He tuhinga mō te whārite o te haere tonu
Ngāna kia āta huaki te pūwero wai, me te aro tonu ki te tere o te wai e puta mai ana i te waha o te pūwero. Whakatairitea, kei hea te tere o te rere o te wai, ina kati te waha o te pūwero, kāore rānei? He aha ai? Hei mārama ki tēnei, akohia te whārite haere tonu.
Whakamaerere
I roto i te rerenga pumau, he rite tonu te tere o ia matūriki wai i tētahi pūwāhi, hei tauira, te pūwāhi A. Ina whiti i te pūwāhi B, ka rerekē pea te tere o ngā matūriki wai. Heoi, ina tae ki te pūwāhi B, ka rere ngā matūriki wai e whai mai ana i muri i te tere kotahi ki ngā matūriki wai e whai mai ana i mua. Waihoki ina tae mai ki te pūwāhi C, ā, pērā tonu. Ko te Raina Rere he kōpiko e hono ana i ngā pūwāhi A, B, me C.
Ngongo rere
Ka taea e tātou te whakaahua i ia rerenga wai mā roto i ia pūwāhi o te rere wai. Mēnā ka kitea he rere wai pumau, ka hangaia he ngongo rere e whiti ana i tētahi koki motuhake i runga i te horahanga mata pohewa. Kāore he matūriki wai e tūtaki ana engari he whakarara tonu, ā, ka rite te ngongo rere ki tētahi paipa e mau tonu ana tōna āhua. Ko te wai e tomo ana i tētahi pito o te ngongo ka puta mai i te ngongo i tērā pito.
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Tauwehenga
E whakaatu ana te rerenga i te rōrahi o te wai e rere ana i roto i tētahi wāhanga whakawhiti i tētahi wā kua whakaritea. Mā te pāngarau, ka taea te kī:
Tukunga = Te nui o te wai / wā
Q = V / t
Hei whakanui ake i tō māramatanga, ka whakamahia e mātou tētahi tauira. Hei tauira, ka rere te wai i roto i tētahi paipa. He porotaka te āhua o ngā paipa, ā, he horahanga whakawhiti motuhake tō rātou. He roa anō hoki tō te paipa.
Ina rere te wai i roto i te paipa tae noa ki te L, ko te rōrahi o te wai i roto i te paipa ko V = AL (V = rōrahi o te wai, A = horahanga whakawhiti me L = roa o te paipa). Nā te mea i te mea ka rere tonu i roto i te paipa i te taha o L, me whai wā motuhake te wai, kātahi ka taea te kī ko te nui o te wai ko:
Nā te mea ko v = s / t = L / t —> L = vt, ka hurihia te whārite i runga ake nei ki:
Nō reira, ina rere te wai i roto i tētahi paipa he horahanga whakawhiti me te roa tōna, mō tētahi wā kua whakaritea, ko te nui o te rerenga wai (Q) he ōrite ki te horahanga whakawhiti (A) kua whakareatia ki te tere rere wai (v).
Te whārite o te haere tonu
Arotakehia te rere o te wai i roto i tētahi paipa he rerekē te diameter, e whakaaturia ana i te pikitia i raro nei.
E whakaatu ana tēnei whakaahua i te rere o te wai mai i te maui ki te matau (ka rere te wai mai i tētahi paipa whānui nui ki tētahi whānui iti). He rārangi pītiti te rārangi kua whakarārangihia.
A 1 = te horahanga whakawhiti o te paipa whānui, A 2 = te horahanga whakawhiti o te paipa whānui, v 1 = te tere o te rere o te wai i roto i te paipa whānui, v 2 = te tere o te rere o te wai i roto i te paipa whānui iti, L = te tawhiti i haerea e te wai.
I roto i te rerenga pumau, ko te tere o te rere o ngā matūriki wai i tētahi pūwāhi he rite ki te tere o te rere o ētahi atu matūriki wai e tika ana mā taua pūwāhi. Kāore hoki te rere o te wai e tūtaki (he rite ngā rārangi). Nō reira, me rite te taumaha o te wai e tomo ana ki tētahi pito o te paipa ki te taumaha o te wai e puta ana i tērā pito. Mena he taumaha motuhake tō te wai e haere mai ana ki te ngongo he whānui te diameter, ka puta te wai i runga i tētahi paipa he whānui iti te diameter, he ōrite te taumaha.
Whakaarohia te ahua o te paipa i runga ake nei. Arotakehia te paipa whānui me te paipa iti.
I roto i tētahi wā kua whakaritea, ka rere ētahi wai mā roto i te wāhanga o te paipa he whānui te diameter (A 1 ) tae atu ki te L 1 (L 1 = v 1 t). Ko te rōrahi o te wai e rere ana ko V 1 = A 1 L 1 = A 1 v 1 t. I roto i taua wā anō, ka rere ētahi atu wai mā roto i te wāhanga paipa iti te diameter (A 2 ) tae atu ki te L 2 (L 2 = v 2 t). Ko te rōrahi o te wai e rere ana ko V 2 = A 2 L 2 = A 2 v 2 t.
