+_HS by juanagao

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									                                  amocana abazanis Sesaxeb

onkanis saSualebiT abazanaSi yovel wuTSi Caedineba 30 litri wyali, ris Sedegadac abazana
ivseba 5 wuTSi. saangariSoa yovel wuTSi abazanidan gasuli wylis raodeneoba, Tu savse
abazana icleba 6 wuTSi.

misi amoxsna TiqTqos Zneli ar unda iyos. marTlac, saves abazanaSi iqneba 5x30=150l wyali,
xolo yovel wuTSi abazanidan gaeineba 150:6=25l wyali.

ganvixiloT aseTi amocana: abazana SemSvebi miliT ivseba 6 wuTSi, xolo savse abazana
gamSvebi miliT icleba 10 wuTSi. ramden wuTSi gaviseba carieli abazana orive milis erTdrouli
moqmedebiT?

arc am amocanis amoxsnaa, erTi SexedviT, Zneli. abazanSi yovel wuTSi Caedineba mTeli
moculobis 1/6, xolo gaedineba – 1/10. e.i. yovel wuTSi abazanaSi wyali matulobs 1/6-1/10=1/15
nawiliT mTliani moculobisa. advili misaxvedria, rom abazanis avsebas dasWirdeba 15 wuTi.

aRniSnul amocanas, odnav Secvlili saxiT, oriaTasi wlis istoria aqvs da miekuTvneba heron
aleqsandrielis cnobil amocanas abazanis Sesaxeb.

tradiciul amocanaSi daSvebuli Secdoma gamowveulia im mcdari daSvebiT, TiTqos abazanidan
wylis gamodineba xdeba mudmivi siCqariT da ar aris damokidebuli masSi wylis donis
simaRleze. sinamdvileSi ki wylis gamodinebis siCqare iangariSeba toriCelis formuliT
V=        sadac L wlis donea abazanaSi.

ganvixiloT zogadi saxis amocana: Sveuli kedlebis mqone marTkuTxa paralelepipedis formis
abazana ivseba T wuTSi, xolo daketili onkanis SemTxvevaSi saves abazana icleba t wuTSi.
ramden wuTSi aivseba carieli abazana SemSvebi da gamSvebi milebis erTdrouli moqmedebiT?

zogadi amoxsnis Semdeg ganvixiloT kerZo SemTxvevebi:

     a) T=8wT , t=12wT
     b) T=8wT , t= 8wT

     g) T=8wT , t=6wT

     d) T=30wT , t=5 wT

     e) t<<T Cadgeba Tu ara abazanSi cotaTi mainc wyali ?

     amocanis amoxsnisTvis SemovitanoT aRniSvnebi:

     H – savse abazanaSi wylis donis simaRle;

     T – H simaRlemde wylis avsebis xangrZlivoba;
t – savse abazanis daclis xangrZlivoba;

S – abazanis kveTis farTobi;

S0 - gamoSvebi milis kveTis farTobi;

V – abazanSi wylis donis erTeul droSi dawevis siCqare;

V0 _ abazanidan erTeul droSi wylis gamodinebis siCqare;

L – SemSvebi da gamSvebi milebis erTdrouli moqmedebisas wylis mudmivi done;

vTqvaT garkveul droSi wylis donem daiwia V-Ti, maSin abazanidan gaedineboda SV
moculobis wyali, rac tolia S0V0 wylis Wavlis moculobisa: SV= S0V0, saidanac V=(S0/S)V0
rogorc ukve avRniSneT, toriCelis formulis Tanaxmad, V0=        xolo meors mxriv
abazanaSi wylis donis mateba daketili gamSvebili milis SemTxvevaSi tolia H/T-si. wylis
done abazanaSi aRar Seicvleba, rodesac donis dawevis siCqare gautoldeba donis matebis
siCqares. e.i. H/T=(S0/S)x  . am formulidan vRebulobT abazanaSi wylis donis zRvrul
simaRles SemSvebi da gamSvebi milebis erTdrouli moqmedebisas: L =H2S2 / 2gT2S02

abazanaSi wylis donis daweva Tanabarcvladia, romelic iwyeba V siCqariT da mTavrdeba
nulovani siCqariT. aRniSnuli procesi mimdinareobs a aCqarebiT da V2=2aH, saidanac a=V2/
2H. Tu SevitanT aRniSnul formulaSi V=(S0/S)V0 mniSvnelobas da gavixsenebT, rom
V0=       , miviRebT: a= S02V02 / 2S2H = S02x2gH / 2S2H = gS02 / S2 radgan H=at2/2=
=gS02t2/2S2, t2=2HS2/gS02 , saidanac vRebulobT:L=H2S2/2gT2S02=Hx2HS2/4T2gS02=
=Ht2/4T2 sabolood gveqneba:

                                          L/H=t2/4T2




sainteresoa, rom wylis donis zRvruli simaRle ar aris damokidebuli arc avzis formasa da
kveTis farTobze, arc gamSvebi milis formasa da kveTis farTobze. ar aris igi damokidebuli
arc Tavisufali vardnis g aCqarebaze. nebismier planetaze wylis done abazanaSi igive iqneba,
rac dedamiwaze.

exla ganvixiloT kerZo SemTxvevebi:

a) T=8wT , t= 12 wT.

