Ngā mihi nui ki a koe mō tō toro mai ki Nature.com. He iti noa te tautoko a te putanga pūtirotiro e whakamahia ana e koe mō te CSS. Mō te wheako pai rawa atu, ka tūtohu mātou kia whakamahia e koe he pūtirotiro kua whakahoutia (kia whakawetohia rānei te aratau hototahi i roto i te Internet Explorer). I taua wā, kia mau tonu ai te tautoko, ka whakaatuhia e mātou te pae me te kore he momo kāhua me te JavaScript.
I whakahaerehia ngā whakamātautau i roto i tētahi awaawa tapawhā kua āraia e ngā rārangi whakawhiti o ngā tokotoko porotaka e whā e anga whakarara ana. I inehia te pēhanga i runga i te mata o te tokotoko waenga me te hekenga pēhanga puta noa i te awaawa mā te whakarerekē i te koki anga o te tokotoko. E toru ngā huihuinga tokotoko rerekē te whānui i whakamatautauria. Ka tātarihia ngā hua ine mā te whakamahi i te mātāpono o te tiakitanga o te nekehanga me ngā whakaaro ā-haurua-whakamātautau. He maha ngā huinga pūmau o ngā tawhā kore-ahu ka whakaputaina e hono ana i te pēhanga i ngā wāhi tino nui o te pūnaha ki ngā āhuatanga o te tokotoko. Ka kitea te mātāpono motuhake e mau ana mō te nuinga o ngā tau Euler e tohu ana i te pēhanga i ngā wāhi rerekē, arā, ki te kore-ahu te pēhanga mā te whakamahi i te matapae o te tere tomo noa ki te tokotoko, ka motuhake te huinga i te koki heke. Ka taea te whakamahi i te hononga ā-haurua-whakamātautau ka puta mō te Hoahoa i ngā waipēhi rite.
He maha ngā taputapu whakawhiti wera me te papatipu he huinga kōwae, he awa, he pūtau rānei e haere ai ngā wai i roto i ngā hanganga ā-roto tino uaua pēnei i te tokotoko, te ārai, te whakauru, me ētahi atu. Nō nā tata nei, kua hoki mai te hiahia ki te mārama ake ki ngā tikanga e hono ana i te tohatoha pēhanga ā-roto me ngā kaha ki ngā ā-roto uaua ki te hekenga pēhanga whānui o te kōwae. I roto i ētahi atu mea, kua whakakahangia tēnei hiahia e ngā auahatanga i roto i te pūtaiao rauemi, te whānui ake o ngā āheinga rorohiko mō ngā whakatauira tau, me te piki haere o te whakaitiiti o ngā taputapu. Ko ngā rangahau whakamātautau tata nei mō te tohatoha pēhanga ā-roto me ngā ngaronga ko ngā awa kua whakararohia e ngā rara āhua rerekē 1 , ngā pūtau tauhohenga hiko 2 , te whakawhāititanga capillary 3 me ngā rauemi anga whatunga 4 .
Ko ngā hanganga ā-roto tino noa ko ngā tokotoko porotaka i roto i ngā waeine wae, he mea hono, he mea wehe rānei. I roto i ngā whakawhiti wera, he mea noa tēnei whirihoranga i te taha anga. Ko te hekenga pēhanga o te taha anga e pā ana ki te hoahoa o ngā whakawhiti wera pēnei i ngā whakaputa mamaoa, ngā whakapūmau me ngā kaiwhakamomona. I roto i tētahi rangahau tata nei, i kitea e Wang et al. 5 ngā āhua rere honohono me te wehe-tahi i roto i te whirihoranga takirua o ngā tokotoko. I ine a Liu et al. 6 i te hekenga pēhanga i roto i ngā awa tapawhā me ngā paihere ngongo āhua-U takirua kua hangaia ki roto me ngā koki piko rerekē, ā, i whakatikatika i tētahi tauira tau e whakaata ana i ngā paihere tokotoko me ngā pāpāho porowhita.
