Izinto Zokulinganisa Okuqhubekayo
Zama ukuvula impompi yamanzi kancane ngenkathi ubheka ukugeleza kwamanzi ephuma empompini. Uma impompi isiyekile ukujika, vala impompi kancane ngesandla sakho. Manje qhathanisa ukuthi yikuphi ukugeleza kwamanzi okukhulu. Uma kuvaliwe noma kuvuliwe kancane? Uma unepayipi elivame ukusetshenziselwa ukunisela izimbali, vumela amanzi ageleze kulo. Vimba ipayipi kancane ngesandla noma ngomunwe wakho. Uma ingxenye enkulu yepayipi ivaliwe, kulapho amanzi azogeleza khona ngokushesha. Ngokuphambene nalokho, uma ipayipi lingavaliwe, amanzi azogeleza ngokushesha. Kungani kunjalo? Ukuze uqonde lokhu, sicela ufunde i-continuity equation.
Ama-Streamline nama-Flow Tubes
Okokuqala, ake siqonde imiqondo yokuqondisa kanye namapayipi okugeleza. Lo mqondo ubalulekile ngoba uzokusiza uqonde i-continuity equation.
Umugqa wokusakaza
Bheka isithombe esingezansi, umugqa oluhlaza okwesibhakabhaka yi-Streamline.
Ekugelezeni okuzinzile, ijubane lenhlayiya ngayinye yoketshezi endaweni ethile, isibonelo iphuzu A, lihlala lingaguquki. Njengoba lidlula iphuzu B, ijubane lezinhlayiya zoketshezi lingashintsha. Kodwa-ke, lapho lifika endaweni B, izinhlayiya zoketshezi ezilandela ngemuva ziyaqhubeka nokugeleza ngejubane elifanayo nezinhlayiya zoketshezi ezandulele. Kusebenza okufanayo lapho lifika endaweni C, njalo njalo. I-streamline yi-curve exhumanisa amaphuzu u-A, B, no-C.
Ipayipi lokugeleza
Empeleni, singadweba ukujikeleza ngakunye ngephuzu ngalinye lokugeleza koketshezi. Uma sicabangela ukugeleza koketshezi okuzinzile, ukujikeleza okuningana okudlula ekhoneni elithile endaweni engokomfanekiso (indawo engokomfanekiso) kwakha ipayipi lokugeleza. Azikho izinhlayiya zoketshezi ezihlangana kodwa zihlala zihambisana, futhi ipayipi lokugeleza lizofana nepayipi elihlala linesimo esifanayo. Uketshezi olungena komunye umkhawulo wepayipi luzophuma epayipini komunye umkhawulo.
Umdwebo
Ukukhishwa kwegesi kubonisa umthamo woketshezi olugeleza engxenyeni ethile ngesikhathi esithile. Ngokwezibalo, lungachazwa kanje:
Ukuze uqonde kangcono, ake sisebenzise isibonelo. Ake sithi uketshezi lugeleza epayipini. Amapayipi ngokuvamile ayindilinga futhi anendawo ethile enqamulayo. Ipayipi nalo linobude.
Uma uketshezi lugeleza epayipini kuze kufike ku-L, khona-ke umthamo woketshezi epayipini ngu-V = AL (V = ivolumu yoketshezi, A = indawo enqamulayo kanye no-L = ubude bepayipi). Ngoba ngesikhathi sokugeleza epayipini eceleni kuka-L uketshezi luhamba isikhathi esithile, khona-ke singasho ukuthi ubukhulu bokukhishwa koketshezi:
Ngoba u-v = s/t = L/t —> L = vt, i-equation engenhla ishintshelwe ku:
Ngakho-ke, lapho uketshezi lugeleza ngepayipi elinendawo ethile enqamulayo kanye nobude besikhathi esithile, ubukhulu bokukhishwa koketshezi (Q) bulingana nendawo engaphezulu enqamulayo (A) ephindaphindwe ngejubane lokugeleza koketshezi (v).
Isibalo Sokuqhubeka
Cabanga ngokugeleza koketshezi epayipini elinobubanzi obuhlukene, njengoba kuboniswe esithombeni esingezansi.
Lesi sithombe sibonisa ukugeleza koketshezi kusuka kwesobunxele kuye kwesokudla (uketshezi lugeleza lusuka epayipini elinobubanzi obukhulu luye epayipini elinobubanzi obuncane). Imigqa enamachashazi iyashelela.
