Kusintha kwa madzi m'thupi - mavuto ndi mayankho

Kusintha kwa madzi m'thupi - mavuto ndi mayankho

Chiphunzitso cha Torricelli

1. Chidebe chodzazidwa ndi madzi ndipo pali dzenje , monga momwe chithunzi chili pansipa chikusonyezera. Ngati kuthamanga chifukwa cha mphamvu yokoka ndi 10 ms ^-2 , kodi liwiro la madzi kudzera m'dzenjelo ndi lotani?

Zodziwika:

Kutalika (h) = 85 cm – 40 cm = 45 cm = 0.45 metres

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Liwiro la madzi (v)

Yankho:

Chiphunzitso cha Torricelli chimanena kuti madzi amachoka m'dzenjelo ndi liwiro lomwelo monga momwe chinthu chimagwera kuchokera kutalika komweko. Kutalika (h) = 85 cm – 40 cm = 45 cm = 0.45 metres

Liwiro la madzi limawerengedwa pogwiritsa ntchito equation ya kayendedwe ka kugwa kwaulere :

v _t ² = 2 gh

v _t ² = 2 gh = 2(10)(0.45) = 9

v _t = √9 = 3 m/s

2. Chidebe chodzazidwa ndi madzi ndipo pali dzenje, monga momwe chithunzi chili pansipa. Ngati kuthamanga chifukwa cha mphamvu yokoka ndi 10 ms ^-2 , kodi liwiro la madzi kudzera m'dzenjelo ndi lotani?

Zodziwika:

Kutalika (h) = 1.5 m – 0.25 m = 1.25 mamita

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Liwiro la madzi (v)

Yankho:

v _t ² = 2 gh = 2(10)(1.25) = 25

v _t = √25 = 5 m/s

3. Chidebe chodzazidwa ndi madzi ndipo pali dzenje, monga momwe chithunzi chili pansipa. Ngati kuthamanga chifukwa cha mphamvu yokoka ndi 10 ms ^-2 , kodi liwiro la madzi kudzera m'dzenjelo ndi lotani?

Zodziwika:

Kutalika (h) = 1 m – 0.20 m = 0.8 mamita

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Liwiro la madzi (v)

Yankho:

v _t ² = 2 gh = 2(10)(0.8) = 16

v _t = √16 = 4 m/s

4. Chidebe chodzazidwa ndi madzi ndipo pali dzenje, monga momwe chithunzi chili pansipa. Ngati kuthamanga chifukwa cha mphamvu yokoka ndi 10 ms ^-2 , kodi liwiro la madzi kudzera m'dzenjelo ndi lotani?

Zodziwika:

Kutalika (h) = 20 cm = 0.2 mamita

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Liwiro la madzi (v)

Yankho:

5. Chidebe chodzazidwa ndi madzi ndipo pali mabowo awiri , monga momwe chithunzi chili pansipa chikusonyezera. Kodi chiŵerengero cha x ₁ mpaka x ₂ ndi chotani?

Yankho

Nthawi yopuma yopanda madzi kuchokera pa dzenje 1:

h = 1/2 pa ²

0.8 = 1/2 (10) t ²

0.8 = 5 t ²

t ² = 0.8 / 5 = 0.16

t = masekondi awiri

Nthawi yopuma yopanda madzi kuchokera pa dzenje 2:

h = 1/2 pa ²

0.5 = 1/2 (10) t ²

0.5 = 5 t ²

t ² = 0.5 / 5 = 0.1

t = √0.1 sekondi

Mtunda wopingasa (x):

x ₁ = v ₁ t ₁ = (2)(0.4) = mamita 0.8

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

Chiŵerengero cha x ₁ mpaka x ₂ :

x _{1 :} x ₂ = 0.8: 1 = 8: 10 = 4: 5

Kulinganiza kwa kupitiriza

6. Madzi amayenda kudzera mu chitoliro cha mainchesi osiyanasiyana, A mpaka B kenako C. Chiŵerengero cha A mpaka C ndi 8 : 3. Ngati liwiro la madzi mu chitoliro A ndi v, kodi liwiro la madzi mu chitoliro C ndi lotani?

Zodziwika:

Chigawo cha A (A)_A= = 8

Chigawo cha C (A _C ) = 3

Liwiro la madzi mu chitoliro A (v _A ) = v

Kufunidwa: Liwiro la madzi mu chitoliro C (v _C )

Yankho:

Chiyerekezo cha kupitiriza:

A _A v _A = A _C v _C

8 v = 3 v _C

v _C = 8/3 v

7. Ngati liwiro la madzi mu chitoliro chokhala ndi mainchesi 12 ndi 10 cm/s, kodi liwiro la madzi mu chitoliro chokhala ndi mainchesi 8 ndi lotani?

