
beltramy pravaah

drav gatiki mein, beltramy pravaah pravaah hotey hain jisamen verticity vector sootra _ 1 aur wegg vector sootra _ 2 ack dusare key samanantar hotey hain. dusare shabdon mein, beltramy pravaah ack pravaah haye jahan bhed kaa maans shoonya hotaa haye. iska naam italvi ganitshastri eugenio beltramy key naam parr rakhaa gayaa haye kyonki unaki beltramy vector kshetra kii vyutpatti key kaaran, jabaki drav gatiki mein praarambhik vikas russie vaigyaanik epolit aiss dwara kiya gayaa thaa. 1881 mein gromeca.
varnan.
choonki verticity vector sootra _ 3 aur wegg vector sootra _ 2 ack dusare key samanantar hain, humm likh sakate hain
jahan sootra _ 6 kuchh scalar function haye. beltramy pravaah kaa ack tatkaal parinam yeh haye kii yeh kabhi bhee samtal yaa aksh-samamit pravaah naheen hoe sakata haye kyonki una pravaahon mein, verticity hamesha wegg kshetra key lambavat hoti haye. anya mahatvapurna parinam asampeedit mahadhamani sameekaran koo dekhkar mahsoos kiya jaayega.
jahan sootra _ 8 ack baahari shareer bull haye jaise kii gurutvaakarshan kshetra, vidyut kshetra aadi., aur sootra _ 9 gatij chipchipahat haye. choonki sootra _ 3 aur sootra _ 2 samanantar hain, uparokt sameekaran mein gair-raikhik shabd samaan roop seey shoonya sootra _ 12 hain. iss prakaar beltramy pravaah raikhik sameekaran koo santusht kartaa haye.
jaba sootra _ 14 hotaa haye, tou verticity key ghatak ack saral ooshmaa sameekaran koo santusht karate hain.
trikal pravaah.
victor trikal koo 1919 mein scalar function sootra _ 15, i key liye kissy bhee baahari balon key binaa beltramy pravaah maanaa gayaa.ee.,
charon key nimnalikhit prithakkaran kaa parichay dein
taba sootra _ 18 seey santusht sameekaran bunn jaataa haye
chandrekhar-kendall falan iss sameekaran koo santusht karate hain.
barkar kaa samadhan.
 1963 mein sootra _ 18 key liye cartasian nirdeshank mein samadhan praapt kiya,
saamaanyikrit beltramy pravaah.
saamaanyikrit beltramy pravaah sthiti koo santusht kartaa haye
joe kii beltramy sthiti sootra _ 23 kii tulanaa mein cumm pratibandhaatmak haye. samanya beltramy pravaah key vipareet, samtal aur akshasamamit pravaah key liye saamaanyikrit beltramy pravaah kaa adhyayan kiya jaa sakata haye.
sthir samtal pravaah.
sthir saamaanyikrit beltramy pravaah key liye, hamaare paas sootra _ 24 haye aur choonki yeh bhee samtal haye isaliye hamaare paas sootra _ 25 haye.
sootra _ 22 kaa ekikaran sootra _ 28 detaa haye. isaliye, poorna samadhan sambhav haye yadi yeh nimnalikhit sabhi teen samikaranon koo santusht kartaa haye.
ack vishesh mamle parr vichaar kiya jaataa haye jaba pravaah kshetra mein samaan verticity sootra _ 30 hotaa haye. wang (1991) ney saamaanyikrit samadhan diyaa
sootra _ 32 key liye ack raikhik falan maanate hue. ise verticity sameekaran mein pratisthaapit karna aur sthir sootra _ 34 koo alag karane key saath charr sootra _ 33 key prithakkaran kaa parichay denaa parinam mein
sootra _ 36 key vibhinn vikalpon key liye praapt samadhan kii alag-alag vyakhya kii jaa sakati haye, udaaharan key liye, sootra _ 37 ack samaan grid key pravaah koo darshaata haye, sootra _ 38 ack stretching plate dwara banaae gaye pravaah koo darshaata haye, sootra _ 39 ack koney mein pravaah koo darshaata haye, sootra _ 40 ack asymptotic suction profile aadi kaa pratinidhitva kartaa haye.
asthir samtal pravaah.
yahaan,
teller key kshaysheel vertice.
jee. aaee. teller ney ack vishesh mamle key liye samadhan diyaa jahaan sootra _ 42, jahaan sootra _ 43 1923 mein ack sthiraank haye. unhone dikhaaya kii prithakkaran sootra _ 44 sameekaran koo santusht kartaa haye aur yeh bhee kii
teller ney ack udaaharan bhee maanaa, vipareet dishaaon mein baari-baari seey ghoomane vaali aur aaytaakaar sarani mein vyavasthit eddi kii ack kshay pranali.
joe uparokt sameekaran koo sootra 47 key saath santusht kartaa haye, jahan sootra 48 ack eddi dwara banaae gaye varg kii lambai haye. isaliye, eddi kii yeh pranali kshay karati haye
oh. 1992 mein walsh saamaanyikrit teller kaa addie samadhan. walsh kaa samadhan sootra _ 50 kaa haye, jahan sootra _ 51 aur sootra _ 52 haye.
sthir akshasamamit pravaah.
yahaan hamaare paas sootra _ 53 haye. sootra _ 54 kaa ekikaran sootra _ 55 detaa haye aur teen sameekaran hain
pahala sameekaran hicks sameekaran haye. marris aur aswani (1977) ney dikhaaya kii ekmatra sambhaavit samadhan sootra _ 30 haye aur shesh samikaranon koo ghataakar
uparokt sameekaran key samadhan kaa ack saral samooh haye
sootra _ 60 ack paravalayik satah parr dou virodhi ghoornan dhaara key kaaran ack pravaah kaa pratinidhitva kartaa haye, sootra _ 61 ack samtal deewaar parr ghoornan pravaah kaa pratinidhitva kartaa haye, sootra _ 62 ack pravaah dirghvrittakar bhanwar (vishesh mamle-pahaadi kaa golakar bhanwar) kaa pratinidhitva kartaa haye, sootra _ 63 ack prakaar key toroidal bhanwar aadi kaa pratinidhitva kartaa haye.
sootra _ 64 key liye sajaatiya samadhan jaisa kii barkar dwara dikhaaya gayaa haye
jahan sootra _ 66 kramshah pratham prakaar key besal falan aur dwiteeya prakaar key besal falan hain. uparokt samadhan kaa ack vishesh mamla divaaron parr anupravaah wegg key saath belnakar jyaamiti key liye poisule pravaah haye. chiyaa-shuna yih ney 1958 mein sootra _ 67 key saath ack sink mein poisuil pravaah key liye ack samadhan paaya.
drav yantriki mein beltramy pravaah.
beltram kshetra euler sameekaran kaa ack shaastriya sthir samadhan haye. beltramy kshetra santulan mein (aadarsh) drav yantriki mein ack mahatvapurna bhoomika nibhaate hain, kyonki inn kshetron key liye kewal jatilata kii ummeed kii jaati haye.

