Zvinhu zveBernoulli zvePrinciple and Equation
Kana tichityaira mudhudhudhu nekukurumidza, mbatya dzatinopfeka dzinoita sedzinoputika kumashure. Kana usingakwanise kutasva mudhudhudhu parizvino, teerera vabereki vako kana shamwari dzinotyaira mudhudhudhu. Kumashure kwembatya dzavo kunowanzoita sedzinoputika kumashure kana mudhudhudhu uchimhanya. Dzimwe nguva kana mhepo ikavhuvhuta nesimba, musuwo wemba unogona kuvharika wega. Kunyangwe mhepo ichivhuvhuta kunze kwemba, musuwo uri mukati memba.
Izvi zvinogona kutsanangurwa uchishandisa musimboti waBernoulli. Daniel Bernoulli (1700–1782) akawana musimboti unogona kushandiswa kutsanangura zvimwe zvezvinhu zviri pamusoro apa.
Nheyo yaBernoulli
Nheyo yaBernoulli inoti kana kumhanya kwemvura kwakakwira, kumanikidzwa kwemvura kwakaderera. Kusiyana neizvi, kana kumhanya kwemvura kwakaderera, kumanikidzwa kunowedzera. Kana mota yemudhudhudhu ichifamba nekukurumidza, kumhanya kwemhepo kumberi nepadivi pemuviri wako kwakakwira. Saka, kumanikidzwa kwemhepo kunowedzera. Kumashure kwemuviri wako kunovharirwa nepamberi pemuviri wako, saka kumhanya kwemhepo kuseri kwemuviri wako hakuchinji kuenda kumusoro (kumashure kwemuviri wako). Nekuda kweizvozvo, kumanikidzwa kwemhepo kuseri kwemuviri wako kunowedzera. Nekuti pane musiyano mukumanikidzwa kwemhepo, apo kumanikidzwa kwemhepo kuseri kwemuviri wako kwakawedzera, mhepo inosundira shati yako kumashure, ichiita sekunge yakazvimba kumashure.
Zvakadini negonhi rinozvivhara roga kana mhepo ichivhuvhuta nesimba kunze? Mhepo iri kunze inofamba nekukurumidza kupfuura mhepo iri mukati. Nekuda kweizvi, kumanikidzwa kwemhepo iri kunze kwakaderera pane kumanikidzwa kwemhepo iri mukati. Nekuda kwemusiyano uyu wekumanikidzwa, apo kumanikidzwa kwemhepo iri mukati kwakakwira, gonhi rinosundirwa kunze. Nemamwe mashoko, gonhi rinofamba kubva panzvimbo ine kumanikidzwa kwemhepo kwakakwira kuenda kunzvimbo ine kumanikidzwa kwemhepo kwakaderera.
Equation yaBernoulli
Kare, takadzidza nezvepfungwa yaBernoulli. Bernoulli akagadzirawo pfungwa iyi nehuwandu. Kuti tiwane equation yaBernoulli, tinofunga kuti mvura inoyerera zvakanaka, isingapindiki, uye ine viscosity shoma, izvo zvinogona kuregeredzwa.
Mukukurukurirana kweContinuity Equation, takadzidza kuti mwero wekuyerera kwemvura unogona kusiyanawo zvichienderana nenzvimbo yechubhu yekuyerera. Zvichibva panheyo yaBernoulli yakatsanangurwa pamusoro apa, kumanikidzwa kwemvura kunogona kusiyanawo zvichienderana nemwero wekuyerera kwemvura. Kumanikidzwa kwemvura kunogona kusiyanawo zvichienderana nekukwirira kwemvura. Hukama huripo pakati pekumanikidzwa, mwero wekuyerera, uye kukwirira kwekuyerera hunogona kuwanikwa kubva kuBernoulli equation.
Equation yeBernoulli yakakosha zvikuru nekuti inogona kushandiswa kuongorora kubhururuka kwendege, ma hydroelectric power plants, ma pombi systems, nezvimwewo. Kuti equation yeBernoulli yatichawana ishande zvakanyanya, tichafungidzira kuti mvura inoyerera nemuchubhu ine nzvimbo dzisina kuenzana uye hurefu hwakasiyana (ona mufananidzo uri pazasi). Kuti tiwane equation yeBernoulli, tinoshandisa work and energy theorem kumuchubhu uri munharaunda yechubhu inoyerera. Tevere, tichaverenga huwandu hwemvura nebasa rinoitwa kufambisa mvura.
Ruvara rusina kujeka ruri muchubhu yekuyerera kwemvura mumufananidzo runoratidza kuyerera kwemvura ukuwo ruvara ruchena ruchiratidza kusava nemvura.
