Foromo ea Bernoulli: Melao-motheo le Litšebeliso
Molao-motheo oa Bernoulli ke mohopolo oa motheo oa mechanics ea mokelikeli, o sibolotsoeng ke Daniel Bernoulli, rasaense oa Switzerland, lekholong la bo18 la lilemo. Molao-motheo ona o hlalosa kamano pakeng tsa lebelo la phallo ea mokelikeli le khatello e ka har'a phallo eo. Sehlooho sena se tla tšohla foromo ea Bernoulli ka botebo, likhopolo tsa eona tsa motheo, litšibollo tsa lipalo, mehlala ea lipalo, le ts'ebeliso ea eona bophelong ba letsatsi le letsatsi.
Ho utloisisa Foromo ea Bernoulli
Foromo ea Bernoulli e bolela hore phallong e ntle ea mokelikeli (ntle le khohlano), bongata ba matla a mechini (matla a ka bang teng, matla a kinetic le khatello) ka yuniti ea bophahamo bo lula bo tsitsitse nakong eohle ea phallo. Foromo ena e boletsoe tjena:
\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]
Moo:
– \( P \) ke kgatello ya mokelikeli (ka pascals, Pa),
– \( \rho \) ke boima ba mokelikeli (ka lik'hilograma ka mithara ya dikhubu, kg/m³),
– \( v \) ke lebelo la phallo ea mokelikeli (ka limithara ka motsotsoana, m/s),
– \( g \) ke ho potlaka ho bakwang ke matla a khoheli (ka dimithara ka motsotsoana, m/s²),
– \( h \) ke bophahamo ba mokelikeli ka hodima referense (ka dimetara, m).
Molao-motheo oa Bernoulli
Molao-motheo oa Bernoulli o thehiloe molaong oa paballo ea matla. Phallong ea mokelikeli, matla ohle a tsamaisong a tlameha ho lula a tsitsitse haeba ho se na matla a eketsoang kapa a tlosoang tsamaisong. Matla ohle ka yuniti a na le:
1. Matla a Kgatelelo (\( P \)): Matla a bakwang ke kgatelelo ya mokelikeli.
2. Kinetic Energy (\( \frac{1}{2} \rho v^2 \)): Matla a bakoang ke motsamao wa mokelikeli.
3. Matla a Kgoheli a ka Kgoheli (\( \rho gh \)): Matla a bakwang ke boemo ba mokelikeli tshimong ya kgoheli.
Tšimoloho ea lipalo ea Foromo ea Bernoulli
Ho utloisisa hore na Foromo ea Bernoulli e tsoa hokae, re nahana ka karolo e nyane ea mokelikeli o tsamaeang ka lebelo \(v \) ho tloha ntlheng ea 1 ho ea ntlheng ea 2. Haeba re nahana hore ha ho na tahlehelo ea matla ka lebaka la khohlano kapa mocheso, matla ohle a lintlheng tsa 1 le 2 a tlameha ho tšoana.
Kakaretso ea matla ntlheng ea 1 (\( E_1 \)) ke:
\[ E_1 = P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 \]
Kakaretso ea matla ntlheng ea 2 (\( E_2 \)) ke:
\[ E_2 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2 \]
Kaha matla ohle a tlameha ho ba a sa fetoheng:
\[ P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2 \]
Sena ke seo ho thoeng ke Foromo ea Bernoulli.
Palo ea Mohlala e Sebelisang Foromo ea Bernoulli
A re re re na le phaephe e rapameng e nang le metsi a phallang ho tloha ntlheng ea A ho ea ntlheng ea B. Ntlha ea A, lebelo la metsi ke 2 m/s 'me khatello ke 150,000 Pa. Ntlha ea B, lebelo la metsi ke 4 m/s. Boima ba metsi ke 1000 kg/m³. Bala khatello ntlheng ea B.
Sebelisa Foromo ea Bernoulli:
\[ P_A + \frac{1}{2} \rho v_A^2 + \rho gh_A = P_B + \frac{1}{2} \rho v_B^2 + \rho gh_B \]
Kaha phaephe e rapame, \( h_A = h_B \), kahoo \( \rho gh \) dintlheng ka bobedi e ka hlokomolohuwa:
\[ P_A + \frac{1}{2} \rho v_A^2 = P_B + \frac{1}{2} \rho v_B^2 \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ 150,000 + \frac{1}{2} \times 1000 \times (2)^2 = P_B + \frac{1}{2} \times 1000 \times (4)^2 \]
Bala matla a kinetic lintlheng tsena ka bobeli:
\[ 150,000 + 2000 = P_B + 8000 \]
\[ 152,000 = P_B + 8000 \]
\[P_B = 152,000 – 8000 \]
\[ P_B = 144,000 \, \mongolo{Pa} \]
Kahoo, kgatello ntlheng ya B ke 144,000 Pa.
Tšebeliso ea Molao-motheo oa Bernoulli
1. Lifofane: Molao-motheo oa Bernoulli o sebelisoa ho rala mapheo a sefofane. Sebopeho sa lepheo la sefofane se entsoe ka tsela eo lebelo la moea ka holim'a lepheo le leng le leholo ho feta ka tlase ho lepheo. Sena se fella ka khatello e tlase ka holim'a lepheo le khatello e phahameng ka tlase ho lepheo, e leng se etsang hore sefofane se khone ho fofa.
