Fomura yaBernoulli: Nheyo uye Mashandisirwo
Pfungwa yaBernoulli ipfungwa huru mu fluid mechanics, yakawanikwa naDaniel Bernoulli, nyanzvi yesainzi yekuSwitzerland, muzana remakore rechi18. Iyi nheyo inotsanangura hukama huripo pakati pekumhanya kwekuyerera kwemvura uye kumanikidzwa kuri mukati mekuyerera ikoko. Chinyorwa chino chichakurukura zvakadzama fomura yaBernoulli, pfungwa dzayo dzekutanga, masvomhu anobva, mienzaniso yekuverenga, uye mashandisirwo ayo muhupenyu hwezuva nezuva.
Kunzwisisa Fomura yaBernoulli
Fomura yaBernoulli inoti mukuyerera kwemvura kwakakodzera (pasina kukweshana), huwandu hwesimba remuchina (simba rinogona kuitika, simba rekinetic, uye kumanikidzwa) payuniti yega yega vhoriyamu inogara iripo mukuyerera kwemvura. Fomura iyi inotsanangurwa seizvi:
\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]
di mana:
– \( P \) isimba remvura (mumapascals, Pa),
– \( \rho \) ndiko kuwanda kwemvura (mumakirogiramu pa cubic meter, kg/m³),
– \( v \) ndiyo kumhanya kwekuyerera kwemvura (mumamita pasekondi, m/s),
– \( g \) ndiko kukurumidza kunokonzerwa negiravhiti (mumamita pasekondi imwe chete, m/s²),
– \( h \) ndiko kukwirira kwemvura pamusoro pechirevo (mumamita, m).
Nheyo yaBernoulli
Nheyo yaBernoulli yakavakirwa pamutemo wekuchengetedza simba. Mukuyerera kwemvura, simba rose riri muhurongwa rinofanira kuramba rakafanana kana pasina simba rinowedzerwa kana kubviswa muhurongwa. Simba rose payuniti imwe neimwe rinosanganisira:
1. Simba reKudzvanyirira (\( P \)): Simba rinokonzerwa nekudzvanyirira kwemvura.
2. Kinetic Energy (\( \frac{1}{2} \rho v^2 \)): Simba rinokonzerwa nekufamba kwemvura.
3. Simba Rinogona Kukweva Simba (\( \rho gh \)): Simba rinokonzerwa nenzvimbo yemvura mumunda wegiravhiti.
Kutorwa kwemasvomhu kweForamu yaBernoulli
Kuti tinzwisise zvakatorwa neBernoulli's Formula, tinofunga nezvechinhu chidiki chemvura chinofamba mukuyerera nekukurumidza \( v \) kubva pachikamu 1 kusvika pachikamu 2. Kana tikafunga kuti hapana kurasikirwa kwesimba nekuda kwekukweshana kana kupisa, simba rese riri pamapoinzi 1 ne2 rinofanira kunge rakafanana.
Simba rose riri pachikamu chechipiri (\( E_1 \)) nderinotevera:
\[ E_1 = P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 \]
Simba rose riri pachikamu chechipiri (\( E_2 \)) nderinotevera:
\[ E_2 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2 \]
Sezvo simba rose rinofanira kugara riine:
\[ P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2 \]
Izvi ndizvo zvinonzi Fomura yaBernoulli.
Muenzaniso wekuverenga uchishandisa Fomura yaBernoulli
Ngatitii tine pombi yakataramuka ine mvura inoyerera kubva panzvimbo A kuenda panzvimbo B. Panzvimbo A, kumhanya kwemvura i2 m/s uye kumanikidzwa i150,000 Pa. Panzvimbo B, kumhanya kwemvura i4 m/s. Kuwanda kwemvura i1000 kg/m³. Verenga kumanikidzwa panzvimbo B.
Shandisa Fomura yaBernoulli:
\[ P_A + \frac{1}{2} \rho v_A^2 + \rho gh_A = P_B + \frac{1}{2} \rho v_B^2 + \rho gh_B \]
Sezvo pombi yacho yakatwasuka, \( h_A = h_B \), saka \( \rho gh \) panzvimbo dzese mbiri dzinogona kuregeredzwa:
\[ P_A + \frac{1}{2} \rho v_A^2 = P_B + \frac{1}{2} \rho v_B^2 \]
Tsiva tsika dzinozivikanwa:
\[ 150,000 + \frac{1}{2} \times 1000 \times (2)^2 = P_B + \frac{1}{2} \times 1000 \times (4)^2 \]
Verenga simba rekinetic panzvimbo mbiri idzi:
\[ 150,000 + 2000 = P_B + 8000 \]
\[ 152,000 = P_B + 8000 \]
\[P_B = 152,000 – 8000 \]
\[ P_B = 144,000 \, \text{Pa} \]
Saka, kumanikidzwa kuri padanho B i144,000 Pa.
Kushandiswa kweMutemo waBernoulli
1. Ndege: Pfungwa yaBernoulli inoshandiswa pakugadzira mapapiro endege. Chimiro chebapiro rendege chakagadzirwa kuitira kuti kumhanya kwemhepo pamusoro pebapiro kuve kukuru kupfuura pasi pebapiro. Izvi zvinoita kuti kumanikidzwa kuderera pamusoro pebapiro uye kumanikidzwa kwakakwira pasi pebapiro, zvichiita kuti ndege ikwanise kubhururuka.
