Zinthu Zokhudzana ndi Kuyenderana kwa Kupitiriza
Yesani kutsegula pompo yamadzi pang'onopang'ono mukuyang'ana madzi akutuluka mumpopi. Pompo ikasiya kutembenuka, tsekani pang'ono pompo ndi dzanja lanu. Tsopano yerekezerani kuti madzi ndi otani omwe ali ochulukirapo. Mukatsekeka pang'ono kapena osatsekeka pang'ono? Ngati muli ndi payipi yomwe nthawi zambiri imagwiritsidwa ntchito pothirira maluwa, lolani madzi adutsemo. Tsekani pang'ono payipi ndi dzanja lanu kapena chala chanu. Gawo lalikulu la payipi likatsekeka, madzi adzatuluka mwachangu. Mosiyana ndi zimenezi, ngati payipi silinatsekeke, madzi adzayenda mofulumira. N'chifukwa chiyani zili choncho? Kuti mumvetse izi, chonde phunzirani za continuity equation.
Ma streamlines ndi ma flow tubes
Choyamba, tiyeni timvetse mfundo za ma streamlines ndi ma flow tubes. Lingaliro ili ndi lofunika chifukwa lidzakuthandizani kumvetsetsa continuity equation.
Mzere wa mtsinje
Yang'anani chithunzi chili pansipa, mzere wabuluu ndi Streamline.
Mu kuyenda kokhazikika, liwiro la tinthu tamadzimadzi pa mfundo imodzi, mwachitsanzo mfundo A, limakhalabe lokhazikika. Pamene likudutsa mfundo B, liwiro la tinthu tamadzimadzi likhoza kusintha. Komabe, likafika pa mfundo B, tinthu tamadzimadzi timene timatsatira kumbuyo timapitiriza kuyenda pa liwiro lomwelo monga tinthu tamadzimadzi timene tinali patsogolo pake. Zomwezo zimagwiranso ntchito pofika pa mfundo C, ndi zina zotero. Kuthamanga kwa madzi ndi malo olumikizira A, B, ndi C.
Chubu choyenda
Kwenikweni, tingathe kujambula mtsinje uliwonse kudzera pa mfundo iliyonse ya madzi. Ngati tiganizira za kuyenda kwa madzi kokhazikika, mtsinje wambiri womwe umadutsa pa ngodya inayake pamalo ongopeka (malo ongopeka) umapanga chubu choyenda. Palibe tinthu tamadzi tomwe timakumana koma nthawi zonse timakhala ofanana, ndipo chubu choyenda chidzafanana ndi chitoliro chomwe nthawi zonse chimakhala ndi mawonekedwe ofanana. Madzi olowa kumapeto kwa chubu adzatuluka mu chubucho kumapeto kwina.
Debit
Kutuluka kwa madzi kumasonyeza kuchuluka kwa madzi omwe akuyenda kudutsa gawo linalake panthawi inayake. Mwa masamu, akhoza kufotokozedwa motere:
Kuti mumvetse bwino, tiyeni tigwiritse ntchito chitsanzo. Tiyerekeze kuti madzi akuyenda mu chitoliro. Mapaipi nthawi zambiri amakhala ozungulira ndipo amakhala ndi malo enaake opingasa. Chitolirocho chilinso ndi kutalika kwake.
Madzi akamayenda mu chitoliro mpaka L, ndiye kuti voliyumu ya madzi mu chitoliro ndi V = AL (V = voliyumu ya madzi, A = malo opingasa ndi L = kutalika kwa chitoliro). Chifukwa panthawi yoyenda mu chitoliro motsatira L madziwo amayenda nthawi inayake, ndiye kuti tinganene kuti kukula kwa kutuluka kwa madzi ndi:
Chifukwa v = s/t = L/t —> L = vt, equation yomwe ili pamwambapa yasinthidwa kukhala:
Motero, madzi akamayenda kudzera mu chitoliro chomwe chili ndi malo enaake opingasa ndi kutalika kwa nthawi inayake, kukula kwa kutuluka kwa madzi (Q) kumakhala kofanana ndi malo opingasa (A) ochulukitsidwa ndi liwiro la kuyenda kwa madzi (v).
Chiyerekezo Chopitilira
Taganizirani za madzi omwe amatuluka mu chitoliro chokhala ndi mainchesi osiyanasiyana, monga momwe chithunzi chili pansipa chikusonyezera.
Chithunzichi chikuwonetsa kuyenda kwa madzi kuchokera kumanzere kupita kumanja (madzi akuyenda kuchokera ku chitoliro chokhala ndi mainchesi akulu kupita ku chitoliro chokhala ndi mainchesi ochepa). Mizere yokhala ndi madontho ndi yosalala.
Chithunzi: A 1 = Malo ozungulira gawo lalikulu la chitoliro, A 2 = Malo ozungulira gawo laling'ono la chitoliro, v 1 = Liwiro la kuyenda kwa madzi m'gawo lalikulu la chitoliro, v 2 = Liwiro la kuyenda kwa madzi m'gawo laling'ono la chitoliro, L = Mtunda woyenda ndi madzi.
Poyambitsa njira zamadzimadzi, tafotokoza kuti mu njira zamadzimadzi, timakambirana za kuyenda kwa madzimadzi omwe sagwedezeka, osasinthasintha, komanso okhazikika. Mu kuyenda kokhazikika, liwiro la tinthu tamadzimadzi pamalo amodzi ndi lofanana ndi liwiro la tinthu tina tamadzimadzi tomwe timadutsa pamalopo. Kuyenda kwa madzimadzi sikumakumana (kusinthasintha kumakhala kofanana). Chifukwa chake, kuchuluka kwa madzimadzi omwe amalowa kumapeto kwa chitoliro kuyenera kukhala kofanana ndi kuchuluka kwa madzimadzi omwe amatuluka kumapeto ena. Ngati madzimadzi okhala ndi kulemera kwina alowa mu chitoliro chokhala ndi kukula kwakukulu, ndiye kuti madzimadziwo adzatuluka mu chitoliro chokhala ndi kukula kochepa kokhala ndi kulemera kosasintha.
Tsopano, yang'anani chithunzi cha chitoliro pamwambapa. Yang'anani gawo la chitoliro lomwe lili ndi dayamita yayikulu ndi gawo la chitoliro lomwe lili ndi dayamita yaying'ono.
Pa nthawi inayake, madzi enaake amatuluka m'chitoliro chokhala ndi mainchesi akulu (A).1) mpaka L1 (L1 =v1 t). Kuchuluka kwa madzi otuluka ndi V1 =A1 L1 =A1 v1 t. Mu nthawi yomweyi, kuchuluka kwina kwa madzi kumadutsa mu gawo la chitoliro chokhala ndi mainchesi ochepa (A).2) mpaka L2 (L2 =v2 t). Kuchuluka kwa madzi otuluka ndi V2 =A2 L2 =A2 v2 t.
Kuyenderana kwa Zinthu Zosagwedezeka (Continuity Equation for Incompressible Fluids)zosamveka)
Choyamba, tiyeni tiganizire za madzi osagwedezeka. Mu madzi osagwedezeka, kuchuluka kwa madzi nthawi zonse kumakhala kofanana pamalo aliwonse omwe amadutsa. Kuchuluka kwa madzi omwe akuyenda mu chitoliro chokhala ndi malo opingasa A1 ( m'mimba mwake waukulu wa chitoliro) panthawi inayake ndi:
Momwemonso, kuchuluka kwa madzi omwe akuyenda mu chitoliro chokhala ndi gawo lopingasa la A 2 (m'mimba mwake wa chitoliro chaching'ono) panthawi inayake ndi:
Poganizira kuti mu kuyenda kokhazikika, kuchuluka kwa madzi omwe amalowa ndi kofanana ndi kuchuluka kwa madzi omwe amatuluka, ndiye kuti:
m 1 = m 2
ρ A 1 v 1 t = ρ A 2 v 2 t (kuchuluka kwa madzi ndi nthawi ndi zofanana kotero zimachotsedwa)
A 1 v 1 = A 2 v 2
Kotero, mu madzi osagwedezeka, equation yopitilira imagwira ntchito:
A 1 v 1 = A 2 v 2 — Equation 1
Zambiri:
A 1 = dera lopingasa 1, A 2 = dera lopingasa 2, v 1 = liwiro la kuyenda kwa madzi pa gawo lopingasa 1, v 2 = liwiro la kuyenda kwa madzi pa gawo lopingasa 2, A v = kuchuluka kwa kuyenda kwa madzi V/t aka kutulutsa
Equation 1 ikuwonetsa kuti kuchuluka kwa madzi omwe amatuluka, komwe kumadziwikanso kuti kutuluka, nthawi zonse kumakhala kofanana pamalo aliwonse omwe ali pa chitoliro kapena chubu choyendera. Pamene gawo lodutsa madzi limachepa, kuchuluka kwa madzi omwe amatuluka kumawonjezeka; mosiyana, pamene gawo lodutsa madzi lomwe limatuluka limawonjezeka, kuchuluka kwa madzi omwe amatuluka kumachepa.
Tikamatsegula pang'ono pompo, madzi amatuluka mofulumira kuposa pompo yatsekedwa pang'ono. Izi zili choncho chifukwa malo ozungulira pompo amachepa pompo yatsekedwa pang'ono, zomwe zimawonjezera kuchuluka kwa madzi (madzi amatuluka mwachangu). Izi ndi zomwezo ndi mapaipi. Komabe, ndikofunikira kudziwa kuti kuchuluka kwa madzi omwe amatuluka kapena kuchuluka kwa madzi kumakhalabe komweko nthawi zonse pamene madzi akuyenda, kaya pompo yatsekedwa pang'ono kapena ayi. Chifukwa chake, chomwe chimasintha ndi kuchuluka kwa madzi omwe amatuluka.
Nanga bwanji za kuyenda kwa madzi mumtsinje? Magawo akuya a mtsinje ali ndi gawo lalikulu kuposa magawo osaya, kotero liwiro la kuyenda kwa madzi m'magawo akuya ndi lotsika kuposa m'magawo osaya. Ngati muwona kuyenda kwa mtsinje bata kwambiri, zikutanthauza kuti mtsinjewo ndi wozama. Koma ngati mtsinjewo mwadzidzidzi ukuyenda mofulumira, gawo limenelo ndi losaya kwambiri. Komabe, liwiro la kuyenda kwa madzi nthawi zonse limakhala lofanana, kaya m'magawo akuya kapena odekha a mtsinjewo.
Kuyenderana kwa Zinthu Zopanikizika (Continuity Equation for Compressible Fluids)chopanikizika)
Pankhani ya madzi opanikizika , kuchuluka kwa madzi sikofanana nthawi zonse. Mwanjira ina, kuchuluka kwa madzi kumasintha akapanikizika. Ngakhale kuti madzi osagwedezeka , kuchuluka kwa madzi kumachotsedwa mu equation, pamenepa, kuchuluka kwa madzi kumaphatikizidwabe. Ponena za equation yomwe idachokera kale, tiyeni tipeze equation ya madzi opanikizika.
Poganizira kuti mu kuyenda kokhazikika, kuchuluka kwa madzi omwe amalowa ndi kofanana ndi kuchuluka kwa madzi omwe amatuluka, ndiye kuti:
m 1 = m 2
ρ A 1 v 1 t = ρ A 2 v 2 t
Nthawi yoyendera madzi ndi yofanana kotero imatha kuchotsedwa. Equation imasintha kukhala:
ρ A 1 v 1 = ρ A 2 v 2 → Equation 2
Iyi ndi njira yowerengera madzi opanikizika. Kusiyana kokha kuli mu kuchuluka kwa madzi. Madzi akapanikizika, kuchuluka kwake kumasintha. Mosiyana ndi zimenezi, madzi akamasungunuka, kuchuluka kwake kumakhalabe kofanana ndipo kumatha kuchotsedwa.
Chitsanzo cha funso 1:
Madzi amayenda kudzera mu chitoliro chokhala ndi mainchesi 10 cm pa liwiro la 2 m/s. Kodi madziwo amatuluka bwanji?
Zokambirana
Amadziwika kuti:
Chitoliro cha mapaipi = 10 cm (ichi ndi chitoliro chamkati cha mapaipi)
Utali wa chitoliro (r) = 5 cm = 0,05 m
madzi = 2 m/s
Anafunsa: Debit
Yankho:
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
Chitsanzo cha funso 2:
Chitoliro cha madzi chokhala ndi mainchesi 20 cm chimalumikizidwa ku chitoliro china chokhala ndi mainchesi 10. Ngati chiŵerengero cha madzi mu chitoliro cha mainchesi 20 cm chili ndi 4 m/s, kodi chiŵerengero cha madzi mu chitoliro cha mainchesi 10 chili chotani?
Zokambirana
Amadziwika kuti:
Chidutswa 1 = 20 cm (r 1 = 10 cm = 0,1 m)
v 1 = 4 m/s
Chidutswa 2 = 10 cm (r 2 = 5 cm = 0,05 m)
Anafunsa: v 1
Yankho:
Funso 1 = Funso 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
