Inonzi Poiseuille equation nekuti yakawanikwa naJean Louis Marie Poiseuille (1799-1869) mushakabvu. Sezvakatsanangurwa, mvura yega yega inogona kunzi mvura yakakwana. Mvura yakakodzera haina viscosity. Kana tikafungidzira mvura yakakodzera inoyerera mupombi, chikamu chimwe nechimwe chemvura chinofamba nekumhanya kwakafanana (v). Kusiyana nemvura yakakodzera, mvura chaiyo, kana mvura yatinosangana nayo muhupenyu hwezuva nezuva, ine viscosity. Nekuti ine viscosity, kana ichiyerera mupombi, semuenzaniso, kumhanya kwechikamu chimwe nechimwe chemvura kunosiyana. Rutivi rwemvura pakati runofamba nekukurumidza (v yakakura), nepo rutivi rwemvura rwakabatana nepombi rusingafambi, zvakare (v = 0). Saka, kubva pakati kusvika kumucheto wepombi, chikamu chimwe nechimwe chemvura chinofamba nekumhanya kwakasiyana. Kuti zvive nyore kwauri kunzwisisa, tarisa mufananidzo uri pazasi…
Information :
R = nharaunda yepombi/chubhu
v1 = mwero wekuyerera kwemvura pakati/pamucheto wechubhu
v2 = mwero wekuyerera kwemvura uri kure r2 kubva kumucheto kwechubhu
v3 = mwero wekuyerera kwemvura uri kure r3 kubva kumucheto kwechubhu
v4 = mwero wekuyerera kwemvura uri kure r4 kubva kumucheto kwechubhu
r = daro
Kuti tive nechokwadi chekuti mwero wekuyerera kwemvura imwe neimwe wakafanana, panofanira kuva nemusiyano wekumanikidzwa kumativi ese epombi kana chubhu chero ipi zvayo inoyerera mvura. Nekuyerera kwemvura pano, tinoreva mvura chaiyo, yakaita semvura kana mafuta anoyerera nemupombi, ropa rinoyerera nemutsinga dzeropa, nezvimwewo. Kunze kwekubatsira kuti mvura chaiyo ifambe zvakanaka, musiyano wekumanikidzwa kwemvura unogona zvakare kubvumira mvura kuti ifambe mumapombi pakakwirira zvakasiyana.
Jean Louis Marie Poiseuille, aimbova musayendisiti wekuFrance aifarira zvinhu zvemuviri zvekutenderera kweropa revanhu, akaita tsvakiridzo kuti aongorore kuti zvinhu zvakaita sekusiyana kwekumanikidzwa, nzvimbo yechubhu, uye saizi yechubhu zvinokanganisa sei kumhanya kwemvura chaiyo. Mhedzisiro yakawanikwa naJean Louis Marie Poiseuille inozivikanwa sePoiseuille equation.
Poiseuille equation inogona kuwanikwa tichishandisa viscosity coefficient equation yakawanikwa kare. Tinoshandisa viscosity equation nekuti nyaya yacho yakafanana, kunyange isina kufanana. Pakutsvaga viscosity coefficient equation, tinofunga nezvekuyerera kwemvura chaiyo pakati pemaplate maviri akafanana, uye mvura yacho inokwanisa kufamba nekuda kwesimba rekudhonza (F). Musiyano ndewekuti Poiseuille equation yatichawana inotaura zvinhu zvinopesvedzera kuyerera kwemvura chaiyo mupombi/chubhu, uye mvura inoyerera nekuda kwekusiyana kwekumanikidzwa. Saka, viscosity coefficient equation inofanira kugadziriswa zvakare.
Mvura inogona kuyerera nekuda kwekusiyana kwekumanikidzwa (mvura inoyerera kubva kunzvimbo dzine kumanikidzwa kwakanyanya kuenda kunzvimbo dzine kumanikidzwa kwakaderera), saka tinotsiva F ne p1 - p2 (p1 > p2).
Pakutsvaga equation ye viscosity coefficient, tinofunga nezvekuyerera kwechikamu chemvura chaiyo pakati pemaplate maviri akafanana. Chikamu chimwe nechimwe chemvura chinosangana nekuchinja kwekukurumidza nedaro l. Muchiitiko ichi, mwero wekuyerera kwemvura unochinja nguva dzose kubva ku axis yechubhu kuenda kumucheto wechubhu. Mvura iri pa axis yechubhu inoyerera nekumhanya kukuru (v). Kana ichienda mberi kumucheto, kumhanya kwemvura kunoderera. Radius yechubhu = daro riri pakati pe axis yechubhu nemupendero wechubhu = R. Daro riri pakati pechikamu chimwe nechimwe chemvura nemupendero wechubhu = r. Sezvo nhamba yechikamu chimwe nechimwe chemvura yakakura kwazvo uye daro rayo kubva kumucheto wechubhu richisiyanawo, tinongonyora seizvi:
v1 = kumhanya kwemvura iri kure r1 kubva kumucheto kwechubhu (r1 = R)
v2 = kumhanya kwemvura iri kure r2 kubva kumucheto kwechubhu (r2 < r1)
v3 = kumhanya kwemvura iri kure r3 kubva kumucheto kwechubhu (r3 < r2 < r1)
v4 = kumhanya kwemvura iri kure r4 kubva kumucheto kwechubhu (r4 < r3 < r2 < r1)
……………………………………… ..
