Ngā awe wai – ngā raruraru me ngā otinga

Ngā awe wai – ngā raruraru me ngā otinga

Te ariā a Torricelli

1. He ipu kī tonu i te wai, ā, he kōhao kei reira , e whakaaturia ana i te pikitia i raro nei. Mena ko te whakaterenga nā te kaha ā-papa he 10 ms ^-2 , he aha te tere o te wai i roto i taua kōhao?

Mōhiotia:

Teitei (h) = 85 henimita – 40 henimita = 45 henimita = 0.45 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te tere o te wai (v)

Rongoā:

E ai ki te ariā a Torricelli, ka puta te wai i te poka me te tere ōrite ki te tere o te takanga noa o te mea mai i te teitei ōrite. Teitei (h) = 85 cm – 40 cm = 45 cm = 0.45 mita

Ka tatauhia te tere o te wai mā te whakamahi i te whārite o te nekehanga taka noa :

v _t ² = 2 gh

v _t ² = 2 gh = 2(10)(0.45) = 9

v _t = √9 = 3 m/s

2. He ipu kī tonu i te wai, ā, he kōhao kei reira, e whakaaturia ana i te pikitia i raro nei. Mēnā ko te whakaterenga nā te kaha ā-papa he 10 ms ^-2 , he aha te tere o te wai i roto i taua kōhao?

Mōhiotia:

Teitei (h) = 1.5 m – 0.25 m = 1.25 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te tere o te wai (v)

Rongoā:

v _t ² = 2 gh = 2(10)(1.25) = 25

v _t = √25 = 5 m/s

3. He ipu kī tonu i te wai, ā, he kōhao kei reira, e whakaaturia ana i te pikitia i raro nei. Mēnā ko te whakaterenga nā te kaha ā-papa he 10 ms ^-2 , he aha te tere o te wai i roto i taua kōhao?

Mōhiotia:

Teitei (h) = 1 m – 0.20 m = 0.8 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te tere o te wai (v)

Rongoā:

v _t ² = 2 gh = 2(10)(0.8) = 16

v _t = √16 = 4 m/s

4. He ipu kī tonu i te wai, ā, he kōhao kei reira, e whakaaturia ana i te pikitia i raro nei. Mēnā ko te whakaterenga nā te kaha ā-papa he 10 ms ^-2 , he aha te tere o te wai i roto i taua kōhao?

Mōhiotia:

Teitei (h) = 20 cm = 0.2 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te tere o te wai (v)

Rongoā:

5. He ipu kī tonu i te wai, ā, e rua ngā kōhao , e whakaaturia ana i te pikitia i raro nei. He aha te ōwehenga o te x ₁ ki te x ₂?

Otinga

Te wā o te hinganga wai kore utu mai i te poka 1:

h = 1/2 i te ²

0.8 = 1/2 (10) t ²

0.8 = 5 t ²

t ² = 0.8 / 5 = 0.16

t = 0.4 hēkona

Te wā o te hinganga wai kore utu mai i te poka 2:

h = 1/2 i te ²

0.5 = 1/2 (10) t ²

0.5 = 5 t ²

t ² = 0.5 / 5 = 0.1

t = √0.1 hēkona

Te tawhiti whakapae (x):

x ₁ = v ₁ t ₁ = (2)(0.4) = 0.8 mita

x ₂ = v ₂ t ₂ = (√10)(√0.1) = (10)(0.1) = 1 mita

Ko te ōwehenga o x ₁ ki x ₂ :

x1 _: x2 = _0.8 : 1 = 8: 10 = 4: ₅

Te whārite o te haere tonu

6. Ka rere te wai i roto i tētahi paipa he rerekē te diameter, mai i A ki B, kātahi ka rere ki C. Ko te ōwehenga o A ki C he 8:3. Mena ko te tere o te wai i roto i te paipa A he v, he aha te tere o te wai i roto i te paipa C?

Mōhiotia:

Horahanga o A (A_A) = 8

Te horahanga o C (A _C ) = 3

Te tere o te wai i roto i te paipa A (v _A ) = v

E hiahiatia ana: Te tere o te wai i roto i te paipa C (v _C )

Rongoā:

Te whārite o te haere tonu:

A _A v _A = A _C v _C

8 v = 3 v _C

v _C = 8/3 v

7. Mena ko te tere o te wai i roto i tētahi paipa he 12 henimita te whānui he 10 henimita/hekona, he aha te tere o te wai i roto i tētahi paipa he 8 henimita te whānui?

