiyana.
Jean Louis Marie Poiseuille, aimbove musayendisiti wekuFrance aifarira zvinhu zvemuviri zvekutenderera kweropa revanhu, akaongorora kuti zvinhu zvakaita sekusiyana kwekumanikidzwa, nzvimbo yechubhu, uye saizi yechubhu zvinokanganisa sei mwero chaiwo wemvura. Zvakawanikwa naJean Louis Marie Poiseuille, inozivikanwa sePoiseuille's equation.
Equation yaPoiseuille inogona kuwanikwa tichishandisa rubatsiro rwe equation ye viscosity coefficient yakamboverengwa kare. Tinoshandisa equation ye viscosity nekuti ma cases akafanana, kunyangwe asiri akafanana. Pakutsvaga equation ye viscosity coefficient, tinoongorora kuyerera kwe layer ye fluid chaiyo pakati pemaplate maviri akafanana, uye fluid inogona kufamba nekuda kwekukwezva (F). Musiyano ndewekuti equation yaPoiseuille yatichawana inotaura zvinhu zvinopesvedzera kuyerera kwe fluid chaiyo mupipe/tube uye fluid inoyerera nekuda kwekusiyana kwekumanikidzwa. Saka, equation ye viscosity coefficient inofanira kugadziriswa zvakare.
Mvura inogona kuyerera nekuda kwekusiyana kwekumanikidzwa (mvura inoyerera kubva panzvimbo ine kumanikidzwa kwakanyanya kuenda kunzvimbo ine kumanikidzwa kwakaderera), tobva tatsiva F ne p 1 – p 2 (p 1 > p 2 ).
Pakutsvaga viscosity coefficient equation, tinoongorora kuyerera kwechikamu chemvura chaiyo pakati pemaplate maviri akafanana. Chikamu chimwe nechimwe chemvura chinochinja kumhanya kwacho kwakajairika kusvika pa l. Muchiitiko ichi, mwero wekuyerera kwemvura unochinja nguva dzose kubva pa axis yechubhu kuenda kumucheto wechubhu. Mvura iri mu axis yechubhu inoyerera nekukurumidza kukuru (v). Mupendero wakawanda, kumhanya kwemvura kudiki. Tube radius = daro riri pakati pe axis yechubhu nemupendero wechubhu = R. Daro riri pakati pechikamu chimwe nechimwe chemvura nemupendero wechubhu = r. Nekuti huwandu hwechikamu chimwe nechimwe chemvura yakakura uye daro kubva kumucheto wechubhu rakasiyanawo, saka tinongonyora seizvi:
v 1 = kumhanya kwemvura iri kure r 1 kubva kumucheto kwechubhu (r 1 = R)
v 2 = kumhanya kwemvura iri kure r 2 kubva kumucheto kwechubhu (r 2 < r 1 )
v 3 = kumhanya kwemvura iri kure r 3 kubva kumucheto kwechubhu (r 3 < r 2 < r 1 )
v 4 = kumhanya kwemvura iri kure r 4 kubva kumucheto kwechubhu (r 4 < r 3 < r 2 < r 1 )
……………………………………… ..
v n = mwero wemvura iri kure rn kubva kumucheto kwechubhu (rn <…… <r 4 <r 3 <r 2 <r 1 )
Huwandu hwechikamu chimwe nechimwe chemvura hwakakura, uye hatiziviwo kuti huwandu hwacho hwakakura sei, saka zvakakwana kunyorwa nechiratidzo n. Chikamu chimwe nechimwe chemvura chinochinja kumhanya (v) nguva nenguva, kubva pa axis yechubhu (r 1 = R) kusvika kumucheto wechubhu (rn). Kubva pa axis yechubhu (r 1 = R) kusvika kumucheto wechubhu (rn), mwero wechikamu chimwe nechimwe chemvura chidiki (v 1 > v 2 > v 3 > v 4 > ….> v n ).
