Fomula Yotulutsira ndi Equation Yopitilira
Mu fizikisi yamadzimadzi ndi uinjiniya, kumvetsetsa kayendedwe ka madzimadzi n'kofunika kwambiri. Mfundo ziwiri zazikulu zomwe zimagwiritsidwa ntchito nthawi zambiri pofufuza kayendedwe ka madzimadzi ndi kutulutsa madzi ndi equation yopitilira. Nkhaniyi ifotokoza mwatsatanetsatane njira yotulutsira madzi, equation yopitilira, ndi momwe amagwiritsidwira ntchito m'magawo osiyanasiyana.
Tanthauzo la Debit
Kutulutsa madzi ndi muyeso wa kuchuluka kwa madzi omwe akuyenda kudzera mu gawo lopingasa mu unit of time. Mu SI system, kutulutsa madzi nthawi zambiri kumayesedwa mu cubic meters pa sekondi (m³/s) kapena malita pa sekondi (L/s). Fomula yoyambira yowerengera kutulutsa madzi (\(Q \)) ndi iyi:
\[ Q = A \nthawi v \]
Kumene:
– \( Q \) ndi debit,
– \( A \) ndi gawo lodutsa la madzi oyenda,
– \( v \) ndi liwiro la kuyenda kwa madzi.
Mwa kuyankhula kwina, kutuluka kwa madzi kumachitika chifukwa cha kuchulukitsa malo odutsa ndi liwiro la madzi.
Chitsanzo cha Kuwerengera Debit
Mwachitsanzo, tiyerekeze kuti tili ndi chitoliro chokhala ndi mainchesi 0,5 ndi kuthamanga kwa madzi kwa mamita awiri pa sekondi. Choyamba, timawerengera dera lozungulira chitoliro (\( A \)):
\[ A = \pi \left(\frac{d}{2}\right)^2 \]
\[ A = \pi \left(\frac{0,5}{2}\right)^2 \]
\[ A = \pi \nthawi 0,25^2 \]
\[ A = \pi \nthawi 0,0625 \]
\[ A \pafupifupi 0,196 \, \text{m}^2 \]
Kenako, timawerengera kutulutsa (\( Q \)):
\[ Q = A \nthawi v \]
\[ Q = 0,196 \, \text{m}^2 \times 2 \, \text{m/s} \]
\[ Q = 0,392 \, \malemba{m}^3/\malemba{s} \]
Chifukwa chake, kuchuluka kwa madzi mu chitoliro ndi 0,392 cubic metres pa sekondi.
Chiyerekezo Chopitilira
Chiyerekezo cha continuity ndi mfundo yofunikira mu makina amadzimadzi yomwe imati mu kuyenda kwamadzimadzi kosagwedezeka, kutuluka kwamadzimadzi kuyenera kukhala kokhazikika nthawi yonse yoyenda. Izi zikutanthauza kuti zomwe zimachitika m'dera lopingasa ndi liwiro la kuyenda nthawi iliyonse mu kuyenda ndi zomwezo.
Fomula ya continuity equation ya incompressible fluid flow ndi iyi:
\[ A_1 v_1 = A_2 v_2 \]
Kumene:
– \( A_1 \) ndi dera lopingasa lomwe lili pa mfundo yachiwiri,
– \( v_1 \) ndi liwiro la kuyenda kwa madzi pa mfundo 1,
– \( A_2 \) ndi dera lopingasa lomwe lili pa mfundo yachiwiri,
– \( v_2 \) ndi liwiro la kuyenda kwa madzi pa mfundo 2.
Chitsanzo cha Kuwerengera ndi Continuity Equation
Tiyerekeze kuti tili ndi chitoliro chomwe chaphwanyika. Pa mfundo yoyamba, chitolirocho chili ndi mainchesi 0,5 ndi liwiro la kuyenda kwa mamita awiri pa sekondi. Pa mfundo yachiwiri, chitolirocho chimachepa kufika pa mainchesi 0,25. Tikufuna kupeza liwiro la kuyenda kwa madzi pa mfundo yachiwiri.
Choyamba, timawerengera dera lozungulira mbali zonse ziwiri:
\[ A_1 = \pi \kumanzere(\frac{d_1}{2}\kumanja)^2 \]
\[ A_1 = \pi \kumanzere(\frac{0,5}{2}\kumanja)^2 \]
\[ A_1 = \pi \nthawi 0,25^2 \]
\[ A_1 \pafupifupi 0,196 \, \text{m}^2 \]
\[ A_2 = \pi \kumanzere(\frac{d_2}{2}\kumanja)^2 \]
\[ A_2 = \pi \kumanzere(\frac{0,25}{2}\kumanja)^2 \]
\[ A_2 = \pi \nthawi 0,125^2 \]
\[ A_2 \pafupifupi 0,049 \, \text{m}^2 \]
Kenako, tigwiritsa ntchito equation yopitilira kuti tipeze \( v_2 \):
\[ A_1 v_1 = A_2 v_2 \]
\[ 0,196 \nthawi 2 = 0,049 \nthawi v_2 \]
\[ 0,392 = 0,049 v_2 \]
\[ v_2 = \frac{0,392}{0,049} \]
\[ v_2 \pafupifupi 8 \, \text{m/s} \]
Choncho, liwiro la kuyenda pa mfundo yachiwiri ndi pafupifupi mamita 8 pa sekondi.