E ai ki te whakaaro, he maha ngā āhuatanga whirihoranga e pā ana ki te mahi waipēhi o te peeke rango: te momo whakaritenga (hei tauira, he whakarara, he rārangi rānei), ngā inenga whanaunga (hei tauira, te piko, te whānui, te roa), me te koki piko, me ētahi atu. He maha ngā kaituhi i arotahi ki te kimi paearu kore-ira hei ārahi i ngā hoahoa ki te hopu i ngā pānga whakakotahi o ngā tawhā āhuahanga. I roto i tētahi rangahau whakamātautau tata nei, i whakaarohia e Kim et al. 7 tētahi tauira porosity whai hua mā te whakamahi i te roa o te pūtau wae hei tawhā whakahaere, mā te whakamahi i ngā rarangi tandem me te whakarara me ngā tau Reynolds i waenga i te 103 me te 104. I ako a Snarski8 me pēhea te rerekētanga o te whānuitanga mana, mai i ngā inenga tere me ngā waea wai e piri ana ki tētahi rango i roto i tētahi kauhanga wai, me te piko o te ahunga rere. I ako a Marino et al. 9 i te tohatoha pēhanga pakitara huri noa i tētahi tokotoko rango i roto i te rere o te hau. I tuhia e Mityakov et al. 10 te mara tere i muri i tētahi rango piko mā te whakamahi i te stereo PIV. Alam et al. I whakahaerehia e te 11 tētahi rangahau whānui mō ngā rango takirua, me te arotahi ki ngā pānga o te tau Reynolds me te ōwehenga āhuahanga ki te whakahekenga o te vortex. I taea e rātou te tautuhi i ngā āhua e rima, arā, te raka, te raka wā poto, te kore raka, te raka haurua-haumāori me ngā āhua tāpiringa paparanga kutikuti. Kua tohu ngā rangahau tau tata nei ki te hanganga o ngā hanganga vortex i roto i te rere mā roto i ngā rango yaw kua herea.
I te nuinga o te wā, ko te mahi waipēhi o tētahi pūtau kotahi e tumanakohia ana ka whakawhirinaki ki te whirihoranga me te āhua o te hanganga o roto, e inehia ana e ngā hononga ā-wheako o ngā inenga whakamātautau motuhake. I roto i te maha o ngā taputapu i hangaia mai i ngā wāhanga ā-wā, ka whakahokia ngā tauira rere i roto i ia pūtau, nō reira, ka taea te whakamahi i ngā mōhiohio e pā ana ki ngā pūtau tohu hei whakaatu i te whanonga waipēhi whānui o te hanganga mā roto i ngā tauira maha-tauine. I roto i ēnei take taurite, ka taea te whakaiti i te taumata o te motuhaketanga e whakamahia ai ngā mātāpono tiaki whānui. Ko tētahi tauira noa ko te whārite tukunga mō tētahi pereti orifice 15. I roto i te take motuhake o ngā tokotoko piko, ahakoa i roto i te rere here, i te rere tuwhera rānei, he paearu whakamere e whakahuatia pinepinetia ana i roto i ngā tuhinga me te whakamahi a ngā kaihoahoa ko te nui waipēhi matua (hei tauira, te maturuturunga pēhanga, te kaha, te auau whakaheke vortex, me ētahi atu) ) ki te whakapā atu.) ki te wāhanga rere poutū ki te tuaka rango. Ka kiia tēnei ko te mātāpono motuhake, ā, e whakaaro ana ko te kaha rere te mea matua e peia ana e te wāhanga noa o te rerenga mai, ā, ko te pānga o te wāhanga tuaka e hangai ana ki te tuaka rango he iti noa iho. Ahakoa kāore he whakaae i roto i ngā tuhinga mō te whānuitanga whai mana o tēnei paearu, i roto i te maha o ngā take e whakarato ana i ngā whakatau tata whai hua i roto i ngā āwangawanga whakamātautau e kitea ana i ngā hononga ā-wheako. Ko ngā rangahau tata nei mō te mana o te mātāpono motuhake ko te wiri i puta mai i te vortex16 me te tōia toharite kotahi-wāhanga me te rua-wāhanga417.