Zodziwika:

Chidutswa 1 (d ₁ ) = 12 cm, utali wozungulira 1 (r ₁ ) = 6 cm

Chidutswa 2 (d ₂ ) = 8 cm, utali wozungulira 2 (r ₂ ) = 4 cm

Liwiro la madzi 1 (v ₁ ) = 10 cm/s

Kufunidwa: Liwiro la madzi 2 (v ₂ )

Yankho:

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

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

Chiyerekezo cha kupitiriza:

A ₁ v ₁ = A ₂ v ₂

(36π)(10) = (16π) v ₂

(36)(10) = (16) v ₂

360 = (16) v ₂

v ₂ = 360/16

v ₂ = 22.5 cm/s

8. Madzi amayenda kudzera mu chitoliro cha mainchesi osiyanasiyana, monga momwe chithunzi chili pansipa chikusonyezera. Ngati dera 1 (A ₁ ) = 8 cm ² , A ₂ = 2 cm ² ndi liwiro la madzi mu chitoliro 2 = v ₂ = 2 m/s ndiye liwiro la madzi mu chitoliro 1 = v ₁ ndi lotani.

Zodziwika:

Gawo 1 (A)₁) = 8 cm²

Malo 2 (A ₂ ) = 2 cm ²

Liwiro la madzi mu chitoliro 2 (v ₂ ) = 2 m/s

Kufunidwa: liwiro la madzi mu chitoliro 1 (v ₁ )

Yankho:

Chiyerekezo cha kupitiriza:

A ₁ v ₁ = A ₂ v ₂

8 v ₁ = (2)(2)

8 v ₁ = 4

v ₁ = 4 / 8 = 0.5 m/s

9. Ngati kukula kwa chitoliro chachikulu kuli kawiri kuposa kukula kwa chitoliro chaching'ono, kodi liwiro la madzi pa chitoliro chaching'ono ndi lotani?

Zodziwika:

Chitoliro chachikulu (d)₁= = 2

Ulalo wa chitoliro chachikulu (r ₁ ) = ½ d ₁ = ½ (2) = 1

Dera la chitoliro chachikulu ( A ₁ ) = π r ₁ ² = π (1) ² = π (1) = π

Chitoliro cha chitoliro chaching'ono (d ₂ ) = 1

Utali wa chitoliro chaching'ono (r ₂ ) = ½ d ₂ = ½ (1) = ½

Malo a chitoliro chaching'ono ( A ₂ ) = π r ₂ ² = π (1/2) ² = π (1/4) = ¼ π

Liwiro la madzi pa chitoliro chachikulu ( v ₁ ) = 4 m/s

Kufunidwa: Liwiro la madzi pa chitoliro chaching'ono ( v ₂ )

Yankho:

Chiyerekezo cha kupitiriza:

A ₁ v ₁ = A ₂ v ₂

π 4 = ¼ π (v ₂ )

4 = ¼ (v ₂ )

v ₂ = 8 m/s

Mfundo ndi ma equation a Bernoulli

10. Madzi amapopedwa ndi compressor ya 120 kP kulowa mu chitoliro chapansi (1) ndipo amayenderera mmwamba pa liwiro la 1 m/ s. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/ s ndipo kuchuluka kwa madzi ndi 1000 kg/m ^-3 . Kodi kuthamanga kwa madzi pa chitoliro chapamwamba ndi kotani (II ).

Zodziwika:

Ulalo wa chitoliro chapansi (r)₁) = 12 cm

Ma radius a chitoliro chapansi (r ₂ ) = 6 cm

Kuthamanga kwa madzi mu chitoliro chapansi (tsamba ₁ ) = 120 kPa = 120,000 Pascal

Liwiro la madzi mu chitoliro chapansi (v ₁ ) = 1 ms ^-1

Kutalika kwa chitoliro chapansi (h ₁ ) = 0 m

Kutalika kwa chitoliro chapamwamba (h ₂ ) = 2 m

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms ^-2

Kuchuluka kwa madzi = 1000 kg.m ^-3

Kufunika: Kupanikizika kwa madzi mu chitoliro 2 (tsamba ₂ )

Yankho:

Liwiro la madzi mu chitoliro 2 limawerengedwa pogwiritsa ntchito equation ya continuity:

Kupanikizika kwa madzi mu chitoliro 2 kumawerengedwa pogwiritsa ntchito equation ya Bernoulli:

11. Chitoliro chachikulu mamita 5 pamwamba pa nthaka ndi chitoliro chaching'ono mita 1 pamwamba pa nthaka. Liwiro la madzi mu chitoliro chachikulu ndi 36 km/h ndi kupanikizika kwa 9.1 x 10 ⁵ Pa, pomwe kupanikizika mu chitoliro chaching'ono ndi 2.10 ⁵ Pa. Kodi liwiro la madzi mu chitoliro chaching'ono ndi lotani ? Kuchuluka kwa madzi = 10 ³ kg/ ^m3

Zodziwika:

Kupanikizika kwa madzi mu chitoliro chachikulu (p₁) = 9.1 x 10⁵ Pascal = Ma Pascal 910,000

Kuthamanga kwa madzi mu chitoliro chaching'ono (tsamba ₂ ) = 2 x 10 ⁵ Pascals = 200,000 Pascals

Liwiro la madzi mu chitoliro chachikulu (v ₁ ) = 36 km/h = 36(1000)/(3600) = 36000/3600 =10 m/s

Kutalika kwa chitoliro chachikulu (h ₁ ) = -4 mamita

Kutalika kwa chitoliro chaching'ono (h ₂ ) = mamita 0

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms ^-2

Kuchuluka kwa madzi = 1000 kg/ ^m3

Kufunidwa: Liwiro la madzi mu chitoliro chaching'ono (v ₂ )

Yankho:

Liwiro la madzi mu chitoliro chaching'ono (v ₂ ) limawerengedwa pogwiritsa ntchito equation ya Bernoulli:

12. Chitoliro chokhala ndi utali wa masentimita 15 cholumikizidwa ndi chitoliro china chokhala ndi utali wa masentimita 5. Zonse ziwiri zili pamalo opingasa. Liwiro la kuyenda kwa madzi mu chitoliro chachikulu ndi 1 m/s pakapanikizika kwa 10 ⁵ N/ m2 . Kodi kuthamanga kwa madzi pa chitoliro chaching'ono ndi kotani (1 g cm ^-3 )^?

Zodziwika:

Utali wa chitoliro chachikulu (r ₁ ) = 15 cm = 0.15 m

Utali wa chitoliro chaching'ono (r ₂ ) = 5 cm = 0.05 m

Kuthamanga kwa madzi mu chitoliro chachikulu (tsamba ₁ ) = 10 ⁵ N m ^-2 = 100.000 N m ^-2

Liwiro la madzi mu chitoliro chachikulu (v ₁ ) = 1 ms ^-1

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms ^-2

Kuchuluka kwa madzi = 1 gr cm ^-3 = 1000 kg m ^-3

Kusiyana kwa kutalika (Δh) = 0.

Kufunika: Kupanikizika mu chitoliro chaching'ono (tsamba ₂ )

Yankho:

Liwiro la madzi mu chitoliro 2 limawerengedwa pogwiritsa ntchito equation of continuity:

Kuthamanga kwa madzi mu chitoliro chaching'ono (p ₂ ) kumawerengedwa pogwiritsa ntchito equation ya Bernoulli:

1. Kodi mphamvu ya madzimadzi ndi chiyani?
   • Yankho: Mphamvu yamadzimadzi ndi nthambi ya fizikisi yomwe imaphunzira kayendedwe ka madzimadzi (zamadzimadzi ndi mpweya) ndi mphamvu zomwe zimagwira ntchito pa iwo. Ikuphatikizapo mfundo ndi ma equation omwe amafotokoza momwe madzimadzi amayendera, momwe amagwirira ntchito ndi malire olimba, komanso momwe amakhudzirana.
2. Kodi kusiyana pakati pa laminar ndi turbulent flow ndi kotani?
   • Yankho: Kuyenda kwa laminar kumadziwika ndi zigawo zosalala, zofanana zamadzimadzi zomwe zimayenda m'njira zolongosoka. Kumbali ina, kuyenda kwa chisokonezo kumakhala kosokonezeka, komwe kumazungulira, kumazungulira, komanso kusinthasintha kwachangu. Kugwedezeka nthawi zambiri kumachitika pa liwiro lalikulu kapena m'njira zosafanana.
3. Kodi lingaliro la kukhuthala ndi lofunika bwanji mu mphamvu zamadzimadzi?
   • Yankho: Kukhuthala kumayesa kukana kwa madzi ku kumeta kapena kuyenda. Madzi okhala ndi kukhuthala kwakukulu (monga uchi) amakana kuyenda kuposa madzi okhala ndi kukhuthala kochepa (monga madzi). Mu kayendedwe ka madzi, kukhuthala kumachita gawo lofunika kwambiri pozindikira mtundu wa kuyenda kwa madzi, kutayika kwa mphamvu, ndi mphamvu yokoka.
4. Kodi mfundo ya Bernoulli ndi iti?
   • Yankho: Mfundo ya Bernoulli imati mu kayendedwe kokhazikika, kuchuluka kwa mphamvu ya kupanikizika, mphamvu ya kinetic, ndi mphamvu yomwe ingakhalepo pa voliyumu ya unit iliyonse kumakhalabe kofanana, makamaka, komwe liwiro la madzi lili lalikulu, kupanikizika kumakhala kotsika, ndipo mosemphanitsa.
5. Kodi mfundo ya kukweza mu aerodynamics ikugwirizana bwanji ndi mphamvu yamadzimadzi?
   • Yankho: Kukweza kwa phiko la ndege kungafotokozedwe pogwiritsa ntchito mfundo ya Bernoulli ndi lamulo lachitatu la Newton. Mpweya ukamayenda pamwamba pa phiko, umayenda mofulumira pamwamba pa malo opindika kuposa pansi, zomwe zimapangitsa kusiyana kwa kuthamanga. Kusiyana kumeneku kwa kuthamanga, kuphatikiza ndi kutsika kwa mpweya ndi phiko, kumabweretsa mphamvu kapena kukweza mmwamba.
6. Kodi equation ya continuity mu fluid dynamics ndi chiyani?
   • Yankho: Chiyerekezo cha kupitirira chimatanthauza kuti chinthu chochokera ku dera lopingasa (A) la kuyenda ndi liwiro lake (v) chimakhalabe chokhazikika motsatira njira yolunjika mu kuyenda kokhazikika. A₁​v_1​=A₂​v₂​, kumene A_1​ ndi A₂​ ndi madera ozungulira ndipo v₁​ ndi v_2​ ndi liwiro lomwe lili pamalo awiri m'mphepete mwa msewu.
7. Kodi nambala ya Reynolds imagwira ntchito yotani pakusintha kwa madzi?
   • Yankho: Nambala ya Reynolds ndi kuchuluka kopanda muyeso komwe kumathandiza kuneneratu kayendedwe ka kayendedwe ka madzi (laminar, transitional, kapena turbulent) mu fluid dynamics. Imatanthauzidwa ngati chiŵerengero cha mphamvu zopanda mphamvu ku mphamvu zokhuthala ndipo imadalira zinthu monga liwiro la madzi, kutalika kwa khalidwe, ndi makhalidwe a madzi.
8. Kodi mphamvu yokoka imagwira ntchito bwanji pa zinthu zomwe zikuyenda mumadzimadzi?
   • Yankho: Mphamvu yokoka imatsutsana ndi kuyenda kwa chinthu kudzera mumadzimadzi. Izi zimachitika chifukwa cha kukana kwa madzimadzi komanso kusiyana kwa kuthamanga kwa chinthucho. Kukula ndi mtundu wa kukoka kumadalira zinthu monga mawonekedwe a chinthucho, kuuma kwake, liwiro lake, ndi mawonekedwe a madzimadziwo.
9. Kodi zotsatira za Venturi ndi zotani?
   • Yankho: Zotsatira za Venturi zimatanthauza kuchepa kwa kuthamanga kwa madzi komwe kumachitika pamene madzi akuyenda kudzera mu gawo lochepa la chitoliro. Pamene liwiro la madzi likuwonjezeka mu gawo lochepa (chifukwa cha kusunga kulemera), kuthamanga kwake kumachepa malinga ndi mfundo ya Bernoulli.
10. N’chifukwa chiyani madzi amathamanga akamayenda kudzera mu gawo lopapatiza la chitoliro kapena ngalande?

• Yankho: Khalidweli lingathe kufotokozedwa ndi mfundo yosungira kulemera. Pakuyenda bwino, kuchuluka kwa madzi omwe amalowa mu gawo la chitoliro kuyenera kufanana ndi kuchuluka komwe kumachoka. Ngati chitolirocho ndi chopapatiza, madziwo ayenera kufulumira kuti alole kuchuluka komweko kudutsa munthawi inayake.