Chinyorwa pamusoro peEquation of continuity
Edza kuvhura pombi yemvura zvishoma nezvishoma uchinyatsoteerera kumhanya kwemvura inobuda mumuromo wepombi. Zvino enzanisa, mwero wemvura unoyerera nekukurumidza kupi, kana muromo wepombi wakavharwa here kana kuti kwete? Sei zvakadaro? Kuti unzwisise izvi, ndapota dzidza nezve continuity equation.
Streamline
Mukufamba kwenguva, kumhanya kwechinhu chimwe nechimwe chine mvura panguva imwe chete, ngatitii poindi A kunogara kwakafanana. Pakupfuura poindi B, kumhanya kwechinhu chine mvura kunogona kuchinja. Zvisinei, kana chasvika papoindi B, zvinhu zvine mvura zvinotevera kubva kumashure zvinoyerera nekukurumidza kwakafanana nezvikamu zvine mvura zvinoitangira. Saizvozvowo kana chasvika papoindi C nezvimwewo. Mutsetse weFlow igwara rinobatanidza mapoinzi A, B, naC.
Chubhu yekuyerera
Tinogona kutsanangura kuyerera kwega kwega kwemvura kuburikidza nepfungwa yega yega yekuyerera kwemvura. Kana tikaona kuyerera kwemvura kwakadzikama, mamwe mafambisirwo emvura anopfuura nekona yakati panzvimbo yekufungidzira inoumba chubhu yekuyerera. Hapana zvimedu zvemvura zvinosangana asi zvinogara zvakafanana, uye chubhu yekuyerera kwemvura inenge yakafanana nepombi ine chimiro chakafanana. Mvura inopinda pamugumo wechubhu ichabuda muchubhu kune rumwe rutivi.
Chikwereti
Kubuda kwemvura kunoratidza huwandu hwemvura inoyerera nepakati pechikamu chakati panguva yakatarwa. Pamasvomhu, zvinogona kutaurwa:
Kubuda = Huwandu hwemvura / nguva yekubuda
Q = V / t
Kuti tiwedzere kunzwisisa kwenyu, tinoshandisa muenzaniso. Semuenzaniso, mvura inoyerera nemupombi. Mapombi anowanzova akaita sedenderedzwa uye ane nzvimbo yakati chechetere. Pombi yacho inewo kureba.
Kana mvura ichiyerera mupombi kusvika L, huwandu hwemvura iri mupombi ndiV = AL (V = huwandu hwemvura, A = nzvimbo yepakati uye L = kureba kwepombi). Nekuti chero bedzi ichiyerera mupombi iri paL, mvura yacho inoda nguva yakati, saka tinogona kutaura kuti huwandu hwemvura ndei:
Nekuti v = s / t = L / t —> L = vt, equation iri pamusoro inoshandurwa kuita:
Saka, kana mvura ichiyerera nemupombi ine nzvimbo yakatarwa uye kureba, kwenguva yakati, huwandu hwemvura inobuda (Q) hwakaenzana nenzvimbo yakatarwa (A) yakawedzerwa nekumhanya kwekuyerera kwemvura (v).
Kuenzanisa kwekuenderera mberi
Ongorora kuyerera kwemvura mupombi ine dhayamita yakasiyana, sezvakaratidzwa mumufananidzo uri pazasi.
Mufananidzo uyu unoratidza kuyerera kwemvura kubva kuruboshwe kuenda kurudyi (mvura inoyerera kubva papombi ine dhayamita hombe kuenda padhayamita diki). Mutsetse wakakamurwa wakarongeka.
A1 = nzvimbo yepakati pemapaipi ine dhayamita hombe, A2 = nzvimbo diki ine dhayamita, v1 = kumhanya kwekuyerera kwemvura mupombi ine dhayamita hombe, v2 = kumhanya kwekuyerera kwemvura mupombi diki, L = daro rinofambwa nemvura.
Mukufamba kwakadzikama, kumhanya kwekuyerera kwezvikamu zvemvura panzvimbo imwe kwakaenzana nekumhanya kwekuyerera kwezvimwe zvikamu zvemvura zvinopfuura nepo. Kuyerera kwemvura hakusangani (mitsara yacho yakafanana). Saka huwandu hwemvura hunopinda kumucheto kwepombi hunofanira kuenzana nehuwandu hwemvura hunobuda kune rumwe rutivi. Kana mvura yacho iine huwandu hwakati hunouya kupombi ine dhayamita yakakura, mvura yacho ichabuda papombi diki ine dhayamita yakafanana.
Zvino funga nezvemufananidzo wepombi iri pamusoro. Ongorora pombi yakakura ine dhayamita nepaipi diki ine dhayamita.
Munguva yakati rebei, mamwe manyoro anoyerera nepakati pechikamu chepombi ine dhayamita yakakura (A1) kusvika kuL1 (L1 =v1 t). Huwandu hwemvura inoyerera iV1 =A1 L1 =A1 v1 t. Munguva imwe cheteyo, mamwe manyoro anoyerera nepakati pechikamu chidiki chepombi (A2) kusvika kuL2 (L2 =v2 t). Huwandu hwemvura inoyerera iV2 =A2 L2 =A2 v2 t.