I roto i tēnei mahi, ka whakaaturia ngā hua o te rangahau i te pēhanga ā-roto me te hekenga pēhanga i roto i tētahi awaawa me te rārangi whakawhiti o ngā tokotoko porotaka e whā e anga whakarara ana. Inehia kia toru ngā huihuinga tokotoko me ngā diameter rerekē, me te whakarerekē i te koki o te anga whakarara. Ko te whāinga whānui ko te tirotiro i te tikanga e pā ana te tohatoha pēhanga i runga i te mata o te tokotoko ki te hekenga pēhanga whānui i roto i te awaawa. Ka tātarihia ngā raraunga whakamātautau mā te whakamahi i te whārite a Bernoulli me te mātāpono o te tiaki i te nekehanga hei aromatawai i te mana o te mātāpono motuhake. Hei whakamutunga, ka hangaia he hononga haurua-empirical kore-ahu ka taea te whakamahi hei hoahoa i ngā taputapu waipēhi rite.
Ko te whakatakotoranga whakamātautau he wāhanga whakamātautau tapawhā rite i whiwhi i te rere o te hau e whakaratohia ana e te pā hau tuaka. Kei roto i te wāhanga whakamātautau he waeine kei roto ko ngā tokotoko pokapū whakarara e rua me ngā tokotoko haurua e rua kua whakauruhia ki roto i ngā pakitara o te awaawa, e whakaaturia ana i te Pikitia 1e, he rite te diameter katoa. E whakaatu ana ngā Pikitia 1a–e i te āhuahanga taipitopito me ngā ine o ia wāhanga o te whakatakotoranga whakamātautau. E whakaatu ana te Pikitia 3 i te whakatakotoranga tukanga.
a Wāhanga tomo (roa i roto i te mm). Waihangatia b mā te whakamahi i te Openscad 2021.01, openscad.org. Wāhanga whakamātautau matua (roa i roto i te mm). I hangaia ki te Openscad 2021.01, openscad.org c Tirohanga whakawhiti-wāhanga o te wāhanga whakamātautau matua (roa i roto i te mm). I hangaia mā te whakamahi i te Openscad 2021.01, openscad.org d wāhanga kaweake (roa i roto i te mm). I hangaia ki te Openscad 2021.01, tirohanga pahū o te wāhanga whakamātautau o openscad.org e. I hangaia ki te Openscad 2021.01, openscad.org.
E toru ngā huinga tokotoko o ngā diameter rerekē i whakamatautauria. Kei te Ripanga 1 ngā āhuatanga āhuahanga o ia kēhi. Ka whakanohoia ngā tokotoko ki runga i tētahi ine-rahi kia rerekē ai te koki e pā ana ki te ahunga rere i waenga i te 90° me te 30° (Pikitia 1b me te 3). He mea hanga ngā tokotoko katoa ki te kowiri tira, ā, kua whakanohoia ki waenganui kia mau tonu te tawhiti āputa i waenganui i a rātou. Ka whakaritea te tūranga whanaunga o ngā tokotoko e ngā mea whakawātea e rua kei waho o te wāhanga whakamātautau.
I inehia te tere rere o te wāhanga whakamātautau mā te whakamahi i tētahi venturi kua whakatikatikaina, e whakaaturia ana i te Pikitia 2, ā, i aroturukitia mā te whakamahi i tētahi DP Cell Honeywell SCX. I inehia te pāmahana wai i te putanga o te wāhanga whakamātautau mā te whakamahi i tētahi inemahana PT100, ā, i whakahaeretia i te 45±1°C. Hei whakarite i te tohatoha tere papatahi me te whakaiti i te taumata o te aueue i te tomokanga o te awaawa, ka akiakihia te rere o te wai e tomo mai ana mā roto i ngā ārai whakarewa e toru. I whakamahia he tawhiti taunga tata ki te 4 ngā diameter waipēhi i waenganui i te ārai whakamutunga me te tokotoko, ā, ko te roa o te putanga he 11 ngā diameter waipēhi.
He hoahoa kauwhata o te ngongo Venturi i whakamahia hei ine i te tere rere o te urunga (te roa i roto i ngā mirimita). I hangaia ki Openscad 2021.01, openscad.org.