2. Mota dzeMijaho: Dhizaini yemota dzemijaho inoshandisa Bernoulli's Principle kuwedzera kumhanya uye kugadzikana. Zvidhinha nemadiffuser zvinoshandiswa kudzora kufamba kwemhepo, zvichiwedzera simba rekufamba, izvo zvinovandudza kubata kwemota mumugwagwa.
3. Kuyerera Kweropa Mumuviri: Mutemo waBernoulli unoshandawo pakuyerera kweropa mutsinga dzeropa. Kusiyana kwekumhanya kweropa nekumanikidzwa kwaro muzvikamu zvakasiyana zvemuviri kunogona kudzidzwa kuti kuongororwe zvirwere.
4. Venturi Meter: Mudziyo unoshandiswa kuyera mwero wekuyerera kwemvura mupombi. Venturi meter ine chikamu chakatetepa, izvo zvinokonzera kuwedzera kwekufamba kwemvura uye kudzikira kwekumanikidzwa zvichienderana neBernoulli's Principle. Musiyano wekumanikidzwa pakati pezvikamu zvakafara nezvitete unoshandiswa kuverenga mwero wekuyerera kwemvura.
5. Zvipfukuto zvePerfume: Zvipfukuto zveperfume kana zvipfukuto zvemvura zvinoshandisa musimboti waBernoulli. Kana mhepo ikafefeterwa nepachubhu yakamanikana, kumanikidzwa kwemhepo kwakatenderedza mugumo wechubhu kunoderera, zvichikwevera mvura yeperfume kumusoro nepachubhu uye kuipfapfaidza semhute diki.
Zvinhu Zvinopesvedzera Kushandiswa kweMutemo waBernoulli
1. Kukweshana: Muchokwadi, mvura haina kunaka uye nguva dzose pane kukweshana kwemukati (kukweshana) kunokonzera kurasikirwa nesimba. Izvi zvinoita kuti kushandiswa kweBernoulli's Principle kuve kwakaoma.
2. Kuomarara kwemvura: Pfungwa yaBernoulli iri nyore kushandisa kune mvura dzisingaomarara (senge mvura). Kune magasi kana mvura dzinoomarara, equation inofanira kugadziriswa.
3. Kusagadzikana: Pfungwa yaBernoulli inoshanda pakuyerera kwemvura kwakajairika. Mukuyerera kwemvura kwakashata (kusingawanzoitiki), ongororo yacho inova yakaoma.
Chidzidzo Chenyaya: Kushandiswa kweMutemo waBernoulli muKugadzira Mapapiro Endege
Magadzirirwo ebapiro rendege muenzaniso weBernoulli's Principle iri kushanda. Chimiro chebapiro chakakombama nechepasi chakati sandara chinobvumira mhepo kuyerera nekukurumidza pamusoro pebapiro kupfuura pasi paro. Sekureva kweBernoulli's Principle, kumhanya kwakanyanya kwemhepo pamusoro pebapiro kunoita kuti kumanikidzwa kuderera pane pasi pebapiro. Musiyano uyu wekumanikidzwa unogadzira simba rekusimudza rinobvumira ndege kubhururuka.
Ngatitii ndege ine nzvimbo yemapapiro ye25 m². Kumhanya kwemhepo pamusoro pemapapiro ndeye 70 m/s, nepo pasi pemapapiro iri 50 m/s. Kuwanda kwemhepo ndeye 1.225 kg/m³. Verenga kukwira kwacho.
1. Verenga musiyano wekumanikidzwa (\( \Delta P \)) uchishandisa Fomura yaBernoulli:
\[ P_{bottom} – P_{top} = \frac{1}{2} \rho (v_{top}^2 – v_{bottom}^2) \]
Tsiva tsika dzinozivikanwa:
\[ \Delta P = \frac{1}{2} \times 1.225 \times (70^2 – 50^2) \]
\[ \Delta P = \frac{1}{2} \times 1.225 \times (4900 - 2500) \]
\[ \Delta P = \frac{1}{2} \times 1.225 \times 2400 \]
\[ \Delta P = 1.225 \kawa 1200 \]
\[ \Delta P = 1470 \, \text{Pa} \]
2. Verenga simba rekusimudza (\( F_{lift} \)):
\[ F_{lift} = \Delta P \times A \]
\[ F_{lift} = 1470 \, \text{Pa} \times 25 \, \text{m}^2 \]
\[ F_{lift} = 36,750 \, \text{
N} \]
Saka, simba rekusimudza rinobuda i36,750 newtons.
Mhedziso
Mutemo waBernoulli ndeimwe yenheyo dzemakanika emvura, ichitsanangura hukama huripo pakati pekumhanya kwemvura nekumanikidzwa. Nekunzwisisa nekushandisa Fomura yaBernoulli, tinogona kuongorora nekugadzira masisitimu akasiyana-siyana anosanganisira kuyerera kwemvura, kubva mundege kusvika kumamita ekuyerera. Kunyangwe mukuita kwedu kazhinji tichifanira kufunga nezvezvinhu zvakaita sekukweshana nekuvhiringika, Mutemo waBernoulli unoramba uri chishandiso chakakosha mukunzwisisa mafambiro emvura uye kugadzira mhinduro dzinoshanda dzeinjiniya.