Mōhiotia:

Te whānui 1 (d ₁ ) = 12 henimita, te pūtoro 1 (r ₁ ) = 6 henimita

Te whānui 2 (d ₂ ) = 8 henimita, te pūtoro 2 (r ₂ ) = 4 henimita

Te tere o te wai 1 (v ₁ ) = 10 cm/s

E hiahiatia ana: Te tere o te wai 2 (v ₂ )

Rongoā:

Rohe 1 (A ₁ ) = π r ² = π 6 ² = 36π cm ²

Rohe 2 (A ₂ ) = π r ² = π 4 ² = 16π cm ²

Te whārite o te haere tonu:

A ₁ v ₁ = A ₂ v ₂

(36π)(10) = (16π) v ₂

(36)(10) = (16) v ₂

360 = (16) v ₂

v2 = _360/16

v ₂ = 22.5 henimita/hekona

8. Ka rere te wai i roto i tētahi paipa he rerekē te whānui, e whakaaturia ana i te pikitia i raro nei. Mēnā ko te horahanga 1 (A ₁ ) = 8 cm² ^, ko A ₂ = 2 cm² ^, ā, ko te tere o te wai i roto i te paipa 2 = v ₂ = 2 m/s, he aha te tere o te wai i roto i te paipa 1 = v ₁?

Mōhiotia:

Rohe 1 (A₁) = 8 henemita²

Horahanga 2 (A ₂ ) = 2 cm ²

Te tere o te wai i roto i te paipa 2 (v ₂ ) = 2 m/s

E hiahiatia ana: te tere o te wai i roto i te paipa 1 (v ₁ )

Rongoā:

Te whārite o te haere tonu:

A ₁ v ₁ = A ₂ v ₂

8 ki te ₁ = (2)(2)

8 ki te ₁ = 4

v ₁ = 4 / 8 = 0.5 m/s

9. Mena e rua ngā wā te whānui o te paipa nui ake i te whānui o te paipa iti ake, he aha te tere o te wai i te paipa iti ake?

Mōhiotia:

Te whānui o te paipa nui ake (d₁) = 2

Te whānui o te paipa nui ake (r ₁ ) = ½ d ₁ = ½ (2) = 1

Te horahanga o te paipa nui ( A ₁ ) = π r ₁ ² = π (1) ² = π (1) = π

Te whānui o te paipa iti ake (d ₂ ) = 1

Te whānui o te paipa iti (r ₂ ) = ½ d ₂ = ½ (1) = ½

Te horahanga o te paipa iti ( A ₂ ) = π r ₂ ² = π (1/2) ² = π (1/4) = ¼ π

Ko te tere o te wai i te paipa nui ake ( v ₁ ) = 4 m/s

E hiahiatia ana: Te tere o te wai i te paipa iti ake ( v ₂ )

Rongoā:

Te whārite o te haere tonu:

A ₁ v ₁ = A ₂ v ₂

π 4 = ¼ π (v ₂ )

4 = ¼ (v ₂ )

v ₂ = 8 m/s

Te mātāpono me ngā whārite a Bernoulli

10. Ka papua te wai mā te whakamahi i tētahi pūwero 120 kP e tomo ana ki te paipa o raro (1) ā, ka rere ki runga i te tere o te 1 m/ s. Ko te tere o te kaha ā-papa he 10 m/ s , ā, ko te mātotoru o te wai he 1000 kg/m ^-3 . He aha te pēhanga wai i runga i te paipa o runga (II ).