Mvura iri munzvimbo ine chikamu 1 (kuruboshwe) inoyerera daro L 1 uye inomanikidza mvura iri muchikamu 2 (kuruboshwe) kuti ifambe daro L 2. Nekuti nzvimbo ine chikamu 2 kurudyi idiki, mwero wekuyerera kwemvura uri kurudyi kwechubhu yekuyerera wakakura (Rangarira continuity equation). Izvi zvinokonzera musiyano wekumanikidzwa pakati pechikamu 2 (kuruboshwe kwechubhu yekuyerera) uye chikamu 1 kuruboshwe (kuruboshwe kwechubhu yekuyerera) - Yeuka musimboti waBernoulli. Mvura iri kuruboshwe rwechikamu 1 inoshandisa kumanikidzwa P 1 mumvura iri kurudyi uye inoita basa re:
Zvadaro equation W 1 inogona kunyorwa seizvi:
W 1 = p 1 A 1 L 1
Pachikamu chechipiri (kurudyi rwechubhu inoyerera), basa rinoitwa pamvura ndeiri:
W 2 = − p 2 A 2 L 2
Chiratidzo chekuramba chinoratidza kuti simba rinoshandiswa rakapesana negwara rekufamba. Saka mvura inoshanda kurudyi rwechikamu 2. Pamusoro pezvo, simba regiravhiti rinoshandawo pamvura. Muchiitiko chiri pamusoro apa, huwandu hwakati hwemvura hunotamiswa kubva muchikamu 1 kusvika kuL 1 kuenda kuchikamu 2 kusvika kuL 2 , uko huwandu hwemvura pachikamu 1 (A 1 L 1 ) = huwandu hwemvura pachikamu 2 (A 2 L 2 ). Basa rinoitwa negiravhiti ndeiri:
W 3 = − mg (h 2 − h 1 )
W 3 = − mgh 2 + mgh 1 )
W 3 = mgh 1 − mgh 2
Chiratidzo chekusaratidza kunaka chinokonzerwa nekuyerera kwemvura mudenga, kwakatarisana nekwakanangana negiravhiti. Saka, basa rose rinoitwa pamvura, sezvakaratidzwa pamufananidzo uri pamusoro, nderekuti:
W = W 1 + W 2 + W 3
W = P 1 A 1 L 1 ‐ P 2 A 2 L 2 + mgh 1 ‐ mgh 2
Dzidziso yesimba rekushanda inotaura kuti basa rose rinoitwa pahurongwa rakaenzana nekuchinja kwesimba rayo rekufamba. Saka, tinogona kutsiva Basa (W) nekuchinja kwesimba rekufamba (EK 2 - EK 1 ).
Tinogona kunyora patsva equation iri pamusoro apa seizvi:
W = P 1 A 1 L 1 ‐ P 2 A 2 L 2 + mgh 1 ‐ mgh 2
EK 2 - EK 1 = P 1 A 1 L 1 - P 2 A 2 L 2 + mgh 1 ‐ mgh 2
1⁄2 mv 2 2 ‐ 1⁄2 mv 1 2 = P 1 A 1 L 1 ‐ P 2 A 2 L 2 + mgh 1 ‐ mgh 2
Huremu hwemvura inoyerera daro L 1 pachikamu chakayambuka A 1 = huremu hwemvura inoyerera daro L 2 (chikamu A 2 ). Huremu hwemvura, ngatiti m, hune vhoriyamu yeA 1 L 1 uye A 2 L 2 apo A 1 L 1 = A 2 L 2 (L 2 yakareba kupfuura L 1 ).
Zvino tinotsiva, kana kuti tinotsiva m muequation iri pamusoro ne m = ρ AL:
Uyu ndiwo muenzanisiro weBernoulli. Takatora muenzanisiro weBernoulli zvichibva papfungwa yekushanda nesimba, saka imhando yeMutemo weKuchengetedza Simba.
Information :
P = Kumanikidzwa
ρ = Kuwanda kwemvura
v = Kumhanya kwekuyerera kwemvura
g = Kukurumidza kunokonzerwa negiravhiti
h = Kureba kwechubhu/pombi inoyerera kubva pamusoro pevhu
Mativi ekuruboshwe nekurudyi eBernoulli equation ari pamusoro anogona kureva chero mapoinzi maviri ari pachubhu yekuyerera kwemvura saka tinogona kunyora patsva equation iri pamusoro seizvi:
Iyi equation inotaura kuti huwandu hwese hwehuwandu huri mu equation hune kukosha kwakafanana mukati me flow tube yese.
Zvino ngationgororei equation yaBernoulli yezvimwe zviitiko.
Equation yaBernoulli yeMafuta Ari Pakuzorora
Muenzaniso wakakosha weBernoulli's equation ndeyemvura iri pakuzorora (static fluids). Kana mvura iri pakuzorora, haina kumhanya. Saka, v 1 = v 2 = 0. Kana iri mvura iri pakuzorora, equation yaBernoulli inogona kuumbwa seizvi:
Kana h 2 - h 1 = h, saka equation iyi inogona kunyorwa seizvi:
p 1 − p 2 = ρ g (h 2 − h 1 )
p 1 − p 2 = ρ gh
Equation yaBernoulli yemachubhu ekuyerera kana mapaipi ane urefu hwakaenzana
Kana kukwirira kwechubhu yekuyerera kana pombi kwakafanana, saka equation yeBernoulli inoshandurwa kuita:
