Lo lus "txoj cai" ntawm Greek keeb kwm, txhais tau tias yog ib qho cim uas yog lub hauv paus rau kev tsim cov kev ntsuas ntawm ib qho khoom lossis qhov tshwm sim. Ntau xyoo dhau los, nws tau siv dav hauv zej zog kev tshawb fawb thiab hauv kev kawm, kev tswj hwm, kev lag luam, kev pabcuam, thiab kev noj qab haus huv. Yog tias cov txheej txheem kev tshawb fawb (cov no yog qee yam xwm txheej thiab cov kev cai uas yuav tsum tau ua) tau nthuav tawm hauv daim ntawv paub daws teeb meem rau tag nrho cov zej zog kev tshawb fawb, ces cov txheej txheem zoo sib xws tsuas yog cuam tshuam rau cov cheeb tsam ntawm kev tshawb fawb uas cuam tshuam nrog lub cev tshwm sim thiab lawv qhov tsis zoo: aerodynamics, tshav kub. hloov thiab loj hloov. Txhawm rau kom nkag siab qhov txiaj ntsig ntawm kev siv cov txheej txheem, nws yog ib qho tsim nyog yuav tsum kawm qee lub tswv yim los ntawm categorical apparatus ntawm txoj kev xav. Nws yog ib qho tsim nyog sau cia tias cov qauv zoo sib xws tau siv rau hauv kev tshwj xeeb ntev ua ntej lawv tau txais lawv lub npe. Qhov tsis tseem ceeb tshaj plaws zoo sib xws cov txheej txheem tuaj yeem hu ua feem pua ntawm tag nrho. Xws li kev ua haujlwm tau ua los ntawm txhua tus tsis muaj teeb meem thiab teeb meem. Thiab qhov ua tau zoo tshaj plaws, uas qhia txog kev vam khom ntawm lub tshuab siv lub zog thiab cov khoom siv hluav taws xob, yeej ib txwm yog qhov zoo sib xws thiab yog li tsis tau pom tias yog ib yam dab tsi vaguely sky-high.
Lub hauv paus ntawm txoj kev xav
Lub cev zoo sib xws ntawm cov xwm txheej, txawm tias qhov xwm txheej lossis tib neeg tsim lub ntiaj teb, yog siv los ntawm tus txiv neej hauv kev tshawb fawb ntawm aerodynamics, huab hwm coj thiab kub hloov pauv. Hauv zej zog kev tshawb fawb, cov txheej txheem ntawm kev kawm cov txheej txheem thiab cov txheej txheem siv kev ua qauv tau ua pov thawj nws tus kheej zoo. Lawm, thaum npaj thiab ua ib qho kev sim, lub zog-dynamic system ntawm ntau thiab cov tswv yim (ESVP) yog ib qho kev txhawb nqa. Nws yuav tsum raug sau tseg tias qhov system ntawm qhov ntau thiab qhov system ntawm units (SI) tsis sib npaug. Hauv kev xyaum, ESWP muaj lub hom phiaj nyob hauv lub ntiaj teb ib puag ncig, thiab kev tshawb fawb tsuas yog qhia lawv, yog li cov khoom siv yooj yim (lossis cov txheej txheem ntawm lub cev zoo sib xws) tsis tas yuav ua ke nrog cov chav hauv paus. Tab sis cov chav hauv paus (systematized hauv SI), ua tau raws li qhov yuav tsum tau ua ntawm kev xyaum, tau txais kev pom zoo (qhov xwm txheej) nrog kev pab los ntawm cov rooj sib tham thoob ntiaj teb.
Txoj kev xav ntawm qhov sib xws
Txoj kev xav ntawm qhov sib xws - cov ntsiab lus thiab cov cai, lub hom phiaj ntawm kev txiav txim siab qhov sib xws ntawm cov txheej txheem thiab cov xwm txheej thiab kom ntseeg tau tias muaj peev xwm hloov pauv qhov kev kawm tshwm sim los ntawm tus qauv mus rau qhov khoom tiag. Lub hauv paus ntawm phau ntawv txhais lus terminological yog cov ntsiab lus xws li homogeneous, eponymous thiab dimensionless kom muaj nuj nqis, zoo sib xws tas li. Txhawm rau kom nkag siab txog qhov tseem ceeb ntawm txoj kev xav, lub ntsiab lus ntawm cov lus teev tseg yuav tsum raug txiav txim siab.
- Homogeneous - qhov ntau uas muaj qhov sib npaug ntawm lub cev lub ntsiab lus thiab qhov loj me (ib qho kev qhia qhia tias chav ntsuas qhov ntsuas ntawm qhov muab ntau npaum li cas yog ua los ntawm cov units ntawm theem pibkom muaj nuj nqis; ceev muaj qhov ntev ntawm qhov ntev muab faib los ntawm lub sijhawm).
- Similar - cov txheej txheem sib txawv ntawm tus nqi, tab sis muaj tib qhov loj me (induction thiab kev sib nrig sib induction).
- Dimensionless - ntau npaum li cas nyob rau hauv qhov ntev ntawm qhov yooj yim lub cev muaj nuj nqis suav nrog cov degree sib npaug rau xoom.
Constant - ib qhov loj me me, uas tus nqi hauv paus yog qhov ntau nrog qhov loj me (piv txwv li, tus nqi hluav taws xob qis). Nws tso cai rau kev hloov pauv ntawm tus qauv mus rau ib qho kev ua haujlwm ntuj.
hom kev zoo sib xws
Txhua lub cev muaj peev xwm ua tau zoo sib xws. Nws yog kev cai kom paub qhov txawv plaub yam:
- geometric (saib thaum qhov sib piv ntawm cov kab sib xws ntawm cov qauv thiab cov qauv sib npaug);
- temporal (saib ntawm cov khoom zoo sib xws ntawm cov tshuab zoo sib xws txav raws txoj hauv kev zoo sib xws nyob rau lub sijhawm);
- lub cev kom muaj nuj nqis (tuaj yeem pom ntawm ob lub ntsiab lus zoo sib xws ntawm tus qauv thiab qauv, uas qhov piv ntawm lub cev qhov ntau yuav tas li);
- pib thiab ciam teb tej yam kev mob (tuaj yeem pom yog tias peb qhov zoo sib xws dhau los tau pom).
Ib yam zoo sib xws invariant (feem ntau denoted idem nyob rau hauv xam thiab txhais tau tias invariant los yog "tib yam") yog ib qho kev qhia ntawm ntau nyob rau hauv cov txheeb ze units (piv txwv li qhov piv ntawm cov ntau npaum li cas nyob rau hauv ib tug system).
Yog tias qhov tsis sib xws muaj qhov sib piv ntawm homogeneous ntau, nws yog hu ua ib qho yooj yim, thiab yog tias muaj ntau ntau, ces qhov zoo sib xws (lawv muajtag nrho cov khoom ntawm invariants).
Laws and rules of similarity theory
Hauv kev tshawb fawb, txhua yam txheej txheem yog tswj hwm los ntawm axioms thiab theorems. Lub axiomatic feem ntawm txoj kev xav suav nrog peb txoj cai:
- tus nqi h ntawm tus nqi H yog tib yam li qhov piv ntawm tus nqi rau chav tsev ntawm nws qhov ntsuas [H];
- ib lub cev kom muaj nuj nqis yog ywj siab ntawm kev xaiv ntawm nws chav;
- lej piav qhia ntawm qhov tshwm sim tsis raug rau cov kev xaiv tshwj xeeb ntawm units.
Basic postulates
Cov cai hauv qab no ntawm kev xav tau piav qhia siv theorems:
- Newton-Bertrand theorem: rau tag nrho cov txheej txheem zoo sib xws, tag nrho cov txheej txheem zoo sib xws hauv kev kawm yog khub sib npaug rau ib leeg (π1=π 1; π2=π2 etc.). Qhov piv ntawm cov qauv ntawm ob lub tshuab (tus qauv thiab qauv) yog ib txwm sib npaug rau 1.
- Buckingham-Federman theorem: cov qauv zoo sib xws muaj feem cuam tshuam nrog kev sib npaug sib npaug, uas yog sawv cev los ntawm qhov tsis muaj qhov sib tov (ib qho) thiab hu ua qhov sib npaug sib npaug.
- Kirinchen-Gukhman theorem: rau qhov zoo sib xws ntawm ob txheej txheem, lawv qhov zoo sib npaug thiab sib npaug sib npaug ntawm cov txheej txheem kev sib xws yog qhov tsim nyog.
- Theorem π (qee zaus hu ua Buckingham lossis Vash): kev sib raug zoo ntawm h ntau, uas yog ntsuas siv m units ntawm kev ntsuas, yog sawv cev raws li tus piv h - m los ntawm qhov sib txuas tsis sib xws π 1, …, πh-m ntawm cov nqi h.
Qhov zoo sib xws yog cov kev sib koom ua ke los ntawm π-theorem. Hom kev ntsuas tuaj yeem tsim los ntawm kev sau cov npe ntawm qhov ntau (A 1, … dependence F(a 1, …, a)=0, uas yog qhov kev daws teeb meem.
Cov qauv zoo sib xws thiab kev tshawb fawb
Muaj kev xav tias lub npe tseeb tshaj plaws ntawm txoj kev xav zoo sib xws yuav tsum zoo li cov qauv ntawm kev sib txawv, vim nws yog ib txoj hauv kev ntawm kev nthuav dav hauv kev tshawb fawb thiab kev tshawb fawb. Lub ntsiab spheres ntawm cawv ntawm txoj kev xav yog cov qauv ntawm kev ua qauv thiab kev sib piv. Kev siv cov txheej txheem zoo sib xws raws li kev xav ntiag tug muaj nyob ntev ua ntej kev qhia txog lo lus no (yav dhau los hu ua coefficients lossis degrees). Ib qho piv txwv yog cov haujlwm trigonometric ntawm txhua lub kaum sab xis ntawm cov duab peb sab zoo sib xws - lawv tsis muaj qhov dav. Lawv sawv cev piv txwv ntawm geometric zoo sib xws. Hauv kev ua lej, cov txheej txheem nto moo tshaj plaws yog tus lej Pi (qhov piv ntawm qhov loj ntawm lub voj voog thiab txoj kab uas hla ntawm lub voj voog). Txog niaj hnub no, txoj kev xav ntawm qhov zoo sib xws yog cov cuab yeej siv dav hauv kev tshawb fawb, uas tau hloov pauv zoo.
Lub cev tshwm sim tau kawm los ntawm kev xav zoo sib xws
Nyob hauv lub ntiaj teb niaj hnub no nws nyuaj rau kev xav txog kev kawm txog cov txheej txheem ntawm hydrodynamics, hloov hluav taws xob, hloov pauv huab cua, aerodynamics, hla txoj kev xav ntawm qhov sib xws. Cov txheej txheem yog muab los rau txhua qhov phenomena. Qhov tseem ceeb tshaj plaws yog tias muaj kev vam khom ntawm lawv qhov sib txawv. Lub ntsiab lus ntawm lub cev ntawm cov qauv zoo sib xws yog tshwm sim hauv kev nkag (formula) thiab cov ua ntejsuav. Feem ntau, cov txheej txheem, zoo li qee txoj cai, muaj npe tom qab cov kws tshawb fawb nto moo.
Study of heat transfer
Cov txheej txheem thermal zoo sib xws muaj ntau yam uas muaj peev xwm piav qhia txog cov txheej txheem ntawm kev hloov hluav taws xob thiab hloov hluav taws xob. Plaub yam uas nto moo tshaj plaws yog:
Reynolds similarity test (Re)
Cov mis muaj cov khoom nram qab no:
- s – cua sov ceev ceev;
- l – geometric parameter (loj);
- v - coefficient ntawm kinematic viscosity
Nrog kev pab los ntawm cov txheej txheem, kev vam khom ntawm lub zog ntawm inertia thiab viscosity yog tsim.
Nusselt test (Nu)
Nws suav nrog cov hauv qab no:
- α yog qhov hloov pauv cua sov;
- l – geometric parameter (loj);
- λ yog thermal conductivity coefficient.
qhov kev ntsuas no piav qhia txog kev sib raug zoo ntawm kev siv hluav taws xob hloov hluav taws xob thiab kev ua haujlwm ntawm lub coolant.
Prandtl kev ntsuas (Pr)
Cov mis muaj cov khoom nram qab no:
- v yog kinematic viscosity coefficient;
- α yog qhov coefficient ntawm thermal diffusivity.
qhov ntsuas no piav qhia qhov piv ntawm qhov ntsuas kub thiab qhov nrawm hauv qhov ntws.
Grashof criterion (Gr)
Cov mis yog tsim los siv cov kev hloov pauv hauv qab no:
- g - qhia qhov nrawm ntawm lub ntiajteb txawj nqus;
- β - yog tus coefficient ntawm volumetric expansion ntawm lub coolant;
- ∆T – qhia qhov txawvkub nruab nrab ntawm lub coolant thiab tus conductor.
qhov ntsuas no piav qhia qhov piv ntawm ob lub zog ntawm kev sib txhuam molecular thiab nqa (vim qhov sib txawv ntawm cov kua dej).