Mōhiotia:

Te whānui o te paipa o raro (r₁) = 12 henemita

Te whānui o te paipa o raro (r ₂ ) = 6 cm

Te pēhanga wai i roto i te paipa o raro (p ₁ ) = 120 kPa = 120,000 Pascal

Ko te tere o te wai i roto i te paipa o raro (v ₁ ) = 1 ms ^-1

Ko te teitei o te paipa o raro (h ₁ ) = 0 m

Ko te teitei o te paipa o runga (h ₂ ) = 2 m

Te whakaterenga nā te kaha ā-papa (g) = 10 ms ^-2

Te mātotoru o te wai = 1000 kg.m ^-3

E hiahiatia ana: Te pēhanga wai i roto i te paipa 2 (p ₂ )

Rongoā:

Ka tatauhia te tere o te wai i roto i te paipa 2 mā te whakamahi i te whārite o te haere tonu:

Ka tatauhia te pēhanga wai i roto i te paipa 2 mā te whakamahi i te whārite Bernoulli:

11. He paipa nui e 5 mita te teitei i runga ake i te whenua, me te paipa iti e 1 mita te teitei i runga ake i te whenua. Ko te tere o te wai i roto i te paipa nui he 36 km/h me te pēhanga o te 9.1 x 105 ^Pa , ko te pēhanga i roto i te paipa iti he 2.105 ^Pa . He aha te tere o te wai i roto i te paipa iti? Te mātotoru o te wai = 103 ^kg / ^m3

Mōhiotia:

Te pēhanga wai i roto i te paipa nui (p₁) = 9.1 x 10⁵ Pākara = 910,000 Pākara

Te pēhanga wai i roto i te paipa iti (p ₂ ) = 2 x 10 ⁵ Ngā Pascal = 200,000 Ngā Pascal

Te tere o te wai i roto i te paipa nui (v ₁ ) = 36 km/h = 36(1000)/(3600) = 36000/3600 =10 m/h

Ko te teitei o te paipa nui (h ₁ ) = -4 mita

Ko te teitei o te paipa iti (h ₂ ) = 0 mita

Te whakaterenga nā te kaha ā-papa (g) = 10 ms ^-2

Te mātotoru o te wai = 1000 kg/ ^m3

E hiahiatia ana: Te tere o te wai i roto i te paipa iti (v ₂ )

Rongoā:

Ka tatauhia te tere o te wai i roto i te paipa iti (v _{2 ) mā te whakamahi i te whārite a Bernoulli:}

12. He paipa he 15 cm te whānui e hono ana ki tētahi atu paipa he 5 cm te whānui . Kei te tūnga whakapae ngā mea e rua. Ko te tere o te rere o te wai i roto i te paipa nui he 1 m/s i te pēhanga o te 105 ^{N /} m2 . He aha te pēhanga wai i runga i te paipa iti (1 karamu cm ^-3 )

Mōhiotia:

Te whānui o te paipa nui (r ₁ ) = 15 cm = 0.15 m

Te whānui o te paipa iti (r2 ₎ = 5 cm = 0.05 m

Ko te pēhanga wai i roto i te paipa nui (p ₁ ) = 10 ⁵ N m ^-2 = 100.000 N m ^-2

Ko te tere o te wai i roto i te paipa nui (v ₁ ) = 1 ms ^-1

Te whakaterenga nā te kaha ā-papa (g) = 10 ms ^-2

Te mātotoru o te wai = 1 karamu henimita ^-3 = 1000 kg m ^-3

Te rerekētanga teitei (Δh) = 0.

E hiahiatia ana: Te pēhanga i roto i te paipa iti (p ₂ )

Rongoā:

Ka tatauhia te tere o te wai i roto i te paipa 2 mā te whakamahi i te whārite o te haere tonu:

Ka tatauhia te pēhanga wai i roto i te paipa iti (p _{2 ) mā te whakamahi i te whārite a Bernoulli:}