Aroturukihia te pēhanga i runga i tētahi o ngā mata o te tokotoko waenga mā te whakamahi i tētahi pato pēhanga 0.5 mm i te papa waenga o te wāhanga whakamātautau. Ko te whānui o te pato he rite ki te whānuitanga koki 5°; nō reira ko te tika koki he tata ki te 2°. Ka taea te huri i te tokotoko e aro turukihia ana i tōna tuaka, e whakaaturia ana i te Pikitia 3. Ko te rerekētanga i waenga i te pēhanga mata o te tokotoko me te pēhanga i te tomokanga ki te wāhanga whakamātautau ka inehia ki tētahi raupapa rerekētanga DP Cell Honeywell SCX. Ka inehia tēnei rerekētanga pēhanga mō ia whakaritenga pae, te tere rere rerekē, te koki piko \(\alpha \) me te koki azimuth \(\theta \).
Ngā tautuhinga rere. Kei te whakaatuhia ngā pakitara o te awa i te hina. Ka rere te rere mai i te maui ki te matau, ā, ka āraia e te tokotoko. Kia mahara ko te tirohanga "A" kei te poutū ki te tuaka tokotoko. Kei roto i ngā pakitara awa taha ngā tokotoko o waho. Ka whakamahia he ine i te koki o te piko \(\alpha \). I hangaia ki Openscad 2021.01, openscad.org.
Ko te whāinga o te whakamātautau he ine me te whakamārama i te hekenga pēhanga i waenga i ngā putanga o te awa me te pēhanga i runga i te mata o te tokotoko pokapū, \(\theta\) me \(\alpha\) mō ngā azimuth me ngā hekenga rerekē. Hei whakarāpopoto i ngā hua, ka whakaatuhia te pēhanga rerekētanga i roto i te āhua kore-ahu hei tau a Euler:
ko \(\rho \) te mātotoru wai, ko \({u}_{i}\) te tere tomo toharite, ko \({p}_{i}\) te pēhanga tomo, ā, ko \({p }_{ w}\) te pēhanga i tētahi pūwāhi i runga i te pakitara tokotoko. Ka whakaritea te tere tomo i roto i ngā awhe rerekē e toru e whakatauhia ana e te whakatuwheratanga o te takirere tomo. Ko ngā tere ka puta mai i waenga i te 6 ki te 10 m/s, e rite ana ki te tau Reynolds o te hongere, \(Re\equiv {u}_{i}H/\nu \) (ko \(H\) te teitei o te hongere, ā, ko \(\nu \) te matotoru kinematic) i waenga i te 40,000 me te 67,000. Ko te tau Reynolds tokotoko (\(Re\equiv {u}_{i}d/\nu \)) kei waenga i te 2500 ki te 6500. Ko te kaha o te turbulence i whakatauhia e te paerewa rerekētanga whanaunga o ngā tohu i tuhia ki te venturi he 5% i runga i toharite.
E whakaatu ana te Pikitia 4 i te hononga o \({Eu}_{w}\) ki te koki azimuth \(\theta \), i whakaritea e ngā koki tuku e toru, \(\alpha \) = 30°, 50° me te 70°. Ka wehea ngā inenga ki ngā kauwhata e toru e ai ki te diameter o te tokotoko. Ka kitea i roto i te koretake o te whakamātautau, ko ngā tau Euler i whiwhi he motuhake i te tere rere. Ko te whakawhirinakitanga whānui ki a θ e whai ana i te ia o te pēhanga pakitara huri noa i te taha o te arai porowhita. I ngā koki e anga ana ki te rere, arā, θ mai i te 0 ki te 90°, ka heke te pēhanga pakitara tokotoko, ka tae ki te iti rawa i te 90°, e rite ana ki te āputa i waenga i ngā tokotoko kei reira te tere nui rawa atu nā ngā herenga o te rohe rere. Muri iho, ka whakahokia te pēhanga o θ mai i te 90° ki te 100°, ā, muri iho ka noho rite tonu te pēhanga nā te wehenga o te paparanga rohe o muri o te pakitara tokotoko. Kia mahara kāore he huringa i te koki o te pēhanga iti rawa, e kī ana ko ngā raruraru pea mai i te taha tata Ko ngā paparanga kutikuti, pērā i ngā pānga Coanda, he tuarua.
Te rerekētanga o te tau Euler o te pakitara huri noa i te tokotoko mō ngā koki piko me ngā diameter tokotoko rerekē. I hangaia ki a Gnuplot 5.4, www.gnuplot.info.
I roto i ngā mea e whai ake nei, ka tātarihia e mātou ngā hua i runga i te whakaaro ka taea anake te whakatau tata i ngā tau Euler mā roto i ngā tawhā āhuahanga, arā, ko ngā ōwehenga roa āhuatanga \(d/g\) me \(d/H\) (ko \(H\) te teitei o te awa) me te piko \(\alpha \). E kī ana tētahi ture mahi rongonui ko te kaha hanganga wai i runga i te tokotoko yaw ka whakatauhia e te whakaaturanga o te tere urunga poutū ki te tuaka tokotoko, \({u}_{n}={u}_{i}\mathrm {sin} \alpha \). I ētahi wā ka kiia tēnei ko te mātāpono o te motuhaketanga. Ko tētahi o ngā whāinga o te tātari e whai ake nei ko te tirotiro mēnā e pā ana tēnei mātāpono ki tā mātou take, ina herea te rere me ngā aukati ki roto i ngā awa kua kati.
Me whakaaro tātou ki te pēhanga i inehia i te taha mua o te mata o te tokotoko waenga, arā, θ = 0. E ai ki te whārite a Bernoulli, ko te pēhanga i tēnei tūranga\({p}_{o}\) e tutuki ana i:
ko \({u}_{o}\) te tere wai e tata ana ki te pakitara tokotoko i te θ = 0, ā, e whakaaro ana mātou he iti noa ngā mate kore e taea te huri. Kia mahara ko te pēhanga hihiri he motuhake i roto i te wā pūngao nekeneke. Mena he kau te \({u}_{o}\) (arā, he āhua tū), me whakakotahi ngā tau Euler. Heoi, ka kitea i roto i te Pikitia 4 i te \(\theta =0\) ko te hua \({Eu}_{w}\) he tata ki tēnei uara engari kāore i te tino ōrite, inā koa mō ngā koki tō nui ake. E kī ana tēnei kāore te tere i runga i te mata tokotoko e ngaro i te \(\theta =0\), ka taea te pehi e te piko ki runga o ngā rārangi iahiko i hangaia e te piko tokotoko. Mai i te mea kua herea te rere ki runga me raro o te wāhanga whakamātautau, me hanga e tēnei piko he hurihanga tuarua, ka whakanui ake i te tere tuaka i raro, ka whakaiti i te tere i runga. Ki te whakaaro ko te rahi o te piko i runga ake nei ko te whakaaturanga o te tere whakauru ki runga i te rakau (arā, \({u}_{i}\mathrm{cos}\alpha \)), ko te hua tau Euler e rite ana ko:
E whakataurite ana te Pikitia 5 i ngā whārite.(3) E whakaatu ana i te whakaae pai ki ngā raraunga whakamātautau e rite ana. Ko te rerekētanga toharite he 25%, ā, ko te taumata whakapono he 95%. Kia mōhio ko te whārite.(3) E rite ana ki te kaupapa o te motuhaketanga.Waihoki, e whakaatu ana te Pikitia 6 ko te tau Euler e rite ana ki te pēhanga i runga i te mata o muri o te tokotoko, \({p}_{180}\), ā, i te putanga o te wāhanga whakamātautau, \({p}_{e}\), e whai ana hoki i tētahi ia e ōrite ana ki te \({\mathrm{sin}}^{2}\alpha \) .Heoi, i ngā take e rua, ka whakawhirinaki te tauwehenga ki te diameter o te tokotoko, he mea whaitake nā te mea ko te mea whakamutunga e whakatau ana i te rohe ārai.He rite tēnei āhuatanga ki te maturuturunga pēhanga o tētahi pereti kōhao, kei reira te awa rere e whakaitihia ana i ētahi wāhi motuhake.I roto i tēnei wāhanga whakamātautau, ko te mahi a te kōhao e takarohia ana e te āputa i waenganui i ngā tokotoko.I roto i tēnei take, ka tino heke te pēhanga i te wā e whakaroa ana, ā, ka hoki anō i ētahi wā i a ia e whānui ana ki muri.Ma te whakaaro ki te here hei aukati poutū ki te tuaka o te tokotoko, ka taea te tuhi i te maturuturunga pēhanga i waenganui i te mua me te muri o te tokotoko hei 18:
ko \({c}_{d}\) he tauwehenga tō e whakamārama ana i te whakaoranga pēhanga wāhanga i waenga i a θ = 90° me θ = 180°, ā, ko \({A}_{m}\) me \ ({A}_{f}\) te wāhanga whakawhiti kore utu iti rawa mō ia wae roa e poutū ana ki te tuaka tokotoko, ā, ko tōna whanaungatanga ki te diameter tokotoko ko \({A}_{f}/{A}_{m}=\ ​​Mauī (g+d\right)/g\). Ko ngā tau Euler e rite ana ko:
Te tau Euler o te pakitara i \(\theta =0\) hei pānga o te hekenga. E rite ana tēnei kōpiko ki te whārite.(3). I hangaia ki a Gnuplot 5.4, www.gnuplot.info.
