Fomula ya Bernoulli: Mfundo ndi Magwiritsidwe Ntchito
Mfundo ya Bernoulli ndi mfundo yofunikira kwambiri mu makina amadzimadzi, yomwe inapezeka ndi Daniel Bernoulli, wasayansi waku Switzerland, m'zaka za m'ma 18. Mfundo imeneyi ikufotokoza ubale womwe ulipo pakati pa liwiro la kuyenda kwa madzimadzi ndi kuthamanga kwa madzi mkati mwa kuyendako. Nkhaniyi ifotokoza mozama za njira ya Bernoulli, mfundo zake zoyambira, zochokera m'masamu, zitsanzo za mawerengedwe, ndi momwe imagwiritsidwira ntchito pa moyo watsiku ndi tsiku.
Kumvetsetsa Fomula ya Bernoulli
Fomula ya Bernoulli imati mu kayendedwe kabwino ka madzi (kopanda kukangana), kuchuluka kwa mphamvu yamakina (mphamvu yothekera, mphamvu ya kinetic, ndi kupanikizika) pa unit volume kumakhala kokhazikika panthawi yonse yoyenda. Fomula iyi yalembedwa motere:
\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]
Kumene:
– \( P \) ndi kuthamanga kwa madzi (mu pascals, Pa),
– \( \rho \) ndi kuchuluka kwa madzi (mu makilogalamu pa mita imodzi ya kiyubiki, kg/m³),
– \( v \) ndi liwiro la kuyenda kwa madzi (mu mamita pa sekondi, m/s),
– \( g \) ndi kufulumira komwe kumachitika chifukwa cha mphamvu yokoka (mu mamita pa sekondi imodzi, sikweya, m/s²),
– \( h \) ndi kutalika kwa madzi pamwamba pa chizindikiro (mu mamita, m).
Mfundo ya Bernoulli
Mfundo ya Bernoulli imachokera ku lamulo losunga mphamvu. Pakuyenda kwa madzi, mphamvu yonse mu dongosolo iyenera kukhala yofanana ngati palibe mphamvu yowonjezeredwa kapena yochotsedwa mu dongosolo. Mphamvu yonse pa unit volume imakhala ndi:
1. Mphamvu Yopanikizika (\( P \)): Mphamvu yoyambitsidwa ndi kuthamanga kwa madzi.
2. Kinetic Energy (\( \frac{1}{2} \rho v^2 \)): Mphamvu yoyambitsidwa ndi kuyenda kwamadzimadzi.
3. Mphamvu Yokokera (\( \rho gh \)): Mphamvu yochokera ku malo a madzi m'munda wa mphamvu yokoka.
Kuchokera kwa Masamba a Fomula ya Bernoulli
Kuti timvetse komwe Fomula ya Bernoulli inachokera, tiganizira za chinthu chaching'ono chamadzimadzi chomwe chimayenda mothamanga \(v \) kuchokera pa mfundo 1 mpaka 2. Ngati tikuganiza kuti palibe kutayika kwa mphamvu chifukwa cha kukangana kapena kutentha, mphamvu yonse pa mfundo 1 ndi 2 iyenera kukhala yofanana.
Mphamvu yonse pa mfundo 1 (\( E_1 \)) ndi:
\[ E_1 = P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 \]
Mphamvu yonse pa mfundo 2 (\( E_2 \)) ndi:
\[ E_2 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2 \]
Popeza mphamvu yonse iyenera kukhala yokhazikika:
\[ P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2 \]
Ichi ndi chomwe chimatchedwa Fomula ya Bernoulli.
Kuwerengera Chitsanzo Pogwiritsa Ntchito Fomula ya Bernoulli
Tiyerekeze kuti tili ndi chitoliro chopingasa chokhala ndi madzi oyenda kuchokera pa mfundo A kupita pa mfundo B. Pa mfundo A, liwiro la madzi ndi 2 m/s ndipo kuthamanga ndi 150,000 Pa. Pa mfundo B, liwiro la madzi ndi 4 m/s. Kuchuluka kwa madzi ndi 1000 kg/m³. Werengani kuthamanga pa mfundo B.