vn = kumhanya kwemvura kure kure rn kubva kumucheto kwechubhu (rn < …… < r4 < r3 < r2 < r1 )
Nhamba yechikamu chimwe nechimwe chemvura yakakura kwazvo uye hatiziviwo kuti yakakura sei chaizvo, saka zvakakwana kuinyora nechiratidzo n. Chikamu chimwe nechimwe chemvura chinosangana nekuchinja kwehuwandu (v) nguva nenguva, kubva pamucheto wechubhu (r1 = R) kusvika kumucheto wechubhu (rn). Kubva pamucheto wechubhu (r1 = R) kusvika kumucheto wechubhu (rn), huwandu hwechikamu chimwe nechimwe chemvura hunowedzera kuderera (v1 > v2 > v3 > v4 > …. > vn).
Kubva patsananguro iri pamusoro, tinogona kuwana pfungwa yekuti kubva paR kuenda ku rn, mwero wemvura unoderera. Kureba kwepombi = L. Equation yakawanikwa ndeiyi:
Nekuti zvatiri kufunga nezvazvo inhamba (v) yekuyerera kwemvura, equation 2 inova:
Uyu ndiwo muyero wehuwandu hwemvura inoyerera iri kure ne r kubva papombi ine radius ye R. Kana wakavhiringidzika paunenge uchitarisa mufananidzo uri pamusoro.... Ndapota cherechedza kuti mvura inoyerera mupombi kana chubhu, saka tinofanira kuongorora huwandu hwemvura inoyerera.
Mukati mechubhu mune mvura. Semuenzaniso, tinokamura mvura kuita zvidimbu zvidiki, apo chidimbu chimwe nechimwe chine nzvimbo yeyuniti dA, chiri kure ne axis yechubhu uye chine flow rate v. Pamasvomhu, izvi zvinogona kunyorwa seizvi:
dA1 = chikamu chemvura 1, chiri chinhambwe che1 kubva pa axis yechubhu
dA2 = chikamu chemvura 2, chiri chinhambwe che2 kubva pa axis yechubhu
dA3 = chikamu chemvura 3, chiri chinhambwe che3 kubva pa axis yechubhu
……………………………….
dA n = chikamu chemvura n, chiri chinhambwe chiri pakati pe dA n nechubhu
Kune zvidimbu zvakawanda zvemvura zvekuti zviri nyore kuzvinyora nechiratidzo n. Mwero wekuyerera kwehuwandu hwechidimbu chemvura chimwe nechimwe unogona kunyorwa nemasvomhu seizvi:
Chikamu chimwe nechimwe chemvura chiri padaro re r = 0 kusvika r = R (R = radius yechubhu). Nemamwe mashoko, daro rechikamu chimwe nechimwe chemvura rinosiyana kana richiyerwa kubva pa axis yechubhu. Kana tikanyatsoongorora calculus (kubatanidzwa), tichawana equation yehuwandu hwekuyerera kwemvura muchubhu:
Information :
Q = Kubhadhara mari
R = Nharaunda yemukati yepombi kana chubhu
η = Kukosha kwekusimba
P1 - p2 = Musiyano wekumanikidzwa pakati pemagumo maviri epombi
L = Kureba kwepombi
p1-p2/L = Kuyerera kwemhepo (kuyerera kwemvura nguva dzose kunoenda munzira yekuderera kwemhepo)
Zvichibva paPoiseuille equation iri pamusoro apa, zvinoita sekunge huwandu hwekuyerera kwemvura, inozivikanwawo se discharge (Q), hwakaenzana nesimba rechina re radius yechubhu (R).4), kudzvanywa kwemhepo (p)2 - p1 /L) uye zvinoenderana nekusimba kwechubhu. Kana radius yechubhu yakawedzerwa (kusimba kwemuchina uye kusimba kwemuchina zvinoramba zvakafanana), saka mwero wekuyerera kwemvura unowedzera ne16.
Pfungwa huru yekugadzira mapaipi, sirinji, nezvimwewo inoshandisa equation iyi. Kubuda kwemvura kwakaenzana neR4 (R = nharaunda yechubhu). Radiyo yesirinji kana nharaunda yepombi inofanira kuverengwa nokungwarira. Semuenzaniso, kana tikapeta nharaunda yetsono kaviri (r x 2), ipapo kubuda kwemvura inopfapfaidza = kunowedzera simba rekumanikidza kwechigunwe kagumi nematanhatu.
Equation yaPoiseuille inoratidzawo kuti simba rechina reradius (r)4), zvinoenderana nekusiyana kwekumanikidzwa kuri pakati pemigumo miviri yepombi. Semuenzaniso, pakutanga ropa rinoyerera mutsinga yeropa ine radius yemukati ye r. Kana paine kutetepa kwetsinga yeropa (semuenzaniso, r/2 = radius yemukati yetsinga yeropa inoderedzwa nekaviri), saka musiyano wekumanikidzwa kweka16 unodiwa kuti ropa rifambe sepakutanga (kuitira kuti kuyerera kweropa kana huwandu hweropa hurambe hwakafanana).