Ka huri te tau Euler o te pakitara, i roto i te \(\theta =18{0}^{o}\) (tohu katoa) me te putanga (tohu kau) me te hekenga. Ka rite ēnei kōpiko ki te mātāpono o te motuhaketanga, arā, \(Eu\propto {\mathrm{sin}}^{2}\alpha \). I hangaia ki te Gnuplot 5.4, www.gnuplot.info.
E whakaatu ana te Pikitia 7 i te whakawhirinakitanga o \({Eu}_{0-180}/{\mathrm{sin}}^{2}\alpha \) ki \(d/g\), e whakaatu ana i te tino ōritetanga Pai.(5). Ko te tauwehenga tōia i whiwhi ko \({c}_{d}=1.28\pm 0.02\) me te taumata whakapono o te 67%. Waihoki, e whakaatu ana hoki te kauwhata kotahi ko te hekenga pēhanga katoa i waenga i te tomokanga me te putanga o te wāhanga whakamātautau e whai ana i tētahi ia rite, engari me ngā tauwehenga rerekē e whai whakaaro ana ki te whakaora pēhanga i te wāhi o muri i waenga i te pae me te putanga o te awaawa. Ko te tauwehenga tōia e rite ana ko \({c}_{d}=1.00\pm 0.05\) me te taumata whakapono o te 67%.
E pā ana te tauwehenga tō ki te \(d/g\) hekenga pēhanga i mua me muri o te tokotoko\(\left({Eu}_{0-180}\right)\) me te hekenga pēhanga katoa i waenga i te tomokanga me te putanga o te hongere. Ko te rohe hina ko te roopu whakawhirinaki 67% mō te hononga. I hangaia ki a Gnuplot 5.4, www.gnuplot.info.
Ko te pēhanga iti rawa \({p}_{90}\) i runga i te mata o te tokotoko i te θ = 90° me whakahaere motuhake. E ai ki te whārite a Bernoulli, i te rārangi iahiko mā roto i te āputa i waenganui i ngā pae, ko te pēhanga i waenganui\({p}_{g}\) me te tere\({u}_{g}\) i roto i te āputa i waenganui i ngā pae (e ōrite ana ki te pūwāhi o te awaawa) e pā ana ki ēnei āhuatanga e whai ake nei:
Ka taea te hono i te pēhanga \({p}_{g}\) ki te pēhanga o te mata o te tokotoko i te θ = 90° mā te whakauru i te tohatoha pēhanga ki runga i te āputa e wehe ana i te tokotoko pokapū i waenganui i te pūwāhi me te pakitara (tirohia te Pikitia 8). Ka homai e te taurite o te mana te 19:
ko \(y\) te taunga noa ki te mata o te tokotoko mai i te pūwāhi pokapū o te āputa i waenganui i ngā tokotoko pokapū, ā, ko \(K\) te piko o te rārangi au i te tūranga \(y\). Mō te aromatawai tātari o te pēhanga i runga i te mata o te tokotoko, e whakaaro ana mātou he ōrite a \({u}_{g}\) ā, he rārangi a \(K\left(y\right)\). Kua manatokohia ēnei whakaaro mā ngā tātaitanga tau. I te pakitara tokotoko, ka whakatauhia te piko e te wāhanga porowhita o te tokotoko i te koki \(\alpha \), arā, \(K\left(g/2\right)=\left(2/d\right){\ mathrm{sin} }^{2}\alpha \) (tirohia te Pikitia 8). Kātahi, mō te piko o te rerenga e ngaro ana i \(y=0\) nā te ōritetanga, ka hoatu te piko i te taunga whānui \(y\) e:
Tirohanga whakawhiti-wāhanga āhuatanga, mua (maui) me runga (raro). I hangaia ki a Microsoft Word 2019,
I tētahi atu taha, mā te tiaki i te papatipu, ko te tere toharite i roto i te papa e poutū ana ki te rere i te wāhi ine \(\langle {u}_{g}\rangle \) e pā ana ki te tere tomo:
ko \({A}_{i}\) te horahanga rere whakawhiti-wāhanga i te tomokanga o te awaawa, ā, ko \({A}_{g}\) te horahanga rere whakawhiti-wāhanga i te wāhi ine (tirohia te Pikitia 8) mā:
Kia mōhio koe, kāore a \({u}_{g}\) i te ōrite ki a \(\langle {u}_{g}\rangle \). Inaa, e whakaatu ana te Pikitia 9 i te ōwehenga tere \({u}_{g}/\langle {u}_{g}\rangle \), i tatauhia e te whārite.(10)–(14), i tuhia kia rite ki te ōwehenga \(d/g\). Ahakoa te āhua motuhake, ka taea te tautuhi i tētahi ia, e whakatatahia ana e te pūrau tuarua:
Ko te ōwehenga o te tere mōrahi\({u}_{g}\) me te tere toharite\(\langle {u}_{g}\rangle \) o te whakawhiti-pokapū o te awa\(.\). Ko ngā ānau totoka me ngā ānau pītiti e rite ana ki ngā whārite.(5) me te whānuitanga rerekētanga o ngā tauwehenga e rite ana\(\pm 25\%\). I hangaia ki a Gnuplot 5.4, www.gnuplot.info.
E whakataurite ana te Pikitia 10 i a \({Eu}_{90}\) ki ngā hua whakamātautau o te whārite.(16). Ko te toharite o te rerekētanga whanaunga he 25%, ā, ko te taumata whakapono he 95%.
Ko te tau Euler o te Pakitara i \(\theta ={90}^{o}\). E rite ana tēnei kōpiko ki te whārite.(16). I hangaia ki a Gnuplot 5.4, www.gnuplot.info.
Ka taea te tatau i te kaha kupenga \({f}_{n}\) e pā ana ki te tokotoko pokapū e poutū ana ki tōna tuaka mā te whakauru i te pēhanga ki te mata o te tokotoko penei:
ko te tauwehenga tuatahi ko te roa o te tokotoko i roto i te hongere, ā, ka mahia te whakaurunga i waenga i te 0 me te 2π.
Ko te whakaputanga o \({f}_{n}\) ki te ahunga o te rere o te wai me ōrite ki te pēhanga i waenga i te tomokanga me te putanga o te awaawa, ki te kore te waku e rite ana ki te tokotoko, ā, he iti ake nā te korenga o te whanaketanga o te wāhanga o muri mai. Kāore i te taurite te rere o te nekehanga. Nō reira,
E whakaatu ana te Pikitia 11 i tētahi kauwhata o ngā whārite. (20) i whakaatu i te ōritetanga pai mō ngā āhuatanga whakamātautau katoa. Heoi, he iti noa te rerekētanga o te 8% ki te taha matau, ka taea te kī me te whakamahi hei whakatau tata mō te kore taurite o te nekehanga i waenga i te tomokanga me te putanga o te hongere.
Taurite mana hongere. E rite ana te rārangi ki te whārite.(20). Ko te tauwehenga taunga Pearson he 0.97. I hangaia ki a Gnuplot 5.4, www.gnuplot.info.
Mā te whakarerekē i te koki piko o te tokotoko, i inehia te pēhanga i te pakitara mata o te tokotoko me te hekenga pēhanga i roto i te awaawa me ngā rārangi whakawhiti o ngā tokotoko porotaka e whā e piko ana. E toru ngā huihuinga tokotoko rerekē te diameter i whakamatauria. I roto i te awhe tau Reynolds i whakamatautauria, i waenga i te 2500 me te 6500, kāore te tau Euler e pā ki te tere rere. Ka whai te pēhanga i runga i te mata o te tokotoko waenga i te ia o te mea e kitea ana i roto i ngā rango, ko te mōrahi kei mua, ko te iti rawa kei te āputa taha i waenga i ngā tokotoko, ka hoki mai i te taha o muri nā te wehenga o te paparanga rohe.
