Chinyorwa pamusoro peBernoullis principle uye Bernoullis equation
Patinotasva mudhudhudhu, mbatya dzatinopfeka dzinozvimba kumashure. Dzimwe nguva, kana mhepo ikavhuvhuta nesimba, gonhi rinogona kuvharika. Kunyange zvazvo mhepo ichivhuvhuta kunze kwemba, gonhi riri mukati memba.
Izvi zvinogona kutsanangurwa uchishandisa musimboti waBernoulli. Daniel Bernoulli (1700-1782) akawana musimboti waigona kushandiswa kutsanangura chiitiko chiri pamusoro apa.
Mutemo waBernoulli
Nheyo yaBernoulli inoti kana kumhanya kwemvura kuchikwira, kumanikidzwa kwemvura kushoma. Kusiyana neizvi, kana kumhanya kwemvura kuchiderera, kumanikidzwa kwemvura kunowedzera. Kana mota yemudhudhudhu ichifamba nekukurumidza, kumhanya kwemhepo kumberi nepadivi pemuviri wako kunowedzera. Saka, kumanikidzwa kwemhepo kunova kwakaderera. Kumashure kwemuviri wako kunovharirwa nepamberi pemuviri wako, saka kumhanya kwemhepo kuseri kwemuviri wako hakukwire. Nekuda kweizvozvo, kumanikidzwa kwemhepo kuseri kwemuviri wako kunowedzera. Nekuti pane musiyano mukumanikidzwa kwemhepo, uko kumashure kwemuviri kumanikidzwa kwemhepo kwakakwira kupfuura mhepo inosundira shati yako kumashure kuitira kuti mbatya dzako dzitaridzike dzakazvimba kumashure.
Ko gonhi remba rinozvivhara roga kana mhepo ichivhuvhuta kunze kwemba? Mhepo iri kunze kwemba inofamba nekukurumidza kupfuura mhepo iri mukati memba. Nekuda kweizvozvo, kumanikidzwa kwemhepo iri kunze kwemba kudiki pane kumanikidzwa kwemhepo iri mukati memba. Nekuti pane musiyano wekumanikidzwa, apo kumanikidzwa kwemhepo iri mukati memba kwakakura, gonhi rinosundirwa kunze. Nemamwe mashoko, shizha regonhi rinofamba kubva panzvimbo ine kumanikidzwa kwemhepo yakakura kuenda kunzvimbo ine kumanikidzwa kwemhepo kudiki.
Equation yaBernoulli
Kare, takadzidza nezvepfungwa yaBernoulli. Bernoulli akagadzirawo pfungwa iyi nekuverenga. Kuti tiwane equation yaBernoulli, tinofunga kuti kuyerera kwemvura kwakadzikama uye kwakadzikama, hakuna kumanikidzwa, uye viscosity shoma zvekuti inogona kuregeredzwa.
Mukukurukura nezve equation of continuity, takadzidza kuti mwero wekuyerera kwemvura unogona kusiyanawo zvichienderana nenzvimbo yekuyerera kwechubhu yekuyerera. Zvichibva papfungwa 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 muBernoulli equation.
Equation yaBernoulli yakakosha nekuti inogona kushandiswa kuongorora ndege dzendege, ma hydroelectric power plants, ma pombi systems, nezvimwewo. Kuti equation yaBernoulli iwanikwe kazhinji, tinofunga kuti mvura inoyerera nemuchubhu yekuyerera ine nzvimbo isina kufanana uye kukwirira kwakasiyanawo. Kuti tiwane equation yaBernoulli, tinoshandisa theorem yebasa nesimba kumuchubhu wekuyerera.
Ruvara rusina kujeka ruri muchubhu yekuyerera kwemvura mumufananidzo uri pazasi runoratidza kuyerera kwemvura, ukuwo ruvara ruchena rusingaratidzi kuyerera kwemvura.