1. He aha te āhua o te wai?
   • whakahoki: Ko te whanaketanga wai te peka o te ahupūngao e ako ana i te nekehanga o ngā wai (ngā wai me ngā hau) me ngā kaha e pā ana ki a rātou. Kei roto ko ngā mātāpono me ngā whārite e whakaahua ana i te rere o ngā wai, te taunekeneke me ngā rohe totoka, me te pānga tetahi ki tetahi.
2. He aha te rerekētanga i waenga i te rere laminar me te rere turbulent?
   • whakahoki: Ko te rere o te wai i roto i te wai e tohuhia ana e ngā paparanga wai maeneene, whakarara e neke ana i ngā ara tika. Ko te rere pōrearea ia, he pōrearea, he huripokitanga, he hurihanga, he tere hoki te piki me te heke. Ko te pōrearea te tikanga ka puta i ngā tere teitei, i roto rānei i ngā awaawa āhua koretake.
3. He pēhea te hiranga o te ariā o te matotoru i roto i ngā āhuatanga wai?
   • whakahoki: Ko te matotoru te ine i te ātete o te wai ki te kutikuti, ki te rere rānei. Ko ngā wai matotoru-nui (pēnei i te honi) ka ātete nui atu i te rere i ngā wai matotoru-iti (pēnei i te wai). I roto i ngā mahi wai, he mea nui te matotoru ki te whakatau i te āhua o te rere o te wai, te marara o te pūngao, me ngā kaha tōia.
4. He aha te mātāpono a Bernoulli?
   • whakahoki: E ai ki te mātāpono a Bernoulli, i roto i te rere pumau, ka noho pūmau te tapeke o te pūngao pēhanga, te pūngao nekeneke, me te pūngao pūmanawa mō ia rōrahi. Ina koa, ki te teitei te tere o te wai, ka iti te pēhanga, ā, ki te iti te pēhanga.
5. He aha te hononga o te mātāpono o te hiki i roto i te aerodynamics ki ngā whanaketanga wai?
   • whakahoki: Ka taea te whakamārama i te hiki i runga i te parirau o te waka rererangi mā te whakamahi i te mātāpono a Bernoulli me te ture tuatoru a Newton. I te rere o te hau i runga i te parirau, ka tere ake te neke i runga i te mata piko o runga i te raro, ka puta he rerekētanga pēhanga. Ko tēnei rerekētanga o te pēhanga, me te piko o te hau ki raro e te parirau, ka hua ake he kaha ki runga, he hiki rānei.
6. He aha te whārite o te haere tonu i roto i ngā āhuatanga wai?
   • whakahoki: E kī ana te whārite o te haere tonutanga ko te hua o te horahanga whakawhiti-wāhanga (A) o te rere me tōna tere (v) ka noho pūmau tonu i te taha o te awaawa i roto i te rere pumau. Mā te pāngarau, A₁​v_1​=A₂​v₂​, i reira A_1​ a A₂​ he horahanga whakawhiti-wāhanga me v₁​ a v_2​ ko ngā tere i ngā pūwāhi e rua i te taha o te awa.
7. He aha te mahi a te tau Reynolds i roto i ngā āhuatanga wai?
   • whakahoki: Ko te Tau Reynolds he rahinga kore-ahu e āwhina ana ki te matapae i te āhua rere (whakapūmau, whakawhiti, turbulent rānei) i roto i ngā āhuatanga wai. E tautuhia ana ko te ōwehenga o ngā kaha ātete ki ngā kaha matotoru, ā, e whakawhirinaki ana ki ngā āhuatanga pēnei i te tere wai, te roa āhuatanga, me ngā āhuatanga wai.
8. He pēhea te pānga o te kaha tō ki ngā mea e neke ana i roto i te wai?
   • whakahoki: Ka ārai te kaha tō i te nekehanga o tētahi mea i roto i tētahi wai. Ka puta mai i te ātete matotoru o te wai me ngā rerekētanga pēhanga huri noa i te mea. Ko te rahi me te āhua o te tō ka whakawhirinaki ki ngā āhuatanga pēnei i te āhua o te mea, te taratara, te tere, me ngā āhuatanga o te wai.
9. He aha te pānga Venturi?
   • whakahoki: Ko te pānga Venturi e pā ana ki te hekenga o te pēhanga wai e puta ana ina rere te wai mā roto i tētahi wāhanga kuiti o tētahi paipa. I te pikinga o te tere o te wai i roto i te wāhanga kuiti (nā te tiakitanga o te papatipu), ka heke tōna pēhanga e ai ki te mātāpono a Bernoulli.
10. He aha i tere ake ai te rere o te wai ina rere mā roto i tētahi wāhanga whaiti o tētahi paipa, o tētahi awa rānei?

• whakahoki: Ka taea te whakamārama i tēnei whanonga mā te mātāpono o te tiaki i te papatipu. I roto i te rere pumau, me rite te rōrahi o te wai e tomo ana ki tētahi wāhanga o te paipa ki te rōrahi e puta ana. Mena he whaiti te paipa, me tere ake te wai kia taea ai te rere o taua rōrahi i roto i tētahi wā kua whakaritea.