Ka tātarihia ngā raraunga whakamātautau mā te whakamahi i ngā whakaaro tiaki nekehanga me ngā aromatawai ā-whāiti-mātauranga hei kimi i ngā tau kore-ira pumau e hono ana i ngā tau Euler ki ngā inenga āhuatanga o ngā awa me ngā tokotoko. Ko ngā āhuatanga āhuahanga katoa o te aukati e whakaatuhia katoatia ana e te ōwehenga i waenga i te diameter o te tokotoko me te āputa i waenga i ngā tokotoko (ki te taha) me te teitei o te awa (poutū).
E kitea ana te mātāpono motuhake e mau ana mō te nuinga o ngā tau Euler e tohu ana i te pēhanga i ngā wāhi rerekē, arā, mēnā he kore-ahu te pēhanga mā te whakamahi i te matapae o te tere tomo noa ki te tokotoko, ka motuhake te huinga i te koki heke. Hei tāpiri, e pā ana te āhuatanga ki te papatipu me te nekehanga o te rere. He rite tonu ngā whārite tiaki, ā, e tautoko ana i te mātāpono wheako i runga ake nei. Ko te pēhanga mata tokotoko anake i te āputa i waenga i ngā tokotoko ka paku rerekē mai i tēnei mātāpono. Ka hangaia ngā hononga haurua-whakaata kore-ahu ka taea te whakamahi hei hoahoa i ngā taputapu waipēhi rite. He rite tonu tēnei huarahi matarohia ki ngā tono rite kua pūrongohia tata nei o te whārite Bernoulli ki ngā waipēhi me ngā hemodynamics20,21,22,23,24.
He hua tino whakamere tēnei i ahu mai i te tātaritanga o te hekenga pēhanga i waenga i te tomokanga me te putanga o te wāhanga whakamātautau. I roto i te koretake o te whakamātautau, ko te tauwehenga tōia e puta mai ana he ōrite ki te kotahi, e tohu ana i te noho o ngā tawhā pumau e whai ake nei:
Kia mōhio ki te rahi \(\left(d/g+2\right)d/g\) i roto i te tauwehenga o te whārite.(23) ko te rahi i roto i ngā parekete i roto i te whārite.(4), ki te kore, ka taea te tatau me te iti rawa me te whakawhiti-wātea poutū ki te tokotoko, \({A}_{m}\) me \({A}_{f}\). E kī ana tēnei kei te whakaarohia ngā tau Reynolds kei roto tonu i te awhe o te rangahau o nāianei (40,000-67,000 mō ngā awa me 2500-6500 mō ngā tokotoko). He mea nui kia mōhio mēnā he rerekētanga pāmahana i roto i te awa, ka pā pea ki te kiato wai. I tēnei take, ka taea te whakatau tata i te huringa whanaunga o te tau Euler mā te whakarea i te tauwehenga whānui wera mā te rerekētanga pāmahana mōrahi e tumanakohia ana.
Ruck, S., Köhler, S., Schlindwein, G., me Arbeiter, F. Ngā inenga whakawhiti wera me te hekenga pēhanga i roto i tētahi awa kua whakararohia e ngā rara āhua rerekē i runga i te pakitara.expert.Heat Transfer 31, 334–354 (2017).
Wu, L., Arenas, L., Graves, J., me Walsh, F. Te āhua o te pūtau rere: te whakaaturanga rere, te hekenga pēhanga, me te kawe papatipu i roto i ngā irahiko rua-ahu i roto i ngā hongere tapawhā. J. Electrochemistry.Socialist Party.167, 043505 (2020).
Liu, S., Dou, X., Zeng, Q. & Liu, J. Ngā tawhā matua o te pānga Jamin i roto i ngā uaua toto me ngā wāhanga whakawhiti kua whakawhāitihia. J. Gasoline.science.Britain.196, 107635 (2021).