Nusselt, Grashof thiab Prandtl cov txheej txheem feem ntau yog hu ua cua sov hloov pauv zoo sib xws raws li lub rooj sib tham pub dawb, thiab Peclet, Nusselt, Reynolds thiab Prandtl cov txheej txheem raws li txoj cai yuam kev.
Kawm txog hydrodynamics
Cov txheej txheem hydrodynamic zoo sib xws tau nthuav tawm los ntawm cov piv txwv hauv qab no.
Froude zoo sib xws xeem (Fr)
Cov mis muaj cov khoom nram qab no:
- υ - qhia qhov nrawm ntawm qhov teeb meem ntawm qhov deb ntawm qhov khoom ntws ncig nws;
- l - piav qhia txog geometric (linear) tsis nyob ntawm qhov kev kawm;
- g - stands rau acceleration vim lub ntiajteb txawj nqus.
Qhov kev ntsuas no piav qhia qhov piv ntawm lub zog ntawm inertia thiab lub ntiajteb txawj nqus hauv cov khoom ntws.
Strouhal zoo sib xws xeem (St)
Tus qauv muaj cov hloov pauv hauv qab no:
- υ – qhia ceev;
- l - qhia txog geometric (linear) tsis;
- T - qhia lub sijhawm luv.
qhov kev ntsuas no piav qhia txog kev txav tsis tu ncua ntawm qhov teeb meem.
Mach similarity criterion (M)
Cov mis muaj cov khoom nram qab no:
- υ - qhia qhov nrawm ntawm qhov teeb meem ntawm ib qho tshwj xeeb;
- s - qhia qhov ceev ntawm lub suab (hauv kua) ntawm ib qho chaw tshwj xeeb.
Qhov kev ntsuas hydrodynamic zoo sib xws piav qhialub dependence ntawm lub zog ntawm cov teeb meem ntawm nws compressibility.
Cov ntsiab lus tseem ceeb hauv luv luv
Cov qauv zoo sib xws ntawm lub cev feem ntau tau teev tseg. Tsis muaj tsawg tseem ceeb xws li:
- Weber (Peb) - piav qhia txog kev vam khom ntawm cov quab yuam saum npoo av.
- Archimedes (Ar) - piav qhia txog kev sib raug zoo ntawm nqa thiab inertia.
- Fourier (Fo) - piav qhia txog qhov kev vam khom ntawm qhov hloov pauv ntawm qhov ntsuas kub, lub cev thiab qhov ntev ntawm lub cev.
- Pomeranttsev (Po) - piav qhia qhov sib piv ntawm qhov kev siv ntawm cov khoom siv hluav taws xob sab hauv thiab qhov ntsuas kub.
- Pekle (Pe) - piav qhia txog qhov piv ntawm qhov sib txawv ntawm cov cua sov thiab molecular hloov pauv hauv qhov ntws.
- Hydrodynamic homochronism (Ho) - piav qhia txog kev vam meej ntawm kev txhais lus (convective) acceleration thiab acceleration ntawm ib qho chaw.
- Euler (Eu) - piav qhia txog kev vam khom ntawm lub zog ntawm lub siab thiab inertia hauv qhov ntws.
- Galilean (Ga) - piav qhia qhov piv ntawm lub zog ntawm viscosity thiab lub ntiajteb txawj nqus hauv qhov ntws.
Zoo kawg
Cov qauv zoo sib xws tuaj yeem muaj qee qhov txiaj ntsig, tab sis kuj tuaj yeem muab los ntawm lwm cov qauv. Thiab xws li kev sib xyaw ua ke kuj yuav yog qhov ntsuas. Los ntawm cov piv txwv saum toj no, nws tuaj yeem pom tau tias lub hauv paus ntsiab lus ntawm qhov zoo sib xws yog qhov tseem ceeb hauv hydrodynamics, geometry, thiab mechanics, ua kom yooj yim rau txoj kev tshawb fawb hauv qee qhov xwm txheej. Cov kev ua tiav ntawm kev tshawb fawb niaj hnub no tau dhau los ua qhov ua tau zoo vim muaj peev xwm ua qauv txheej txheem nyuaj nrog qhov tseeb zoo. Ua tsaug rau txoj kev xav ntawm qhov sib xws, ntau tshaj li ib qho kev tshawb pom tau tsim, uas tom qab ntawd tau txais qhov khoom plig Nobel.