Kubva patsananguro iri pamusoro, tinogona kuva nemufananidzo unoratidza kuti kubva paR kusvika pa rn, mwero wemvura uri kudzikira. Kureba kwepaipi = L. Yakawanikwa equation:
Nekuti zvatiri kuongorora ndezvekumhanya kwekuyerera kwemvura , saka equation 2 inova:
Uyu ndiwo muyero wekumhanya kwekuyerera kwemvura uri kure ne r kubva papombi ine radius ye R. Kana wakavhiringidzika uchitarisa mufananidzo uri pamusoro… Ndapota cherechedza kuti mvura inoyerera muchubhu, saka tinofanira kuongorora mwero wekuyerera kwehuwandu hwemvura.
Mukati mechubhu, mune mvura. Semuenzaniso, tinokamura mvura kuita zvikamu zvidiki, uko chikamu chimwe nechimwe chine unit area ye dA, yakaparadzaniswa nechubhu axis uye ine flow speed v. Masvomhu anogona kunyorwa seizvi:
dA 1 = chikamu chemvura 1, chinova chinhambwe chedr 1 kubva pachubhu
dA 2 = chikamu chemvura 2, chinova chinhambwe chedr 2 kubva pachubhu
dA 3 = chikamu chemvura chikamu 3, chinova chinhambwe chedr 3 kubva pa axis yechubhu
……………………………….
dAn = chikamu chemvura n, chiri chinhambwe che dn kubva pa axis ye tube
Chikamu chemvura chakawanda kwazvo, saka chakanyorwa nechiratidzo n, saka chinoshanda zvakanyanya. Kuyerera kwehuwandu hwechikamu chimwe nechimwe chemvura kunogona kunyorwa nemasvomhu seizvi:
Chikamu chimwe nechimwe chemvura chiri padaro re r = 0 kusvika r = R (R = tube radius). Nemamwe mashoko, daro rechikamu chimwe nechimwe chemvura rinosiyana kana richiyerwa kubva pa tube axis. Tichawana equation ye fluid volume flow rate mu tube:
Q = Kubuda, R = radius yepombi kana chubhu, η = coefficient of viscosity, P 1 – p 2 = Musiyano wekumanikidzwa pakati pemagumo maviri epombi, L = kureba kwepombi, p 1 -p 2 / L = Kuyerera kwekumanikidzwa (kuyerera kwemvura nguva dzose kunoenda kudivi rekudonha kwekumanikidzwa)
Zvichibva paPoiseuille equation iri pamusoro apa, zvinoita sekunge mwero wekuyerera kwehuwandu hwemvura (Q) unoenderana ne tube radius (R 4 ), pressure gradient (p 2 – p 1 / L) uye unoenderana ne viscosity. Kana tube radius yakawedzerwa (viscosity coefficient uye fixed pressure gradient), ipapo fluid flow speed inowedzera ne16 factor.
Mupfungwa huru yekugadzira pombi, shandisa equation iyi. Kubuda kwemvura kwakaenzana neR 4 (R = tube radius). Radius yesirinji kana minwe yepombi inofanira kuverengerwa nokungwarira. Semuenzaniso, kana tikapeta kaviri radius yetsono (rx 2), kubuda kwemvura kunopfapfaidzwa = kunowedzera simba rekumanikidza chigunwe kagumi nematanhatu.
Equation yePoiseuille inoratidzawo kuti radius (r 4 ) inoenderana nekusiyana kwekumanikidzwa pakati pemigumo miviri yepombi. Semuenzaniso, ropa rinotanga kuyerera mutsinga yeropa ine radius yemukati yer. Kana paine kutetepa kwetsinga (semuenzaniso, r/2 = radius yetsinga yeropa yaderedzwa kaviri),
ipapo musiyano wekumanikidzwa kweropa unodiwa ka16 kuti ropa riyerere sezvaraiita kare (kuitira kuti kumhanya kwekuyerera kweropa kuve kwakafanana).