Gwiritsani ntchito njira ya Bernoulli:
\[ P_A + \frac{1}{2} \rho v_A^2 + \rho gh_A = P_B + \frac{1}{2} \rho v_B^2 + \rho gh_B \]
Popeza chitolirocho chili chopingasa, \( h_A = h_B \), kotero \( \rho gh \) pa mfundo zonse ziwiri zitha kunyalanyazidwa:
\[ P_A + \frac{1}{2} \rho v_A^2 = P_B + \frac{1}{2} \rho v_B^2 \]
M'malo mwa mfundo zodziwika bwino:
\[ 150,000 + \frac{1}{2} \times 1000 \times (2)^2 = P_B + \frac{1}{2} \times 1000 \times (4)^2 \]
Werengerani mphamvu ya kinetic pa mfundo zonse ziwiri:
\[ 150,000 + 2000 = P_B + 8000 \]
\[ 152,000 = P_B + 8000 \]
\[P_B = 152,000 – 8000 \]
\[ P_B = 144,000 \, \malemba{Pa} \]
Kotero, kupanikizika pa mfundo B ndi 144,000 Pa.
Kugwiritsa Ntchito Mfundo ya Bernoulli
1. Ndege: Mfundo ya Bernoulli imagwiritsidwa ntchito popanga mapiko a ndege. Mawonekedwe a phiko la ndege amapangidwa kuti liwiro la mpweya pamwamba pa phiko likhale lalikulu kuposa pansi pa phiko. Izi zimapangitsa kuti kuthamanga kwa mpweya kukhale kochepa pamwamba pa phiko ndi kupanikizika kwakukulu pansi pa phiko, zomwe zimapangitsa kuti ndegeyo izitha kuuluka.
2. Magalimoto Othamanga: Kapangidwe ka magalimoto othamanga pogwiritsa ntchito njira yoyendera ndege kamagwiritsa ntchito mfundo ya Bernoulli kuti awonjezere liwiro ndi kukhazikika. Ma spoiler ndi ma diffuser amagwiritsidwa ntchito kulamulira kayendedwe ka mpweya, kuwonjezera mphamvu yotsika, zomwe zimapangitsa kuti galimotoyo igwire bwino ntchito pamsewu.
3. Kuyenda kwa Magazi M'thupi: Mfundo ya Bernoulli imagwiranso ntchito pakuyenda kwa magazi m'mitsempha yamagazi. Kusiyana kwa kuthamanga kwa magazi ndi kuthamanga kwa magazi m'mbali zosiyanasiyana za thupi kungaphunziridwe kuti adziwe matenda.
4. Venturi Meter: Chipangizo chomwe chimagwiritsidwa ntchito poyesa kuchuluka kwa madzi mu chitoliro. Venturi meter ili ndi gawo locheperako, lomwe limayambitsa kuwonjezeka kwa kuthamanga kwa madzi komanso kuchepa kwa kuthamanga motsatira mfundo ya Bernoulli. Kusiyana kwa kuthamanga pakati pa magawo akuluakulu ndi opapatiza kumagwiritsidwa ntchito kuwerengera kuchuluka kwa madzi.
5. Zopopera Mafuta Onunkhira: Zopopera mafuta onunkhira kapena zopopera madzi zimagwiritsa ntchito mfundo ya Bernoulli. Mpweya ukawombedwa kudzera mu chubu chopapatiza, mphamvu ya mpweya yozungulira kumapeto kwa chubu imachepa, zomwe zimakoka mafuta onunkhirawo kudzera mu chubucho ndikupopera ngati nthunzi yopyapyala.
