
vrithaakrithiyilulla silindarinu chuttumulla saadhyathayulla ozhukk

ganithashaasthrathil, oru vrithaakrithiyilulla silindarinu chuttumulla pottensial phloo ennathu oru silindarinu chuttumulla oru inviskid, incumpressible draavakathinte ozhukkinulla oru classical parihaaramaan. silindaril ninnu valare akale, ozhukk ekadishayilum ekeekrithavumaanu. eee ozhukkinu vorttitti illa, athinaal vegatha feeld itrotteshanal aanu, ithu oru pottensial phloo aayi maathrkayaakkaam. oru yadhaartha draavakathil ninnu vyathyasthamayi, eee layani shareerathil oru nettu seero dragg soochippikkunnu, ithu dii 'alamberts paradox ennariyappedunnu.
ganithaparamaya pariharam.
vyaasamulla oru silindar (allengil disk) dvimaana, amarthaanaavaatha, adrishyamaaya ozhukkilaanu sthaapikkunnathu. silindaril ninnu valare akaleyulla vegatha vector (yoonit vektarukalumaayi thaarathamyappeduthumbol) enna vyavasthaykku vidheyamaayi oru thalatthile sthiramaaya vegatha vektarum mardhavum kandethuka ennathaanu lakshyam
evideyaanu oru sthiraangam, silindarinte athirthiyil
silindar uparithalathile saadhaarana vekttar evideyaanu? mukalile ozhukk orupoleyaanu, athinu vorttitti illa. ozhukk adrishyavum amarthaanaavaathathum sthiramaaya pinda saandrathayulathumaanu. athinaal ozhukk vorttitti illaathe thudarunnu, allengil ellaayidathum "erotational" ennu parayappedunnu. bhramanasheshiyillaathathil, oru vegatha pottensial undaayirikkanam
amarthaanaavaathathinaal, laaplesinte samavaakyam thripthippeduthanam
dhruva kordinettukalil ettavum eluppathil pariharam labikkukayum parambaraagatha cartician kordinettukalumaayi bandhappettirikkukayum cheiyunnu. dhruva kordinettukalil, laaplesinte samavaakyam ithaanu (silindar, golaakrithiyilulla kordinettukalil dell kaanuka):
athirthi vyavasthakal thripthippeduthunna pariharam
dhruva kordinettukalile vegatha gadakangal dhruva kordinettukalile gadakangalil ninnaan labhikkunnatha
oppam
avyakthavum bhramanasheshiyillaathathumaayil, bernauliyude samavaakyam marddakshethrathinulla pariharam vegatha feeldil ninnu nerittu nedaan anuvadikkunnu
silindaril ninnu valare akale evideyaanu sthiraangangal kaanappedunnath, evideyaanu. upayogikkunnu,
chithrangalil, "marddam" ennu vilikkunna varnnameriya feeld oru plottaan
silindarinte uparithalathil, allengil, marddam stambhana pooyintukalil paramavadhi 1 (rekhaachithrathil kaanichirikkunnu) muthal silindarinte vashangalil kuranjathu −3 (kaanichirikkunnu) vare vyathyaasappedunnu. athupole, kuranja marddathil, sthambhanasthaanangalil ninnu vashangalilekku vyathyaasappedunnu.
stream function.
ozhukk amarthaanaavaathathinaal, oru stream function kandethaam
vekttar identittikal upayogichu eee nirvachanathil ninnu ithu pinthudarunnu,
athinaal, sthiramaaya moolyamulla oru kondoor oru streamline aayirikkum, oru line taanjant. oru silindarinu mukaliloode ozhukunnathinu, nammal kandethunnu
bhouthikamaaya vyaakhyaanam.
laaplesinte samavaakyam rekheeyamaanu, ithu ettavum praadhamikamaaya bhagika deferential samavaakyangalilonnaan. eee lalithamaaya samavaakyam randinum muzhuvan pariharavum nalkunnu, kaaranam erotteshanaalittiyudeyum incumpressibilityum parimithikal kaaranam. pariharavum, aaksilareshanukalumaayulla mardha gradiantinte sthirathayum manassilakkaam.
mukalile stambhana binduvile chalanathmaka marddathinu moolyam undu. swathanthramaaya pravaahatthinte vegatha kuraykkunnathinu aavashyamaaya oru moolyam. ithe moolyam thaazhekkulla stambhana binduvil drishyamaakunnu, ozhukk poojya vegathayilekku kuraykkunnathinu eee uyarnna marddam veendum aavasyamaanu. ozhukk poornnamaayum gharshanarahithamaayathinaal maathramaan eee samamiti undaakunnath.
ozhukkinte kendreekritha thvaranam nalkunnathinu silindarinte vashangalile thaazhnna marddam aavasyamaanu
ozhukkinte vakrathayude aaram evideyaanu? ennaal, oppam. dooratthilulla kendreekritha thwaranathinulla samavaakyathinte avibhaajyaghadakam angane phalam nalkum.
ettavum kuranja marddathinu krithyamaaya pariharam undu,
marddatthinte uyarnna moolyangalil ninnu thaazhnna moolyangalilekku draavakam sanjarikkumbol, kendratala thvaranam nalkunnathinu undaayirikkenda thaazhnna mardhavum ozhukkinte vegatha vardhippikkum. angane silindarinte vashangalile thaazhnna marddathil, ozhukkil paramavadhi vegatha naam kandethunnu.
oru moolyam draavakathinte alavu samrakshikkunnathumaayi poruthappedunnu. silindar chila ozhukkil thadassam srishtikkunnathinaal, silindarinte madhyabhaagathukoodi prathalatthil evideyengilum ullathinekkaal valuthum ozhukkilekku kadannupokunnathumaayirikkanum.
oru silindarinu mukaliloode oru yadhaartha draavakathinte ozhukkumaayi thaarathamyam cheyyuka.
eee anuyojyamaaya parihaaratthinte samamithiyil silindarinte pinbhaagatthum munvashathum oru stambhana binduvundu. munvashathum pinvashathum mardha vitharanam samaanamaan, ithu silindaril poojya valichidunnathinte savisheshathayilekku nayikkunnu, ithu dii 'alambert paradox ennariyappedunna oru savisheshathayaanu. anuyojyamaaya oru inviskid draavakathil ninnu vyathyasthamayi, oru silindarine marikadakkunna viscos ozhukk, viscosity ethra cheruthaayaalum, silindarinte uparithalathodu chernnulla nerttha athirthi paali nedum. athirthi paali verthirikkal sambhavikkum, silindarinu pinnile ozhukkil oru trailing wake nilanilkkum. silindarinte wake saidile oro pooyintileyum marddam mukalile vashathekkaal kuravaayirikkum, ithu thaazhekkulla dishayil oru valichidal shakthiyilekku nayikkum.
janson-railey vipuleekaranam.
vrithaakrithiyilulla silindarinu mukalilulla compress cheyyaavunna ozhukkinte prashnam aadyam padichathu oo aanu. 1913-ll janson 1916-ll loard railey cheria compressible efakttukalode. ivide, cheria paaraameettar mack nambar formula _ 18-nte chathuramaanu, shabdathinte vegatha evideyaanu. appol vegatha pottanshyalinte adisthaanathil phastt-oordar ekadesha kanakkinulla pariharam ithaanu
ivide soothravaakyam _ 20 silindarinte aaram aanu.
cheria vyathiyanangalulla oru vrithaakrithiyilulla silindarinu mukaliloode saadhyathayulla ozhukk.
konfigareshanukalil cheria aswasthathayundaakkunna oru silindarinu chuttumulla ozhukkinulla pathiv aswasthatha vishakalanam milttan vaan diekil (1975) kaanam. thazhepparayunnavayil, oru cheria positteev paaraamettarine prathinideekarikkum, ithu silindarinte aaram aanu. kooduthal vishadamaaya vishakalanagalkkum charchakalkkumaayi, vaayanakkaare milttan vaan daikkinte 1975 leeii pusthakam "perterbation metheds inn fluid mechanics" ennu paraamarsikkunnu.
cheruthaayi valachodicha silindar.
ivide silindarinte aaram allah, marichu alpam valachodicha roopamaanu. appol phastt-oordar ekadesha kanakkinulla pariharam ithaanu
cheruthaayi pulsating sarkkil.
ivide silindarinte aaram samayathinanusarichu alpam vyathyaasappedunnu. appol phastt-oordar ekadesha kanakkinulla pariharam ithaanu
cheria vortixodeyaanu ozhukunnathu.
pothuve, swatantra-pravaaha vegatha orupoleyaanu, mattoru vidhathil paranjaal, ennaal ivide baahyapravaahathil oru cheria vorttitti adichelppikkunnu.
leanier shear.
ivide vegathayil oru leanier shear avatharippikkunnu.
cheria paaraameettar evideyaanu? bharana samavaakyam ithaanu
appol phastt-oordar ekadesha kanakkinulla pariharam ithaanu
parabolic shear.
ivide baahyavegathayil oru parabolic shear avatharippikkunnu.
appol phastt-oordar ekadesharekhaykkulla pariharam ithaanu
athirthi vyavasthakal punasthaapikkunna laplace samavaakyathinte ekeekritha pariharam evideyaanu.
cheruthaayi sushira silindar.
abhedyamaaya oru silindarinte uparithala mardha gunakam prathinidheekarikkam
abhedyamaaya silindarinte uparithala marddam evideyaanu? ippol silindarinullile aantharika mardha gunakam ayirikkatte, appol cheria sushirangal kaaranam oru cheria saadhaarana vegatha nalkunnu
ennaal seero nettu fluxes avastha
athu aavasyamundu. athinaal,
appol phastt-oordar ekadesharekhaykkulla pariharam ithaanu
corregated ardha silindar.
silindarinu aksheeya dishayil variable aaram undengil,-axis, trimana vegatha pottanshyalinte adisthaanathil phastt-oordar ekadeshathinulla pariharam ithaanu
aadya tharam oordarinte parishkaricha bessel function evideyaanu.