Isihloko mayelana ne-Equation of continuity
Zama ukuvula impompi yamanzi kancane ngenkathi unaka ijubane lamanzi aphuma emlonyeni wempompi. Manje qhathanisa, izinga lokugeleza kwamanzi lishesha kangakanani, uma umlomo wempompi uvaliwe noma cha? Kungani kunjalo? Ukuze uqonde lokhu, sicela ufunde i-continuity equation.
Ukusakaza
Ekugelezeni okuzinzile, ijubane lenhlayiya ngayinye yoketshezi endaweni ethile, ake sithi iphuzu A lihlala lifana. Lapho kudlula iphuzu B, ijubane lezinhlayiya zoketshezi lingashintsha. Kodwa-ke, lapho zifika endaweni B, izinhlayiya zoketshezi ezilandela ngemuva zigeleza ngesivinini esifanayo nezinhlayiya zoketshezi ezandulelayo. Ngokufanayo lapho zifika endaweni C njalo njalo. Umugqa Wokugeleza uwumugqa oxhumanisa amaphuzu A, B, no-C.
Ipayipi lokugeleza
Singachaza ukuguquguquka ngakunye ngephuzu ngalinye ekugelezeni koketshezi. Uma sibona ukugeleza koketshezi okuzinzile, ezinye ukuguquguquka okudlula i-engeli ethile endaweni engokomfanekiso yakha ipayipi lokugeleza. Azikho izinhlayiya zoketshezi ezihlanganayo kodwa zihlala zihambisana, futhi ipayipi lokugeleza lizofana nepayipi elinesimo esifanayo. Uketshezi olungena komunye umkhawulo wepayipi luzophuma epayipini komunye umkhawulo.
Umdwebo
Ukukhishwa kusho umthamo woketshezi olugeleza engxenyeni ethile ngesikhathi esithile. Ngokwezibalo, kungashiwo:
Ukukhishwa = Umthamo Woketshezi / isikhawu sesikhathi
Q = V / t
Ukuze sandise ukuqonda kwakho, sisebenzisa isibonelo. Isibonelo, uketshezi lugeleza ngepayipi. Amapayipi ngokuvamile ayindilinga futhi anendawo ethile enqamulayo. Ipayipi nalo linobude.
Uma uketshezi lugeleza epayipini kuze kufike ku-L, umthamo woketshezi epayipini ngu-V = AL (V = umthamo woketshezi, A = indawo enqamulayo kanye no-L = ubude bepayipi). Ngoba uma nje lugeleza epayipini eceleni kuka-L, uketshezi ludinga isikhawu esithile sesikhathi, khona-ke singasho ukuthi inani loketshezi lingu:
Ngoba v = s / t = L / t —> L = vt, isibalo esingenhla sishintshelwe ku:
Ngakho-ke, lapho uketshezi lugeleza ngepayipi elinendawo ethile enqamulayo kanye nobude, isikhathi esithile, inani lokukhishwa koketshezi (Q) lilingana nendawo enqamulayo (A) ephindaphindwe ngejubane lokugeleza koketshezi (v).
Isibalo sokuqhubeka
Buyekeza ukugeleza koketshezi epayipini elinobubanzi obuhlukile, njengoba kuboniswe esithombeni esingezansi.
Lesi sithombe sibonisa ukugeleza koketshezi kusuka kwesobunxele kuye kwesokudla (uketshezi lugeleza lusuka epayipini elikhulu lobubanzi luye kububanzi obuncane). Umugqa onamachashazi ulula.
A 1 = indawo yesiphambano sepayipi enobubanzi obukhulu, A 2 = indawo yesiphambano enobubanzi obuncane, v 1 = ijubane lokugeleza koketshezi epayipini enobubanzi obukhulu, v 2 = ijubane lokugeleza koketshezi epayipini enobubanzi obuncane, L = ibanga elihanjwa uketshezi.
Ekugelezeni okuzinzile, ijubane lokugeleza kwezinhlayiya zoketshezi endaweni ethile lilingana nejubane lokugeleza kwezinye izinhlayiya zoketshezi ezidlula kuleyo ndawo. Ukugeleza koketshezi nakho akuhlangani (imigqa iyahambisana). Ngakho-ke isisindo soketshezi esingena kolunye uhlangothi lombhobho kumele silingane nesisindo soketshezi esiphuma kolunye uhlangothi. Uma uketshezi lunobunzima obuthile obufika epayipini elinobubanzi obukhulu, khona-ke uketshezi luzophuma epayipini elincane elinobukhulu obufanayo.
Manje cabanga ngesithombe sepayipi elingenhla. Buyekeza ipayipi elikhulu elinobubanzi kanye nepayipi elincane elinobubanzi.
Ngesikhathi esithile, uketshezi oluthile lugeleza engxenyeni yepayipi enobubanzi obukhulu (A 1 ) kuze kufike ku-L 1 (L 1 = v 1 t). Umthamo woketshezi olugeleza ngu-V 1 = A 1 L 1 = A 1 v 1 t. Ngesikhathi esifanayo, uketshezi oluthile lugeleza engxenyeni yepayipi enobubanzi obuncane (A 2 ) kuze kufike ku-L 2 (L 2 = v 2 t). Umthamo woketshezi olugeleza ngu-V 2 = A 2 L 2 = A 2 v 2 t.