LL/H= 122/4x82=9/16
abazana aivseba mxolod 9/16 nawilis odenobiT da amis Semdeg ramden xansac ar unda
gagrZeldes abazanaSi wylis damateba, done aRar Seicvleba. (igivenairad ganixilav zemoT
moyvanl kerZo SemTxvevebs a)dan d)-mde ).

e) rodesac t<<T , maSin L/H-is mniSvneloba nulis toli iqneba mxolod or SemTxvevaSi:

1) t=0 , T ar udris 0-s. e.i. abazana icleba meyseulad, rac ararealuria.

2) t ar udris 0-s, T miiswrafvis usasrulobisaken , rac niSnavs, rom gamSvebi milis gadaketvis
SemTxvevaSi SemSvebi miliT abazanis avsebas sWirdeba usasrulod didi dro, rac tolfasia
imisa, rom igi daketilia. miviReT, rom Tu SemSvebi mili Riaa da abazana ar icvleba
meyseulad, L/H arasodes ar aris 0-is toli anu abazanaSi yovelTvis iqneba wylis garkveuli
done.

ra SemTxvevaSi SeiZleba aivsos abazana bolomde, to erTdroulad moqmedebSia SemSvebi
da gamSvebi milebi? advili misaxvedria, rom am dros L=H , e.i. t2/4T2=1 , saidanac t=2T ,
miviReT, rom Tu abazanis dacla 2-jer met xans grZeldeba, vidre avseba, abazana srulad
aivseba gamSvebi milis moqmedebis drosac.

sainteresoa agreTve im drois gamoTvla, romelic saWiroa mudmivi donis misaRwevad. unda
aRiniSnos, rom raime zRvrul donemde Sevsebas dasWWirdeba usasrulod didi dro, magram
Tu ganvixilavT saZebni donisagan gansxvavebul – nakleb dones, vTqvaT 0,99LLsaZ ,
maSin saZiebeli dro gamoiTvleba formuliT: t* 2,15 t2/T. Cveni monacemebis mixedviT
gveqneboda :



a) T=8wT , t=12wT             :     t* 39wT
b) T=8wT , t= 8wT            :     t*    wT

g) T=8wT , t=6wT         :        t*     wT

d) T=30wT , t=5 wT        :       t*    wT



rogorc avRniSneT , Tu t=2T, maSin t*




                                       integralebiT amoxsna

rogorc avRniSneT, abazanaSi wylis donis mateba daketili gamSvebi milis SemTxvevaSi
tolia H/T-is, xolo wylis donis dawevis siCqare mocemuli momentisTvis ki – (S0/S)         -is.
   Sesabamisad, wylis donis matebis siCqare mocemul momentSi iqneba : dx / dt = H/T-
   (S0/S)          , saidanac vRebulobT, rom dt = dx / (H/T-(S0/S)      ). dro romlis
   ganmavlobaSic wylis done miaRwevs x=h, avRniSnoT H-iT. miviRebt gantolebas:                    =
                                      marjvena gamosaxulebis integrirebisTvis SemovitanoT

   aRniSvna: H/T-(S0/S)             =y                                = dy ,            = (H/T –

   y)(S/S0)


   dx=                                           S2 da So2 arian S kvadratSi da S indeqsad 0

   kvadratSi )


                        =                                   =                             |0h =
   =                                                                            =


          S/gSo(         +(HS/TSo) ln (                ))


   mocemuli gamosaxuleba SeiZleba gamartivdes, viciT rom SV= S0V0 da V0=          ,
   miviRebT, rom abazanaSi wylis donis dawevis siCqare h simaRlidan abaanis daclisas tolia:
   V=dh/dt=V0S0/S=S0              /S e.i

   dt= (S/S0)         x dh/




                         -1/2
                              dh = h1/2/1/2 |oh = 2

t= - 2S     / So      =-S          / Sog
sabolood moviRebT:   HH= -t


sadac ar gvxvdeba abazanis da gamSvebi milis kveTis S da So farTebi es ukanaskneli miuTiTebs
imaze, rom abazanis avsebis dro nebismier planetaze unda iyos toli. THE END

								
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