2. Likoloi tsa Mabelo: Moralo oa moea o tsamaeang ka lebelo oa likoloi tsa mabelo o sebelisa Molao-motheo oa Bernoulli ho eketsa lebelo le botsitso. Li-spoiler le li-diffuser li sebelisoa ho laola phallo ea moea, ho eketsa matla a ho theoha, e leng se ntlafatsang ho hokahana ha koloi tseleng.
3. Phallo ea Mali 'Meleng: Molao-motheo oa Bernoulli o boetse o sebetsa le phallong ea mali ka har'a methapo ea mali. Phapang ea lebelo la phallo ea mali le khatello likarolong tse fapaneng tsa 'mele e ka ithutoa ho fumana maemo a bongaka.
4. Venturi Meter: Sesebelisoa se sebelisetsoang ho lekanya sekhahla sa phallo ea mokelikeli ka har'a phaephe. Venturi meter e na le karolo e tšesaane, e bakang keketseho ea lebelo la phallo ea mokelikeli le phokotso ea khatello ho latela Molao-motheo oa Bernoulli. Phapang ea khatello lipakeng tsa likarolo tse sephara le tse tšesaane e sebelisoa ho bala sekhahla sa phallo.
5. Di-Spray tsa Monko o Monate: Di-spray tsa monko o monate kapa di-spray tsa metsi di sebedisa molaomotheo wa Bernoulli. Ha moya o fokwa ka hara phaephe e moqotetsane, kgatello ya moya e potileng pheletso ya phaephe e a fokotseha, e hula mokelikeli wa monko o monate hodimo ka hara phaephe mme e o fafatsa e le moholi o mosesaane.
Mabaka a Susumetsang Tšebeliso ea Molao-motheo oa Bernoulli
1. Khohlano: Ha e le hantle, maro ha a lokele 'me kamehla ho na le khohlano ea ka hare (ho teteana) e bakang tahlehelo ea matla. Sena se etsa hore ts'ebeliso ea Molao-motheo oa Bernoulli e be thata haholoanyane.
2. Ho Ikamahanya le Mokelikeli: Molao-motheo oa Bernoulli o bonolo ho o sebelisa ho metsi a sa hatelleng (joalo ka metsi). Bakeng sa likhase kapa metsi a hatelletsoeng, equation e tlameha ho fetoloa.
3. Pherekano: Molao-motheo oa Bernoulli o sebetsa ho phallo e tloaelehileng (e tloaelehileng). Phallong e sa tloaelehang (e sa tloaelehang), tlhahlobo e ba thata le ho feta.
Thuto ea Nyeoe: Tšebeliso ea Molao-motheo oa Bernoulli ho Moralo oa Mapheo a Lifofane
Moralo oa lepheo la sefofane ke mohlala o motle oa Molao-motheo oa Bernoulli o sebetsang. Sebopeho se kobehileng sa karolo e ka holimo le e ka tlase e bataletseng ea lepheo se lumella moea ho phalla ka potlako holim'a lepheo ho feta tlas'a lona. Ho ea ka Molao-motheo oa Bernoulli, lebelo le phahameng la moea holim'a lepheo le hlahisa khatello e tlase ho feta tlas'a lepheo. Phapang ena ea khatello e hlahisa matla a ho phahamisa a lumellang sefofane ho fofa.
A re re sefofane se na le sebaka sa mapheo sa 25 m². Lebelo la moea ka holim'a lepheo ke 70 m/s, ha ka tlase ho lepheo e le 50 m/s. Boima ba moea ke 1.225 kg/m³. Bala bophahamo bo hlahang.
1. Bala phapang ea khatello (\( \Delta P \)) u sebelisa Foromo ea Bernoulli:
\[ P_{bottom} – P_{top} = \frac{1}{2} \rho (v_{top}^2 – v_{bottom}^2) \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ \Delta P = \frac{1}{2} \times 1.225 \times (70^2 – 50^2) \]
\[ \Delta P = \frac{1}{2} \times 1.225 \times (4900 - 2500) \]
\[ \Delta P = \frac{1}{2} \times 1.225 \times 2400 \]
\[ \Delta P = 1.225 \makgetlo a 1200 \]
\[ \Delta P = 1470 \, \text{Pa} \]
2. Bala matla a ho phahamisa (\( F_{lift} \)):
\[ F_{lift} = \Delta P \times A \]
\[ F_{lift} = 1470 \, \text{Pa} \times 25 \, \text{m}^2 \]
\[ F_{lift} = 36,750 \, \mongolo{
N} \]
Kahoo, matla a ho phahamisa a hlahisoang ke li-newton tse 36,750.
Qetello
Molao-motheo oa Bernoulli ke o mong oa metheo ea mechine ea mokelikeli, o hlalosang kamano pakeng tsa lebelo la phallo ea mokelikeli le khatello. Ka ho utloisisa le ho sebelisa Foromo ea Bernoulli, re ka sekaseka le ho rala mefuta e fapaneng ea litsamaiso tse kenyeletsang phallo ea mokelikeli, ho tloha sefofaneng ho ea ho limithara tsa phallo. Leha ho le joalo, ts'ebetsong hangata re tlameha ho nahana ka lintlha tse kang khohlano le moferefere, Molao-motheo oa Bernoulli e ntse e le sesebelisoa sa bohlokoa ho utloisiseng matla a mokelikeli le ho rala litharollo tse sebetsang tsa boenjiniere.