Isihloko sesithombe: A 1 = indawo enqamula ingxenye yepayipi enkulu enobubanzi, A 2 = indawo enqamula ingxenye yepayipi encane enobubanzi, v 1 = ijubane lokugeleza koketshezi engxenyeni yepayipi enkulu enobubanzi, v 2 = ijubane lokugeleza koketshezi engxenyeni yepayipi encane enobubanzi, L = ibanga elihanjwa uketshezi.
Esethulweni se-fluid dynamics, kwachazwa ukuthi ku-fluid dynamics, sixoxa ngokugeleza koketshezi okungacindezeleki, okungacashi, okungaguquguquki, nokuzinzile. Ekugelezeni okuzinzile, ijubane lezinhlayiya zoketshezi endaweni ethile lifana nejubane lezinye izinhlayiya zoketshezi ezidlula kulelo phuzu. Ukugeleza koketshezi nakho akuhlangani (ukugeleza kuyahambisana). Ngakho-ke, isisindo soketshezi esingena komunye umkhawulo wepayipi kumele silingane nesisindo soketshezi esiphuma komunye umkhawulo. Uma uketshezi olunesisindo esithile lungena epayipini elinobubanzi obukhulu, khona-ke uketshezi luzophuma epayipini elinobubanzi obuncane obunobunzima obungaguquki.
Manje, bheka isithombe sepayipi elingenhla. Bheka ingxenye yepayipi enobubanzi obukhulu kanye nengxenye yepayipi enobubanzi obuncane.
Phakathi nesikhathi esithile, inani elithile loketshezi ligeleza engxenyeni yepayipi enobubanzi obukhulu (A).1) kuze kufike ku-L1 (L1 =v1 t). Umthamo woketshezi olugeleza ngu-V1 =A1 L1 =A1 v1 t. Ngesikhathi esifanayo, elinye inani loketshezi ligeleza engxenyeni yepayipi enobubanzi obuncane (A).2) kuze kufike ku-L2 (L2 =v2 t). Umthamo woketshezi olugeleza ngu-V2 =A2 L2 =A2 v2 t.
I-Continuity Equation yama-Incompressible Fluids (engenakucindezelwa)
Okokuqala, ake sicabangele indaba yoketshezi olungacindezeleki. Kuketshezi olungacindezeleki, ubukhulu, noma isisindo, soketshezi buhlala bufana kuzo zonke izindawo oludlula kuzo. Isisindo soketshezi olugeleza epayipini elinendawo enqamulayo A1 ( ububanzi obukhulu bepayipi) ngesikhathi esithile yilesi:
Ngokufanayo, isisindo soketshezi olugeleza epayipini elinendawo enqamulayo engu-A 2 (ububanzi bepayipi elincane) ngesikhathi esithile sokuphumula yilesi:
Uma ubheka ukuthi ekugelezeni okuzinzile, isisindo soketshezi olungena siyafana nesisindo soketshezi oluphumayo, khona-ke:
m 1 = m 2
ρ A 1 v 1 t = ρ A 2 v 2 t (ubuningi boketshezi kanye nesikhathi esiphakathi kuyafana ngakho kuyakhansela)
A 1 v 1 = A 2 v 2
Ngakho-ke, eziketshezini ezingacindezeleki, i-equation yokuqhubeka iyasebenza:
A 1 v 1 = A 2 v 2 — Isibalo 1
Imininingwane:
A 1 = indawo enqamulayo 1, A 2 = indawo enqamulayo 2, v 1 = ijubane lokugeleza koketshezi esigabeni esinqamulayo 1, v 2 = ijubane lokugeleza koketshezi esigabeni esinqamulayo 2, A v = izinga lokugeleza kwevolumu V/t okubizwa ngokuthi ukukhishwa
Isibalo 1 sibonisa ukuthi izinga lokugeleza kwevolumu, okwaziwa nangokuthi ukukhishwa, lihlala lifana kuzo zonke izindawo eziseduze kwepayipi noma ipayipi lokugeleza. Njengoba ingxenye yepayipi incipha, izinga lokugeleza koketshezi liyakhula; ngokuphambene nalokho, njengoba ingxenye yepayipi ikhula, izinga lokugeleza koketshezi liyancipha.