Isibalo sokuqhubeka koketshezi olungacindezeleki
Kuketshezi olungacindezelwa, ubuningi boketshezi buhlala bufana kuzo zonke izindawo oludlula kuzo. Isisindo soketshezi esigeleza epayipini elinendawo enqamulayo engu-A1 (ububanzi obukhulu bepayipi) ngesikhathi esithile yilesi:
Ngokufanayo, isisindo soketshezi olugeleza epayipini elinendawo enqamulayo engu-A 2 (ububanzi bepayipi elincane) ngesikhathi esithile yilesi:
Ekugelezeni okuzinzile, isisindo soketshezi olungenayo sifana nesisindo soketshezi oluphumayo, ngakho-ke:
m 1 = m 2
ρ A 1 v 1 t = ρ A 2 v 2 t
A 1 v 1 = A 2 v 2
Ngakho-ke, i-equation ye-equation yokuqhubeka koketshezi olungenakucindezelwa:
A 1 v 1 = A 2 v 2 — Isibalo 1
A 1 = indawo enqamulayo 1, A 2 = indawo enqamulayo 2, v 1 = ijubane lokugeleza koketshezi esigabeni 1, v 2 = ijubane lokugeleza koketshezi esigabeni 2, A v = izinga lokugeleza komthamo (V / t) = ukuphuma.
Isibalo 1 sibonisa ukuthi ukukhishwa kwamanzi kuhlala kufana endaweni ngayinye eceleni kwepayipi noma ipayipi lokugeleza. Lapho ingxenye yepayipi incipha, izinga lokugeleza koketshezi liyakhuphuka, kanti lapho ingxenye yepayipi iba nkulu, izinga lokugeleza koketshezi liba lincane.
Uma ingxenye yomlomo wempompi ivaliwe, ukugeleza kwamanzi kuba nzima kunalapho ingxenye yomlomo wempompi ingavalwanga. Lokho kungenxa yokuthi indawo enqamula impompi iba ncane lapho ingxenye yomlomo wempompi ivaliwe ukuze izinga lokugeleza kwamanzi likhuphuke. Kodwa kubalulekile ukwazi ukuthi izinga lokugeleza noma ukukhishwa koketshezi kuhlale kufana endaweni ngayinye lapho kugeleza amanzi, kungakhathaliseki ukuthi ingxenye yomlomo wempompi yethu ivaliwe noma cha. Ngakho-ke yini eshintsha izinga lokugeleza koketshezi?
Kuthiwani-ke ngokugeleza kwamanzi emfuleni? Ingxenye yomfula ojulile inengxenye enkulu ewelayo kunengxenye engajulile yomfula, ngakho-ke izinga lokugeleza kwamanzi emfuleni ojulile lincane kunejubane lokugeleza kwamanzi engxenyeni engajulile yomfula.
Isibalo sokuqhubeka koketshezi olucindezelwayo
Kuketshezi olucindezelwe, ubuningi boketshezi abufani ngaso sonke isikhathi. Ngamanye amazwi, ubuningi boketshezi buyashintsha uma lucindezelwe. Uma uketshezi lungacindezelwe ubuningi boketshezi buyasuswa ku-equation, ngakho-ke kulokhu, ubuningi boketshezi bufakiwe ku-equation. Sibhekisela ku-equation etholakale ngaphambili, ake sithole i-equation yoketshezi olucindezelwe.
Isisindo soketshezi olungena silingana nesisindo soketshezi oluphumayo, ngakho-ke:
m 1 = m 2
ρ A 1 v 1 t = ρ A 2 v 2 t
Isikhawu sokugeleza koketshezi siyafana ukuze sisuswe. Izilinganiso ziyashintsha zibe:
ρ A 1 v 1 = ρ A 2 v 2 → Isibalo 2
Lesi yisibalo soketshezi olucindezelwe. Umehluko usebuningini boketshezi. Uma uketshezi lucindezelwe, ubuningi buyashintsha. Ngokuphambene nalokho, uma uketshezi lungacindezelwe, ubuningi buhlala bufana ukuze bususwe kulesi sibalo.
Inkinga yesibonelo 1:
Amanzi ageleza ngepayipi elinobubanzi obuyi-10 cm ngesivinini esingu-2 m/s. Kuyini ukuphuma kwamanzi?
Kwaziwa:
Ububanzi bepayipi = 10 cm
Irediyasi yepayipi (r) = 5 cm = 0.05 m
Isivinini samanzi (v) = 2 m/s
Okufunwayo: Idebithi
Isixazululo:
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
Inkinga yesibonelo 2:
Ipayipi elinobubanzi obungama-20 cm lixhunywe kwelinye ipayipi elinobubanzi obungama-10 cm. Uma ijubane lamanzi epayipini elinobubanzi obungama-20 cm lingu-4 m/s, lingakanani ijubane lamanzi epayipini elinobubanzi obungama-10 cm?
Kwaziwa:
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)
Kufunwa: 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