Zinthu Zomwe Zimakhudza Kugwiritsa Ntchito Mfundo ya Bernoulli
1. Kukangana: M'malo mwake, madzi si abwino ndipo nthawi zonse pamakhala kukangana kwamkati (kukhuthala) komwe kumayambitsa kutayika kwa mphamvu. Izi zimapangitsa kuti kugwiritsa ntchito mfundo ya Bernoulli kukhale kovuta kwambiri.
2. Kukanikizana kwa Madzi: Mfundo ya Bernoulli ndi yosavuta kugwiritsa ntchito pamadzi osakanizika (monga madzi). Pa mpweya kapena madzi okanizika, equation iyenera kusinthidwa.
3. Kugwedezeka: Mfundo ya Bernoulli imagwira ntchito pa kuyenda kwa madzi pang'ono (kwanthawi zonse). Pa kuyenda kwa madzi kosasunthika (kwanthawi zonse), kusanthula kumakhala kovuta kwambiri.
Phunziro la Nkhani: Kugwiritsa Ntchito Mfundo ya Bernoulli Pakupanga Mapiko a Ndege
Kapangidwe ka phiko la ndege ndi chitsanzo chabwino kwambiri cha mfundo ya Bernoulli yomwe ikugwira ntchito. Mawonekedwe opindika pamwamba ndi pansi pa phirilo amalola mpweya kuyenda mofulumira pamwamba pa phiko kuposa pansi pake. Malinga ndi mfundo ya Bernoulli, liwiro lalikulu la mpweya pamwamba pa phiko limapangitsa kuti mpweya ukhale wochepa kuposa pansi pa phiko. Kusiyana kwa mphamvu kumeneku kumapanga mphamvu yokweza yomwe imalola ndege kuuluka.
Tiyerekeze kuti ndege ili ndi malo okwana mapiko a 25 m². Liwiro la mpweya pamwamba pa phiko ndi 70 m/s, pomwe pansi pa phiko ndi 50 m/s. Kuchuluka kwa mpweya ndi 1.225 kg/m³. Werengani kukweza komwe kwachitika.
1. Werengani kusiyana kwa kuthamanga (\( \Delta P \)) pogwiritsa ntchito Fomula ya Bernoulli:
\[ P_{bottom} – P_{top} = \frac{1}{2} \rho (v_{top}^2 – v_{bottom}^2) \]
M'malo mwa mfundo zodziwika bwino:
\[ \Delta P = \frac{1}{2} \times 1.225 \times (70^2 – 50^2) \]
\[ \Delta P = \frac{1}{2} \times 1.225 \times (4900 – 2500) \]
\[ \Delta P = \frac{1}{2} \nthawi 1.225 \nthawi 2400 \]
\[ \Delta P = 1.225 \nthawi 1200 \]
\[ \Delta P = 1470 \, \text{Pa} \]
2. Werengani mphamvu yokwezera (\( F_{lift} \)):
\[ F_{lift} = \Delta P \times A \]
\[ F_{lift} = 1470 \, \text{Pa} \times 25 \, \text{m}^2 \]
\[ F_{lift} = 36,750 \, \text{
N} \]
Kotero, mphamvu yonyamulira yomwe imabwera chifukwa cha izi ndi 36,750 newtons.
Mapeto
Mfundo ya Bernoulli ndi imodzi mwa mfundo zazikulu za kayendedwe ka madzi, zomwe zimafotokoza ubale womwe ulipo pakati pa liwiro la madzi ndi kupanikizika. Mwa kumvetsetsa ndikugwiritsa ntchito Fomula ya Bernoulli, titha kusanthula ndikupanga machitidwe osiyanasiyana okhudzana ndi kuyenda kwa madzi, kuyambira ndege mpaka mita yoyendera. Ngakhale kuti nthawi zambiri timayenera kuganizira zinthu monga kukangana ndi kugwedezeka, Mfundo ya Bernoulli ikadali chida chofunikira kwambiri pakumvetsetsa mphamvu zamadzimadzi ndikupanga njira zogwirira ntchito bwino zaukadaulo.