Kugwiritsa Ntchito Equation Yotulutsa ndi Yopitilira
1. Machitidwe Ogawa Madzi: Mainjiniya amagwiritsa ntchito mfundo za ma equation otulutsa madzi ndi kupitiriza kupanga machitidwe ogawa madzi abwino, kuonetsetsa kuti madzi akuyenda bwino kudzera mu netiweki ya mapaipi.
2. Kusamalira Ngalande Yothirira: Pa ulimi wothirira, kuwerengera madzi otuluka ndikofunikira kwambiri kuti mbeu zipeze madzi okwanira.
3. Makampani ndi Kupanga: Mu mafakitale, kuwongolera kayendedwe ka madzi monga mafuta, gasi, kapena mankhwala ndikofunikira kwambiri pakupanga zinthu. Kugwiritsa ntchito njira yowerengera nthawi kumathandiza kupanga njira zoyendetsera bwino zinthu.
4. Aerodynamics: Pakupanga ndege ndi magalimoto, equation yopitilira imagwiritsidwa ntchito kumvetsetsa kayendedwe ka mpweya mozungulira kapangidwe, komwe ndikofunikira pakukweza magwiridwe antchito ndi magwiridwe antchito.
Mphamvu ya Zinthu Zina
Ngakhale kuti equation yopitilira imatenga madzi osagwedezeka komanso kuyenda kokhazikika, m'machitidwe, zinthu zina monga kuthamanga, kutentha, ndi makhalidwe amadzimadzi zimakhudzanso kuyenda. Mwachitsanzo, madzi opanikizika monga mpweya amakumana ndi kusintha kwakukulu kwa voliyumu ndi kusintha kwa kuthamanga. Chifukwa chake, mu kusanthula kovuta kwambiri, equation yopitilira iyenera kuphatikizidwa ndi malamulo a thermodynamics ndi equation yamadzimadzi ya boma.
Phunziro la Nkhani: Kuyenda kwa Mtsinje
Kuti tifotokoze momwe madzi amagwirira ntchito komanso momwe madzi amayendera, tiyeni tiganizire za kayendedwe ka madzi mumtsinje. Tiyerekeze kuti tikufuna kudziwa momwe madzi amayendera m'malo awiri osiyana m'mbali mwa mtsinje. Pamalo oyamba, mtsinjewu uli ndi mulifupi wa mamita 10 ndipo uli ndi kuya kwa mamita awiri, ndi liwiro la madzi la mita imodzi pa sekondi. Pamalo achiwiri, mtsinjewu umachepa mpaka m'lifupi mwa mamita 5 ndi kuya kwa mamita atatu.
Choyamba, timawerengera kutulutsa kwa madzi pamalo oyamba (\( Q_1 \)):
\[ A_1 = \malemba{m'lifupi} \nthawi \malemba{kuya} \]
\[ A_1 = 10 \nthawi 2 \]
\[ A_1 = 20 \, \malemba{m}^2 \]
\[ Q_1 = A_1 \nthawi v_1 \]
\[ Q_1 = 20 \nthawi 1 \]
\[ Q_1 = 20 \, \malemba{m}^3/\malemba{s} \]
Popeza kutuluka kwa madzi kuyenera kukhala kosalekeza m'mtsinje, ndiye kuti:
\[ Q_2 = Q_1 \]
\[ 20 \, \text{m}^3/\text{s} = A_2 \times v_2 \]
Ndi dera lopingasa pamalo achiwiri (\( A_2 \)):
\[ A_2 = \malemba{m'lifupi} \nthawi \malemba{kuya} \]
\[ A_2 = 5 \nthawi 3 \]
\[ A_2 = 15 \, \malemba{m}^2 \]
Kotero, tikupeza liwiro la kuyenda pa mfundo yachiwiri (\( v_2 \)):
\[ 20 = 15 \nthawi v_2 \]
\[ v_2 = \frac{20}{15} \]
\[ v_2 \pafupifupi 1,33 \, \text{m/s} \]
Choncho, kuchuluka kwa madzi pamalo achiwiri ndi pafupifupi mamita 1,33 pa sekondi.
Mapeto
Kumvetsetsa kuchuluka kwa kayendedwe ka madzi ndi ma equation opitilira ndikofunikira kwambiri pakusanthula ndi kupanga machitidwe oyendera madzi. Pogwiritsa ntchito njira iyi \( Q = A \times v \) ndi equation \( A_1 v_1 = A_2 v_2 \), titha kuwerengera kuyenda kwa madzi m'mikhalidwe yosiyanasiyana, kuyambira mapaipi amafakitale mpaka kuyenda kwa mitsinje yachilengedwe. Kugwiritsa ntchito mfundozi ndi kwakukulu ndipo kumakhudza magawo osiyanasiyana a sayansi ndi uinjiniya. Kumvetsetsa bwino kuyenda kwa madzi sikungothandiza kupanga machitidwe ogwira ntchito komanso kuthetsa mavuto okhudzana ndi kuyenda kwa madzi m'moyo watsiku ndi tsiku.