Uma sixhuma kancane impompi, ukugeleza kwamanzi kuba ngokushesha kunalapho impompi ivaliwe kancane. Lokhu kungenxa yokuthi indawo enqamula impompi iyancipha lapho impompi ivaliwe kancane, okwandisa izinga lokugeleza kwamanzi (uketshezi lugeleza ngokushesha). Kunjalo nangamapayipu. Kodwa-ke, kubalulekile ukuqaphela ukuthi izinga lokuphuma noma lokugeleza kwevolumu lihlala lifana kuzo zonke izindawo ezihambisana nokugeleza kwamanzi, kungakhathaliseki ukuthi impompi ivaliwe kancane noma cha. Ngakho-ke, okushintshayo izinga lokugeleza koketshezi.
Ngakho-ke kuthiwani ngokugeleza kwamanzi emfuleni? Izingxenye ezijulile zomfula zinengxenye enkulu ewelayo kunezingxenye ezingajulile, ngakho-ke izinga lokugeleza kwamanzi ezindaweni ezijulile liphansi kunezingxenye ezingajulile. Uma ubona ukugeleza komfula okuzolile kakhulu, lokho kusho ukuthi umfula ujulile. Kodwa uma umfula ugeleza ngokushesha ngokuzumayo, leyo ngxenye ayijulile neze. Kodwa-ke, izinga lokugeleza komthamo wamanzi lihlala lifana, kungakhathaliseki ukuthi kusezindaweni ezijulile noma ezizolile zomfula.
I-Continuity Equation yama-Compressable Fluids (okucindezelwayo)
Uma kwenzeka uketshezi olucindezelwayo , ubuningi boketshezi abufani ngaso sonke isikhathi. Ngamanye amazwi, ubuningi boketshezi buyashintsha uma bucindezelwa. Ngenkathi kuketshezi olungacindezelwayo , ubuningi boketshezi buyasuswa ku-equation, kulokhu, ubuningi boketshezi busafakiwe. Uma sibhekisela ku-equation ethathwe ngaphambilini, ake sithole i-equation yama-fluid angacindezelwayo.
Uma ubheka ukuthi ekugelezeni okuzinzile, isisindo soketshezi olungena siyafana nesisindo soketshezi oluphumayo, khona-ke:
m 1 = m 2
ρ A 1 v 1 t = ρ A 2 v 2 t
Isikhathi sokugeleza koketshezi siyafana ngakho singasuswa. Isibalo sishintshela ku:
ρ A 1 v 1 = ρ A 2 v 2 → Isibalo 2
Lesi yisibalo soketshezi olucindezelwayo. Umehluko kuphela usebuningini boketshezi. Uma uketshezi lucindezelwa, ubukhulu balo buyashintsha. Ngokuphambene nalokho, uma uketshezi lungacindezelwa, ubukhulu balo buhlala bunjalo futhi bungasuswa.
Isibonelo sombuzo 1:
Amanzi ageleza ngepayipi elinobubanzi obuyi-10 cm ngesivinini esingu-2 m/s. Kuyini ukuphuma kwamanzi?
Ingxoxo
Kuyaziwa ukuthi:
Ububanzi bepayipi = 10 cm (lokhu ububanzi bangaphakathi bepayipi)
Irediyasi yepayipi (r) = 5 cm = 0,05 m
amanzi = 2 m/s
Kubuziwe: Idebithi
Impendulo:
Q = A v
Q = (π r 2 ) (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 m 3 / s
Isibonelo sombuzo 2:
Ipayipi lamanzi elinobubanzi obungama-20 cm lixhunywe kwelinye ipayipi elinobubanzi obungama-10 cm. Uma izinga lokugeleza kwamanzi epayipini elinobubanzi obungama-20 cm = 4 m/s, lingakanani izinga lokugeleza kwamanzi epayipini elinobubanzi obungama-10 cm?
Ingxoxo
Kuyaziwa ukuthi:
Ububanzi 1 = 20 cm (r 1 = 10 cm = 0,1 m)
v 1 = 4 m/s
Ububanzi 2 = 10 cm (r 2 = 5 cm = 0,05 m)
Kubuziwe: v 1
Impendulo:
Umbuzo 1 = Umbuzo 2
A 1 v 1 = A 2 v 2
( π r 12 ) (4 m/s) = (π r 22 ) (v 2 )
(0,1 m) 2 (4 m/s) = (0,05 m) 2 (v 2 )
(0,01 m2 ) (4 m/s) = (0,0025 m2 ) (v 2 )
(0,04 m 3 /s) = (0,0025 m 2 )(v 2 )
v 2 = 16 m/s