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Te whārite o te haere tonu mō ngā wai kore e taea te pēhi
I roto i ngā wai kore e taea te pēhi, he rite tonu te mātotoru o te wai i ia wāhi e haere ana. Ko te papatipu wai e rere ana i roto i tētahi paipa he A1 te horahanga whakawhiti (diameter paipa nui) i roto i tētahi wā kua whakaritea ko:
Waihoki, ko te papatipu o te wai e rere ana i roto i tētahi paipa he horahanga whakawhiti-wāhanga A 2 (diameter paipa iti) i roto i tētahi wā kua whakaritea ko:
I roto i te rerenga pumau, he rite tonu te taumaha o te wai e haere mai ana ki te taumaha o te wai e puta mai ana, arā:
m1 = m2
ρ A 1 v 1 t = ρ A 2 v 2 t
A 1 v 1 = A 2 v 2
Nā, ko te whārite o te whārite haere tonu i roto i ngā wai kore e taea te pēhi:
A 1 v 1 = A 2 v 2 — Whārite 1
A 1 = horahanga whakawhiti-wāhanga 1, A 2 = horahanga whakawhiti-wāhanga 2, v 1 = tere o te rere o te wai i te wāhanga 1, v 2 = tere o te rere o te wai i te wāhanga 2, A v = tere rere o te rōrahi (V / t) = tukunga.
E whakaatu ana te whārite 1 he rite tonu te rerenga wai i ia pūwāhi i te taha o te paipa, i te ngongo rere rānei. Ina heke te wāhanga whakawhiti o te paipa, ka piki ake te tere rere o te wai, engari ina nui te wāhanga whakawhiti o te paipa, ka iti ake te tere rere o te wai.
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Ina kati tetahi wāhanga o te waha o te taputapu, ka taumaha ake te rere o te wai i tērā i te wā kāore tetahi wāhanga o te waha o te taputapu e kati ana. Nā te mea ka iti te horahanga whakawhiti o te taputapu ina kati tetahi wāhanga o te waha o te taputapu, ā, ka piki ake te tere o te rere o te wai. Engari he mea nui kia mōhio ko te tere rere, ko te tukunga rānei o ngā wai he rite tonu i ia wāhi i te rere o te wai, ahakoa kua kati tetahi wāhanga o te waha o tā tātou taputapu, kāore rānei. Nō reira, he aha ngā mea e rerekē ana i te tere rere o te wai?
Ā, me pēhea rā te rere o te wai i roto i te awa? He nui ake te porowhita o te awa hōhonu i te wāhanga pāpaku o te awa, nō reira he iti ake te tere o te rere o te wai i roto i te awa hōhonu i te tere o te rere o te wai i roto i te wāhanga pāpaku o te awa.
Te whārite o te haere tonu mō ngā wai pēhi
Mō te wai kua kōpeketia, kāore te mātotoru o te wai e ōrite tonu. Arā, ka rerekē te mātotoru o te wai ina kōpeketia. Ki te kore te wai e kōpeketia, ka tangohia te mātotoru o te wai i te whārite, nō reira i tēnei wā, ka whakaurua te mātotoru o te wai ki te whārite. E pā ana ki te whārite kua puta ake i mua, me whakaputa e tātou te whārite mō te wai kua kōpeketia.
He ōrite te papatipu o te wai e tomo ana ki te papatipu o te wai e puta ana, nō reira:
m1 = m2
ρ A 1 v 1 t = ρ A 2 v 2 t
He rite tonu te tawhiti o te rere o te wai kia taea ai te whakakore. Ka huri ngā whārite ki:
ρ A 1 v 1 = ρ A 2 v 2 → Whārite 2
Koinei te whārite mō te wai kua pēhia. Ko te rerekētanga kei te mātotoru o te wai. Mēnā ka pēhia te wai, ka rerekē te mātotoru. I tetahi atu taha, ki te kore te wai e pēhia, ka rite tonu te mātotoru kia taea ai te tango atu i te whārite.
Tauira raruraru 1:
E rere ana te wai i roto i tētahi paipa he 10 cm te whānui i te tere o te 2 m/s. He aha te rerenga wai?
Mōhiotia:
Te whānui o te paipa = 10 cm
Te whānui o te paipa (r) = 5 cm = 0.05 m
Te tere o te wai (v) = 2 m/s
E hiahiatia ana: Nama
Rongoā:
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
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Tauira raruraru 2:
E honoa ana tētahi paipa he 20 cm te whānui ki tētahi atu paipa he 10 cm te whānui. Mēnā ko te tere o te wai i roto i tētahi paipa he 20 cm te whānui he 4 m/s, he aha te tere o te wai i roto i tētahi paipa he 10 cm te whānui?
Mōhiotia:
Te whānui 1 = 20 henimita (r 1 = 10 henimita = 0.1 m)
v 1 = 4 m/s
Te whānui 2 = 10 henimita (r2 = 5 henimita = 0.05 m)
E hiahiatia ana: v1
Whakautu:
P1 = P2
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 ) ( v² )
(0.04 m 3 /s) = (0.0025 m 2 )(v 2 )
v 2 = 16 m/s
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