Kuenzanisa kwekuenderera mberi kwemvura dzisingadzvinyiriri
Mumvura dzisingapindiki, huwandu hwemvura hunofanana pese painopfuura. Huremu hwemvura hunoyerera mupombi ine nzvimbo yepakati peA1 (dhayamita hombe yepombi) panguva yakatarwa ndeiyi:
Saizvozvowo, huwandu hwemvura inoyerera mupombi ine nzvimbo yeA2 (dhayamita diki yepombi) panguva yakatarwa ndeiyi:
Mumvura inoyerera zvakanaka, huwandu hwemvura inopinda hwakaenzana nehuwandu hwemvura inobuda, saka:
m1 = m2
ρ A1 v1 t = ρ A2 v2 t
A1 v1 =A2 v2
Saka, equation ye continuity equation mu mvura isingadzvinyike:
A1 v1 =A2 v2 — Equation 1
A1 = nzvimbo ine zvikamu 1, A2 = nzvimbo yepakati pezvikamu 2, v1 = kumhanya kwekuyerera kwemvura muchikamu 1, v2 = kumhanya kwekuyerera kwemvura muchikamu chechipiri, A v = mwero wekuyerera kwevhoriyamu (V / t) = kubuda kwemvura.
Equation 1 inoratidza kuti kubuda kwemvura kunogara kwakafanana panzvimbo imwe neimwe iri papombi kana chubhu yekuyerera kwemvura. Kana chikamu chepombi chadzikira, mwero wekuyerera kwemvura unowedzera, nepo chikamu chepombi chakura, mwero wekuyerera kwemvura unova mudiki.
Kana chikamu chemuromo wepombi chakavharwa, kuyerera kwemvura kunorema kupfuura kana chikamu chemuromo wepombi chisina kuvharwa. Izvi zvinodaro nekuti nzvimbo yepombi inova diki kana chikamu chemuromo wepombi chakavharwa kuitira kuti mwero wekuyerera kwemvura uwedzere. Asi zvakakosha kuziva kuti mwero wekuyerera kana kubuda kwemvura nguva dzose kwakafanana panzvimbo imwe neimwe yekuyerera kwemvura, kungave chikamu chemuromo wepombi yedu chakavharwa kana kwete. Saka chii chinochinja mwero wekuyerera kwemvura?
Ko zvino zvakadini nekuyerera kwemvura murwizi? Chikamu cherwizi rwakadzika chine chikamu chakakura kupfuura chikamu chisina kudzika cherwizi, saka mwero wekuyerera kwemvura murwizi rwakadzika mudiki pane kumhanya kwekuyerera kwemvura muchikamu chisina kudzika cherwizi.
Kuenzanisa kwekuenderera mberi kwemvura inomanikidzwa
Kune mvura yakamanikidzwa, huwandu hwemvura hahuna kufanana nguva dzose. Nemamwe mashoko, huwandu hwemvura hunochinja kana yakamanikidzwa. Kana mvura isina kumanikidzwa huwandu hwemvura hunobviswa kubva mu equation, saka muchiitiko ichi, huwandu hwemvura hunosanganisirwa mu equation. Tichitarisa equation yakambotorwa kare, ngatitore equation yemvura yakamanikidzwa.
Huremu hwemvura inopinda hwakaenzana nehuremu hwemvura inobuda, saka:
m1 = m2
ρ A1 v1 t = ρ A2 v2 t
Nguva yekuyerera kwemvura yakafanana kuitira kuti ikwanise kubviswa. Maequations anoshanduka kuita:
ρ A1 v1 = ρ A2 v2 → Equation 2
Uyu ndiwo muyero wemvura yakamanikidzwa. Musiyano uri muhuwandu hwemvura. Kana mvura yakamanikidzwa, huwandu hunochinja. Kusiyana neizvi, kana mvura isina kumanikidzwa, huwandu hwacho hunogara hwakafanana kuitira kuti hubviswe muyero.
Muenzaniso wedambudziko 1:
Mvura inoyerera nemupombi ine dhayamita ye 10 cm nekumhanya kwe 2 m/s. Chii chinonzi mvura inobuda?
Zvinozivikanwa:
Dhayamita yepombi = 10 cm
Nharaunda yepombi (r) = 5 cm = 0.05 m
Kumhanya kwemvura (v) = 2 m/s
Zvaidiwa: Chikwereti
Solution:
Mubvunzo = A v
Q = (π r2(2 m/s)
Q = (3.14)(0.05 m)2 (2 m/s)
Q = (3.14)(0.0025 m2)(2 m/s)
Q = 0.0157 m3/s
Muenzaniso wedambudziko 2:
Pombi ine dhayamita ye20 cm yakabatana kune imwe pombi ine dhayamita ye10 cm. Kana kumhanya kwemvura mupombi ine dhayamita ye20 cm kuri 4 m/s, kumhanya kwemvura mupombi ine dhayamita ye10 cm chii?
Zvinozivikanwa:
Dhayamita 1 = 20 cm (r)1 = 10 cm = 0.1 m)
v1 = 4 m/s
Dhayamita 2 = 10 cm (r)2 = 5 cm = 0.05 m)
Zvaidiwa: v1
Mhinduro:
Q1 =Q2
A1 v1 =A2 v2
(π r12) (4 m/s) = (π r22) (v2)
(0.1 m)2 (4 m/s) = (0.05 m)2 (v2)
(0.01 m2)(4 m/s) = (0.0025 m2)(v)2)
(0.04 m3 /s) = (0.0025 m2)(v)2)
v2 = 16 m/s