Mvura iri munzvimbo ine chikamu 1 (kuruboshwe) inoyerera kusvika kuL 1 uye inomanikidza mvura iri muchikamu 2 (kurudyi) kuti ifambe kusvika kuL 2. Nekuti nzvimbo ine chikamu 2 kurudyi idiki, kumhanya kwekuyerera kwemvura kurudyi kwechubhu yekuyerera kwakakura (Rangarira equation yekuenderera mberi). Izvi zvinokonzera musiyano wekumanikidzwa pakati pechikamu 2 (kurudyi kwechubhu yekuyerera) nechikamu 1 (kuruboshwe kwechubhu yekuyerera) - Yeuka musimboti waBernoulli. Mvura iri kuruboshwe rwechikamu 1 inopa kumanikidzwa (P 1 ) pamvura iri kurudyi uye inoshanda:
Zvadaro equation yeW1 inogona kunyorwa:
W 1 = p 1 A 1 L 1
Muchikamu chechipiri (kurudyi kwechubhu inoyerera), basa rinoitwa pamvura ndeiri:
W 2 = − p 2 A 2 L 2
Chiratidzo chisina kunaka chinoratidza kuti simba rinoshandiswa rakapesana negwara rekufamba. Saka, mvura inoshanda kurudyi rwechikamu chechipiri. Uyezve, simba regiravhiti rinoshanda pamvura. Muchiitiko chiri pamusoro apa, mamwe mass emvura anotamiswa kubva muchikamu chekutanga kusvika kuL 1 kuenda kuchikamu chechipiri kusvika kuL 2 , uko vhoriyamu yemvura iri muchikamu chekutanga (A 1 L 1 ) = vhoriyamu yemvura muchikamu chechipiri (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, kusiyana nekwainoenda simba regiravhiti. Saka, basa rinoitwa pamvura ndeiri:
W = W 1 + W 2 + W 3
W = P1 A1 L1 - P2 A2 L2 + mgh1 - mgh2
Dzidziso yesimba rekushanda inoti basa remagetsi rinoitwa pahurongwa rakafanana nekuchinja kwesimba remagetsi. Saka, tinogona kutsiva basa (W) nekuchinja kwesimba remagetsi (EK 2 - EK 1 ).
Equation iri pamusoro inogona kunyorwa zvakare:
W = P1 A1 L1 - P2 A2 L2 + mgh1 - mgh2
EK2 ‐ EK1 =P1 A1 L1 - P2 A2 L2 + mgh1 - mgh2
1⁄2 mv22 – 1⁄2 mv12 =P1 A1 L1 - P2 A2 L2 + mgh1 - mgh2
Huremu hwemvura hunoyerera kusvika kuL1 muchikamu A1 = huwandu hwemvura inoyerera kusvika kuL2 (chikamu A)2Huremu hwemvura, ngatiti m, hune vhoriyamu yeA1 L1 uye A2 L2 uko A1 L1 =A2 L2 (L2 yakareba kupfuura L1).
Zvino tinotsiva m muequation iri pamusoro apa ne m = ρ AL:
Uyu ndiwo muenzanisiro waBernoulli. Muenzanisiro waBernoulli unobva panheyo yesimba rekushanda kuitira kuti ive nzira yekuchengetedza simba.
P = kumanikidzwa, ρ = kuwanda, v = kumhanya kwemvura, g = kukurumidza kwegiravhiti, h = kukwirira kwepombi pamusoro pevhu.
Zvikamu zvekuruboshwe nekurudyi zveequation yaBernoulli zviri pamusoro zvinogona kureva mapoinzi maviri chero kupi zvako pachubhu yekuyerera kuitira kuti tigone kunyora patsva equation iri pamusoro kuita:
Zvino ngationgororei equation yaBernoulli yezvimwe zviitiko.
Equation yaBernoulli mu static fluids
Nyaya yakakosha ye equation yaBernoulli ndeye static fluid, uko fluid isina kumhanya. Saka, v 1 = v 2 = 0. Kana iri static fluid, tinogona kugadzira equation yaBernoulli kuti ive:
Kana h 2 - h 1 = h, equation iyi inogona kunyorwa seizvi:
p 1 − p 2 = ρ g (h 2 − h 1 )
p 1 − p 2 = ρ gh
Equation yaBernoulli papombi yakaenzana pakureba
Kana kukwirira kwepombi kwakafanana, equation yaBernoulli inoshandurwa kuita:
