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R.Jauschowetz: HERZ - Sistemi za grejanje toplom vodom - HIDRAULIKA_____________________________________________________________________________________________________

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Jauovec Rudolf (Jauschowetz Rudolf), Prof.Dipl.Ing.

HERZ - Sistemi za grejanje toplom vodom - HIDRAULIKAPriredio: Herz Armaturen Ges.m.b.H.Izdava: Herz d.o.o. - BeogradDizajn, Priprema, Grafika: Herz Armaturen Ges.m.b.HPrevod i adaptacija: Plum Design - Beograd (A.Jovanovi)

2004 Herz Armaturen Ges.m.b.H., Wien

HERZ - Sistemi za grejanje toplom vodom - HIDRAULIKA

Rudolf Jauschowetz

Wien: Herz Armaturen Ges.m.b.H., 2004Beograd: Herz d.o.o. 2005

Zabranjeno je pretampavanje, umnoavanje i kopiranje.Nije dozvoljeno pretampavanje ili kopiranje bilo kog dela knjige bez pismenog odobrenja Herz d.o.o. - BeogradCopyright 2005 Herz d.o.o by Herz Armaturen Ges.m.b.H., Wien 2004

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Predgovor autora

Osnovna pretpostavka za pravilan rad toplana i sistema daljinskog grejanja bazira se na ispravnomplaniranju i izvoenju hidraulinog podsistema. Ova knjiga ima za cilj pomo inenjerima, tehniarima iizvoaima radova u ostvarivanju optimalnih performansi sistema za daljinsko i centralno grejanje.

Sagledali smo sve relevantne standarde i tehnike preporuke. Pored toga, koriene su osnovne jednainetermodinamike i dinamike fluida, u meri u kojoj je to bilo neophodno.

Takoe su obraene sve bitnije komponente (ventili i pumpe) koje se koriste u praksi, tako da se pojasneosnovni principi funkcionisanja, primene i ugradnje. Prilikom izbora komponenti sistema preferirani suAustrijski proizvodi. Zahvaljujem ovom prilikom lektorima dipl.ing. Petru Jauovecu (Peter Jauschowetz,Pinkafeld) i prof. Rudolfu Hohvarteru (Rudolf Hochwarter) na sugestijama i strunoj korekturi. Takoese zahvaljujem kompanijama koje su nam ustupile ilustracije i slike koriene u ovoj knjizi. Specijalno sezahvaljujemo kompaniji HERZ Armaturen G.m.b.H, na ijem je elu direktor Dr. Glincerer (Dr.Glinzerer), bez ije pomoi ova knjiga ne bi bila realizovana.

Predgovor izdavaa

Upravo je poela trka za otkrivanje novih izvora energije. Suoena sa problemima iscrpljenja ogranienihenergetskih resursa, globalnog zagrevanja i ekolokog zagaenja, svest ljudi se mora otrezniti, morasagledati budunost i odluno krenuti u promene ponaanja. Permanentno poveanje cene energije nas

primorava da se ponaamo sve tedljivije. Tehnoloki napredak nam prua mogunost da razmenjujemoznanja i veoma brzo realizujemo svoje zamisli. HERZ je video svoju misiju u budunosti i krenuo uosvajanje proizvodnih tehnologija i integraciju sa informacionim sistemima sa samo jednim ciljem - upotpunosti izvriti funkciju i pritom optimalno utedeti. Ali, ne pridajmo preveliki znaaj tehnologiji ine dozvolimo da nam osnovni cilj bude udobnost. Imamo jedinstvenu priliku da pomerimo granice nae

civilizacije promenom ponaanja prema prirodi - razumevanjem pojava koje nas okruuju i na kojemoemo da utiemo.

Ova knjiga je zamiljena kao veza izmeu teorije i prakse, koja e pruiti inenjerima i tehniarima,projektantima i izvoaima informacije neophodne za razumevanje termodinamikih i hidraulikihzakonitosti primenjivih u konkretnim situacijama. Takoe je ova knjiga odlina dopunska literatura HERZ-ovom softverskom paketu za proraun sistema za grejanje i klimatizaciju.

Ovom prilikom se srdano zahvaljujem dipl.ing. Aleksandru Jovanoviu i apsolventu Mainskog fakultetaMilanu Jovanoviu na znaajnom zalaganju pri prevoenju ove knjige. Posebno se zahvaljujem direktorukompanije HERZ, gospodinu Dr Glincereru, koji je tritu Srbije i Crne Gore posvetio posebnu panju i

bezrezervno podrao izdavanje ove knjige, koja osim na Nemakom, za sada postoji jedino na Srpskomjeziku.

Radislav Omorac

Direktor HERZ d.o.o.Beograd 2005

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Oznake i jedinice1

Oznaka Jedinica Naziv

A m2 Povrina

c kJ.kg-1.K-1 Spec. toplotnikapacitet

D m Unutranji prenik

DN mm Nominalni prenik

h kJ.kg-1 Entalpija

D W.m-2.K-1 Koeficijent prelazatoplote

k, H m Hrapavost cevi

kv m3.h-1 Karakteristika

delimino otvorenogventila

kvs m3.h-1 Karakteristika

potpuno otvorenogventila

l m Duina cevi

m kg Masa

P W Snaga

p Pa=N.m-2 Pritisak

Q J Koliina toplote

q W.m-2 Gustina toplotnogfluksa

ql W.m-1 Redukovano toplotno

optereenje

qm kg.s-1 Maseni protok ( m

x

)

qv m3.h-1 Zapreminski protok (

x

V)

R Pa.m-1 Pad pritiska po metrucevi

1Jedinice koje se koriste u praksi prema ISO, EN i

NORM

Oznaka Jedinica Naziv

R m2.K.W-1 Toplotna otpornost

Re - Rejnoldsov broj

U W.m-2.K-1 Koeficijent prolaza toplote

W Nm Rad

w m.s-1 Brzina

Z,'pE Pa Pad pritiska na deonici

'p Pa Diferencijalni pritisak,

razlika pritisaka

'pR Pa Pad pritiska

'pV Pa Pad pritiska na ventilu

'Tln K Logaritamski temperaturniviak

'T K Temperaturni viak

'T K Temperaturna razlika (TV- TR)

), P W Toplotni fluks ( Q

x

)

K - Stepen iskorienja

O - Koeficijent trenja cevi

O W.m-1.K-1 Toplotna provodljivost

v m2.s-1 Kinematska viskoznost

TR C Temperatura u povratnomvodu (tR)

TV C Temperatura urazvodnom vodu (tV)

U kg.m-3 Gustina

9 - Koeficijent otpora

U

22w Pa Dinamiki pritisak po Prantl-u

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Prefiksi

P (Peta) 1.000.000.000.000.000 1015

T (Tera) 1.000.000.000.000 1012 (Bilion)G (Giga) 1.000.000.000 109 (Milijarda)M (Mega) 1.000.000 106 (Milion)k (Kilo) 1.000 103

h (Hekto) 100 102

da (Deka) 10 101

1d (Deci) 0,1 10-1 1/10c (Centi) 0,01 10-2 1/100

m (Mili) 0,001 10-3 1/1.000P (Mikro) 0,000.001 10-6 1/1.000.000

Vane konverzije

1 bar # 10 mWS = 100 kPa0,1 mbar = 1 mmWS = 10 Pa1 kcal # 4,2 kJ1 kcal = 4,1868 kJ | 4,2 kJ1 kWh # 3600 kJ

1 kcal/h = 1 kcal . h-1 = 4 2 1000

3600 116

, .

, W

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Sadraj:

HERZ - Sistemi za grejanje toplom vodom - HIDRAULIKA ...............................................8

1 Osnovni pojmovi..................................................................................................................... 81.1 Osnovi termodinamike.................................................................................................... 8

1.1.1 Zakon odranja energije.......................................................................................... 81.1.2 Prvi zakon termodinamike (za zatvoreni sistem)................................................... 81.1.3 Toplotni kapacitet Qi .............................................................................................. 81.1.4 Jednaina prvog zakona termodinamike................................................................. 81.1.5 SnagaP................................................................................................................. 91.1.6 Koliina predate toplote = Toplotni fluks )......................................................... 91.1.7 Maseni protokqm u zavisnosti od toplotnog fluksa ) .......................................... 91.1.8 Stepen korisnog dejstva K.................................................................................... 9

1.1.9 Efikasnost KN ....................................................................................................... 101.1.10 Prenos toplote........................................................................................................ 10

1.2 Osnovi mehanike fluida (Hidraulika) ........................................................................... 111.2.1 Jednaina kontinuiteta........................................................................................... 111.2.2 Dinamiki pritisakpd............................................................................................. 111.2.3 (Hidro) statiki pritisakpst .................................................................................. 121.2.4 Hidraulini i ekvivalentni prenik ........................................................................ 121.2.5 Rejnoldsov (Reynold) broj.................................................................................... 131.2.6 Trenje u pravim cevima ........................................................................................ 141.2.7 Koficijent trenja cevi u hidraulici ......................................................................... 141.2.8 Pad pritiska usled otpora trenja u cevovodu .........................................................15

1.2.9 Pad pritiska na regulacionim ventilima i izvrnim elementima upravljakogsistema 17

1.2.10 Karakteristika cevovoda (Karakteristika deonice)................................................ 191.2.11 Paralelna veza grana cevovoda............................................................................. 20

2 Cirkulacione pumpe .............................................................................................................. 242.1 Osnove, Pojmovi........................................................................................................... 24

2.1.1 Kapacitet pumpe ................................................................................................... 242.1.2 Potisna visina H .................................................................................................... 242.1.3 Kapacitet pumpe ................................................................................................... 242.1.4 Elektrina snaga pumpePel i stepen iskorienja pK ............................................ 24

2.1.5 Kavitaciona rezerva hidristatikog pritiska .......................................................... 252.1.6 Zakoni slinosti..................................................................................................... 252.1.7 Karakteristika pumpe i radna taka....................................................................... 262.1.8 Familija linija karakteristike ................................................................................. 26

2.2 Oblici linije karakteristike pumpe................................................................................. 272.2.1 Pumpe sa regulisanjem ......................................................................................... 28

2.3 Izbor pumpe i upotreba grejnih elemenata.................................................................... 292.4 Dizajn............................................................................................................................ 32

2.4.1 Ugradnja................................................................................................................ 333 Karakteristike radnog pritiska............................................................................................... 34

3.1 Raspodela pritiska u mrei............................................................................................ 34

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3.2 Ravnomerna raspodela pritiska prema Tihelmanu ....................................................... 364 Sistem za grejanje prostorija predavanjem toplote ...............................................................38

4.1 Granini uslovi.............................................................................................................. 384.2 Dimenzionisanje sistema za grejanje prostorija............................................................ 384.3 Proraunska temperatura............................................................................................... 384.4 Napomene za planiranje................................................................................................ 394.5 Osnove prorauna ......................................................................................................... 394.6 Grejni elementi kao izmenjivai toplote....................................................................... 404.7 Predavanje toplote preko grejnih tela ........................................................................... 42

4.7.1 Nominalni toplotni fluks....................................................................................... 424.7.2 Redukovano odavanje toplote grejnog tela........................................................... 42

5 Sistem za distribuciju toplotne enegrije................................................................................495.1 Proraun........................................................................................................................ 495.2 Smernice za planiranje i projektovanje......................................................................... 50

5.3 Distribucija toplotne energije u zgradama .................................................................... 516 Sistem za snabdevanje toplotnom energijom........................................................................ 52

6.1 Proraun sistema za snabdevanje toplotnom energijom.............................................. 526.2 Izaunavanje komponente grejanja prostorija .............................................................. 52

6.2.1 Potronja toplotne energije za objekat )n ............................................................ 526.3 Proraun zagrevanja pijae vode .................................................................................. 526.4 Sistemi za ventilaciju i klimatizaciju ............................................................................526.5 Drugi izvori toplote....................................................................................................... 536.6 Sistemi sa vie grejnih jedinica..................................................................................... 53

7 Regulisanje i hidraulini sistem............................................................................................ 547.1 Osnove, Pojmovi........................................................................................................... 54

7.1.1 ta je regulisanje? ................................................................................................. 547.1.2 Proraun i uslovi definisani prema NORM H 5012........................................... 547.1.3 ta je upravljanje?................................................................................................. 567.1.4 Termostatski regulator .......................................................................................... 577.1.5 Regulacioni ventili, karakteristika ventila ............................................................ 59

7.2 Regulisanje optereenja ................................................................................................ 607.2.1 Regulisanje meanja.............................................................................................. 617.2.2 Regulisanje protoka .............................................................................................. 62

7.3 Hidraulini cirkulacioni sistem i dimenzionisanje...................................................... 637.3.1 Regulisanje vodova............................................................................................. 64Povratna cirkulacija (distributivno cirkulaciono kolo) ....................................................... 667.3.2 Sistemi distribucije vode sa pravim ventilom..................................................... 687.3.3 Distributivni sistem sa trokrakim menim ventilom........................................... 707.3.4 Regulisanje dodavanja vode meanjem .............................................................. 727.3.5 Dvostruki meni sistem....................................................................................... 747.3.6 Kolo sa hidraulinim razvodnikom..................................................................... 76

7.4 Kriterijumi izbora regulisanja grejnog sistema........................................................... 787.4.1 Pravilno postavljanje senzora u prostoriji........................................................... 78Pravilno postavljanje spoljanjeg senzora .......................................................................... 797.4.2 Pravilno postavljanje spoljanjeg davaa temperature ....................................... 79

7.5 Regulacija niskotemperaturnih sistema za grejanje.................................................... 79

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8 Specijalne armature u sistemima za grejanje..................................................................... 818.1 Izbor kontrolnih elemenata ......................................................................................... 81

8.1.1 Izbor izvrnih organa .......................................................................................... 818.1.2 Izraunavanje parametara ventila na osnovu projektnih podataka ..................... 818.1.3 Odreivanje nominalne veliine (DN)................................................................ 83Karakteristika ventila.......................................................................................................... 83

8.2 Armature za hidrauliko balansiranje ......................................................................... 848.2.1 Ventil za regulisanje usponskih vodova ............................................................. 848.2.2 Regulator diferencijalnog pritiska....................................................................... 858.2.3 Prelivni ventil...................................................................................................... 858.2.4 Pretpodesivi termostatski ventili sa termostatskom glavom............................... 868.2.5 Izbor termostatskih ventila.................................................................................. 86Izbor i postavljanje senzora ................................................................................................ 87Izbor pumpe i generisanje buke .......................................................................................... 90

9 Dimenzionisanje cevovoda dvocevnih grejnih sistema...................................................... 919.1 Metoda izbora brzine .................................................................................................. 919.2 Metoda usvajanja srednjih gubitaka usled trenja........................................................ 929.3 Sila gravitacije u proraunima grejnih sistema sa vodom .......................................... 939.4 Proraun paralelno postavljenih mrea....................................................................... 93

9.4.1 Princip hidrauline ravnotee ............................................................................. 939.5 Cevovodi sa zadatom pumpom................................................................................... 949.6 Postupak dimenzionisanja cevne mree sa cirkulacionom pumpom.......................... 949.7 Radijatorski regulacioni ventili................................................................................... 969.8 Razvodnici i sabirai................................................................................................... 97

10 Dimenzionisanje cevovoda kod jednocevnih sistema..................................................... 98

10.1 Jednocevni zatvoreni sistemi grejanja ........................................................................ 9810.2 Specijalni ventili za jednocevne sisteme..................................................................... 103

11 Hidraulino balansiranje ................................................................................................. 10411.1 Pretpodeavanje radijatorskih regulacionih ventila .................................................... 10411.2 Regulisanje.................................................................................................................. 106

Regulisanje radnog kola...................................................................................................... 10612 Osiguranje kvaliteta ........................................................................................................ 10713 PRILOG .......................................................................................................................... 108

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Gde je grejanje tu je HERZ

R.Jauschowetz: HERZ - Sistemi za grejanje toplom vodom - HIDRAULIKA

Strana 8

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Strana 9


R

Jedinica: W (Vat) = J/s

1 Wjednak je ravnomernoj promeni energije za 1 J za

vreme od jedne sekunde.

Rad N.m = J 'XO

Snaga W Vat

1 W = 1 J/s = 1 Nm/s

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009.pdf 19.1.2006 11:49:06

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Slika 1-1 Temperaturna raspodela u izolovanom zidu sa (a) unutranjom i (b) spoljanjom izolacijom

Strana 10

1.1.9 Efikasnost

1.1.10 Prenos toplote

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posmatranom sistemu.

2WSRUSUHOD]XWRSORWHVDXQXWUDQMHSRYULQHMHR]QDHQsaRiDRWSRUSUHOD]XWRSORWHVDVSROMDQMHSRYULQHRe.

7RSORWD VH RGDMH SUHNR ]LGRYD SURFHVRP SURODHQMDWRSORWHNRMLMHQHRSKRGQRUD]XPHWL3URODHQMHWRSORWHVHRGUHXMHSUHNR

-HGQDLQD]DRGUHLYDQMHSUHQRVDWRSORWHNUR]JODWNL]LGYDL SRG SUHWSRVWDYNRP VWDFLRQDUQRJ MHGQRGLPHQ]LRQRJWRSORWQRJIOXNVD

=D YLHVORMQR JUDHYLQVNR NRQVWUXNWLYQR UHHQMHXNXSDQRWSRUSURODHQMX WRSORWH RGUHXMH VHNDR ]ELURWSRUDVYLKVORMHYD

7RSORWQL IOXNV NUR] JODWNL ]LG SUL VWDFLRQDUQLPXVORYLPD ]DYLVL RG SRYULQH ]LGD$ L UD]OLNH L]PHXXQXWUDQMH L VSROMDQMH WHPSHUDWXUH QH WHPSHUDWXUHSRYULQD]LGD

-RXYHNVXXXSRWUHELR]QDNHkumesto Ui umesto .RHILFLMHQW SURODHQMD WRSORWH8 VH GRELMD NDRUHFLSURQD YUHGQRVW RWSRUD SURODHQMX WRSORWHR. NaVOLFLSULND]DQMHUDVSRUHGWHPSHUDWXUDX]LGX

NRHILFLMHQWDSUHODHQMDWRSORWHiXQXWUDQMDNRQYHNFLMD

SURYRHQMDWRSORWHNUR]]LGGNRHILFLMHQWDSUHODHQMDWRSORWHeVSROMDQMDNRQYHNFLMD

ul

kor

NQ

Q

energijauloena

energijakorisnaH U

dRRRRei

ei ALAL

Gde su

R m2.K .W

-1otpor prolaenju toplote R =1/U

Ri m2.K.W

-1otporprelaenju toplote sa unutranje strane

RL m2.K.W

-1otpor svih slojeva prolaenju toploteR

=d/

Re m2.K.W

-1otpor prelaenju toplote sa spoljanje strane

Ai W.m

-2K

-1koeficijent prelaenjatoplote sa unutranje strane

Ae W.m-2K-1 koeficijent prelaenjatoplote sa spoljanje strane

d m debljina slojaL W.m-1K-1 koeficijent provoenja toploteU W.m2K koeficijent prolaenja toplote (ranije k)

Qx

& P

QQQ ') .L)(.A.UP eioo

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Strana 11


R

1.2 Osnovi mehanike fluida(Hidraulika)

-HGQDLQDNRQWLQXLWHWD

'LQDPLNLSULWLVDNSd

U prethodnoj jednaini su:

&o , Po W Prenos toplote, toplotni fluksU W.m

-2K

-1Koeficijent prolaenja toplote

A m2

Povrina zida

Q i K Unutranja temperaturaQ

e K Spoljanja temperatura

L=U.A W.K -1 Provodljivost

Pri stacionarnom proticanju fluida kroz cev maseniprotok je konstantan

8VOXDMXVWUXMDQMDQHVWLOMLYRJIOXLGDFRQVW]DSUHminski protok je konstantan.

3ULPLURYDQMXIOXLGSRVHGXMHVWDWLNLSULWLVDNUH]HUYRDUJDVDGRNSULNUHWDQMXLPDVWDWLNXVWUXMQXLGLQDPLNXkomponentu.

Zbir ova dva pritiska daje totalni ili zaustavni pritisak. PriNUHWDQMXDYLRQDQMHJRYYUKQMXNHWUSLWRWDOQLSULWLVDNMHUMH X WRM WDNLEU]LQDVWUXMDQMD IOXLGDMHGQDNDQXOL L VYDNLQHWLND HQHUJLMD SUHWYRUHQD X SRWHQFLMDOQX ]DSUDYR

SUHGVWDYOMDGLQDPLNXNRPSRQHQWXWRWDOQRJ]DXVWDYQRJSULWLVND

Jedinica mere za pritisak pMH3DVNDO3DVFDOu oznaci Pa1 bar = 103 mbar = 105 Pa

Stare jedinice:7HKQLNDDWPRVIHUDDW3D)L]LNDDWPRVIHUD

DWPDWN3D7RUU

%U]LQDIOXLGDXFHYLXQXWUDQMHJSUHQLND'L]UDXQDYDVHpreko obrasca

=DVOXDMSURPHQHSRYULQHSUHQLNDFHYLVDA1 doA2 kaoWRMHSULND]DQRQDVOLFLSULFRQVWYDLVOHGHDMHGQDLQD

-HGQDLQDNRQWLQXLWHWDVHPRH]DSLVDWLLXREOLNX

6OLND&HYSURPHQOMLYRJSRSUHQRJSUHVHND

Brzina strujanja obrnuto je proporcionalna promeniSRYULQHSRSUHQRJSUHVHND

.constA.w.qm R

.constA.wqv

P.D4.q

A

qw

2

vv

Pri emu je:

w m.s -1 BrzinaA m Povrina poprenog preseka ceviD m Unutranji prenik ceviq

v m3.s -1 Zapreminski protok

qm kJ.s-1

Maseni protok

2211v A.wA.wq

1

2

2

1

A

A

w

w

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R



Strana 12

Prantlov pritisak je:

6WUXMQLSULWLVDNVWDWLNDNRPSRQHQWDXNXSQRJSULWLVNDpri strujanju fluida kroz cevi deluje na zidove cevi,RGQRVQRSUDYDFVLOHNRMDMHSRVOHGLFDVWUXMQRJSULWLVNDQDSRYULQXFHYLQRUPDODQMHQDSUDYDFVWUXMDQMDIOXLGD3ULPLURYDQMXIOXLGDVWDWLNLSULWLVDNMHMHGQDN]ELUXSULWLVNDVWXEDWHQRVWLLSULWLVNDVLVWHPD

,]UDXQDWLSULWLVDNYRGHQRJVWXEDQDXQXWUDQML]LGFHYLako visina hRGVORERGQHSRYULQHWHQRVWLXRWYRUHQRPUH]HUYRDUXL]QRVLPVOLND

6DGUXJHVWUDQHQDVLVWHPGHOXMHDWPRVIHUVNLSULWLVDNNDR QDWSULWLVDN $WPRVIHUVNL SULWLVDN ]D PQDGPRVNHYLVLQHL]QRVLEDU

Napomena:PHWDUDYRGHQRJVWXEDVWYDUDKLGURVWDWLNLSULWLVDNRGP:VEDUN3D

Ukupni pritisak

2]QDDYDVHWDNRHNDR radni pritisakXPDLQVNLPVLVWHPLPD7R MH SULWLVDN X RGUHHQRM WDNL SULOLNRPUDGDVLVWHPD

.RGFHYLVDNUXQLPSRSUHQLPSUHVHNRPKLGUDXOLQLSUHQLNMHGQDNMHXQXWUDQMHPSUHQLNXFHYLdh = D

=DSRWUHEHSURUDXQDXVYRMLHPRGDVHVWUXMDQMHNUR]FHYLSURL]YROMQRJSRSUHQRJSUHVHNDRGYLMDSULEOLQRLVWRNDRLNRGFHYLNUXQRJSRSUHQRJSUHVHND

+LGUDXOLQLSUHQLN

=D FHYRYRGH L NDQDOH VD SRSUHQLP SUHVHNRP NRMLRGVWXSDRGNUXQRJYHRPDMHSUDNWLQRXVDJODVQRVWLVDRWSRULPDWXUEXOHQWQRJVWUXMDQMDXVYRMLWLKLGUDXOLQLHNYLYDOHQWQLSUHQLNdh

+LGURVWDWLNLSULWLVDNPHQMDVHOLQHDUQRVDSURPH

QRP YLVLQH h 6OLND 8NXSQL VWDWLNL SULWLVDNDSVROXWQLSULWLVDNMHGQDNMH]ELUXVWDWLNRJSULWLVNDpstiVSROMDQMHJSULWLVNDpo

+LGURVWDWLNLSULWLVDN

+LGUDXOLQLLHNYLYDOHQWQLSUHQLN

2

dw

2p

R

Ovde fiJuriu:

pd Pa

Dinamiki pritisak

R kg.m-3 Gustinaw m.s1 Brzina

pst

Sysst ph.g.p R

Ovde su:

pst Pa = N.m-2

Statiki pritisakR kg.m-3 Gustinag m.s

-2Ubrzanje zemljine tee = 9,81 m/s

2

h m Visina vodenog stubapsys Pa NP

2Pritisak u sistemu

'ph

ostukstppp

Gde su:

6OLND+LGURVWDWLNLSULWLVDN

ukstp Pa = Nm

-2Apsolutni pritisak

pst Pa = Nm-2

-2

Statiki pritisak

po Pa = Nm Atmosferski pritisak

rimer :P ,]UDXQDYDQMHDSVROXWQRJVWDWLNRJpritiska

h.g.pst R 1000 ,81 10 ,81 10 kJ P 2s2 ,81 10 Pa

0,81 Ear ~ 1Ear

bar94,1kPa1,194961,98

kPa96,0kPa1,98ppp ambstabs

stdtukup ppp

U

A4dh

Gde je:

dh P Hidraulini prenikA P2 Povrina poprenog presekaU P Obim cevi okvaen fluidom

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Strana 13


R

.RG FHYL VD SUDYRXJOLP SRSUHQLP SUHVHNRP SUDYRXJDRQLNVDVWUDQLFDPDa i bYDL

(NYLYDOHQWQLSUHQLN

(NYLYDOHQWQL SUHQLN dg VH QDMHH XSRWUHEOMDYD NRGSURUDXQDYD]GXQLKYRGRYDVDSUDYRXJDRQLPSRSUHQLPSUHVHNRP

(NYLYDOHQWQLSUHQLNdg VHSULPHQMXMHNDGDMHSR]QDWSDGSULWLVNDQSUSULOLNRPSURUDXQDGXLQDGHRQLFDXRNYLUXVLVWHPDNDQDOD]DNOLPDWL]DFLMXSRGYLVRNLPSULWLVNRP

.RULHQMHPRGJRYDUDMXHWDEHOHSUHNRdgQHRSKRGQRGLPHQ]LRQLVDQMHNDQDODSUDYRXJDRQRJSURILODPRHELWLL]YUHQRPQRJRMHGQRVWDYQLMH

5HMQROGVRY EURM MH EH]GLPHQ]LRQD YHOLLQD NRMRP MHRSLVDQD NDUDNWHULVWLND VWUXMDQMD IOXLGD 6WUXMDQMD XFHYRYRGXVXMHGQDNDDNRLPDMXMHGQDN5HMQROGVRYEURM

=DYUHGQRVWL5HMQROGVRYRJEURMD5HVWUXMDQMHMHODPLQDUQRWRMHVWUDVSRUHGEU]LQDVWUXMDQMDIOXLGQLKGHOLD

XQXWDUFHYLMHSDUDERORLGQRJREOLND

*GHMH

=DYRGX

=DXOMH]DJUHMDQMHHNVWUDODNR1D RVQRYX dh L WRWDOQH EU]LQH VWUXMDQMD IOXLGD SUHNRGLMDJUDPD]DSUDYRXJDRQLSRSUHQLSUHVHNRGUHXMHPRJXELWNHR XVOHGWUHQMDIOXLGDXFHYL

,]UDXQDWLPDVHQLSURWRNLKLGUDXOLQLSUHQLNFHYLGKXFHYRYRGX VD FHYLPD SUDYRXJDRQRJ REOLND GLPHQ]LMD[PP

=DNYDGUDWQLSRSUHQLSUHVHNGLPHQ]LMHaYDL

baab2

ba2

ab4d

h

aa4

a4d

2

h

3UDYRXJDRQLNDQDOVDKLGUDXOLQLPSUHQLNRPdh pravi isti otpor kretanjuIOXLGDNDRLFHYNUXQRJSRSUHQRJ

SUHVHNDVWYDUQRJXQXWUDQMHJSUHQLNDdhSULLVWLPEU]LQDPDVWUXMDQMDIOXLGD

.DQDOVDSUDYRXJDRQLPSRSUHQLPSUHVHNRPHNYLYDOHQWQRJSUHQLNDdgSUDYLJXELWNHSULWLVNDMHGQDNRNDRL

JODWNDFLOLQGULQDFHYSUHQLNDMHGQDNRJdgSULLVWRP]DSUHPLVNRPSURWRNX

A

qw vst v

Gde su

st vw ms1 Brzinaqv m

s1 Zapreminski protokA m

Referentna povrina poprenog preseka

riPer P &HYVDSUDYRXJDRQLPSRSUHQLPSUHVHNRP

DeElMiQa ]ida s = mmPopreQi preseN A = [ 5 = 1 mm = m

OEim U= + 5) = 184 mm = 184 m

m0435,0184,0

002,0.4

U

A.4dh

Pri sWvarQoM Er]iQi sWruMaQMa od w = m/s maseQi

q A wm R = 1 = 4 Ng/s= 144 Ng/K

proWoN e EiWi

5

33

5

33

52g

ba

ba27,1

ba

ba32d

P

1.2.5 Rejnoldsov (Reynold) broj

v

D.wRe

w ms1 Brzina strujanjaD m Unutranji prenik ceviv m s1 Kinematika viskoznost

1 C v = 111 ms1

8 C v = 71 ms1

C v = 1 ms1

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R



Strana 14

.DGD MH 5HMQROGVRY EURM SUHH YUHGQRVWRe = 2320,VWUXMDQMHSRVWDMH WXUEXOHQWQR 8 LQHQMHUVNLP SURUDXQLPD VHSRG WXUEXOHQWQLP VWUXMDQMHP VPDWUD NUHWDQMHIOXLGQLKGHOLDXUD]OLLWLPSUDYFLPDDSUREOHPVHUD]PDWUD NDR UDYDQVNL SURILO EU]LQD 5DVSRUHG EU]LQD MH

UDYQLMLWRMHYHL5HMQROGVRYEURM

=DSURUDXQSDGRYDSULWLVND IOXLGDXNUXQLPSUDYLPFHYLPDGXLQHONRULVWLVHL]UD]L]UD]

Tab. 1-2 $SVROXWQDKUDSDYRVWk]DUD]OLLWHFHYL

9UHGQRVWRXPa/mR]QDDYDSDGSULWLVNDSRPHWUXFHYLLWDNRHVHQD]LYDVSHFLILQLRWSRUWUHQMDFHYL1MHJRYHYUHGQRVWLVHSULND]XMXWDEHODUQRLOLSUHNRGLMDJUDPD

.RHILFLMHQWWUHQMDXFHYLLMHEH]GLPHQ]LRQDYHOLLQDL]DYLVLRGKUDSDYRVWLFHYLNXPPREOLNDVWUXMDQMDReLWHPSHUDWXUHIOXLGD

=D ODPLQDUQR VWUXMDQMH Re

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Strana 15


R

Dodatni gubici pritiska pri proticanju kroz armature,VSRMQLFHDSDUDWHLVOLQRPRUDMXELWLX]HWLXRE]LU2YLJXELFL VX SURSRUFLRQDOQL GLQDPLNRP SULWLVNX SULVUHGQMRMEU]LQLVWUXMDQMDLPRJXELWLRGUHHQLX]SRPRNRHILFLMHQWDRWSRUD3DGSULWLVNDVHWDGDL]UDDYDNDR

E3URWLFDQMHNUR]UDYX

3UROD]DN NUR] UDYX SRMDYOMXMH VH X VOXDMHYLPDSUDQMHQMD VPDQMHQMH LOL VQDEGHYDQMD SRYHDQMH5D]GHOMLYDQMHPLOLVDELUDQMHPPDVHIOXLGDXVWUXMDQMXNUR]RGYRGRGOLYLOLGRYRGSULOLYGROD]LGRJXELWDNDSULWLVNDJODYQRJWRND

.RHILFLMHQWRWSRUDVWUXMDQMX]DYLVLRGYLHIDNWRUD

2YL IDNWRUL PRUDMX ELWL X]HWL X RE]LU SUL RGUHLYDQMXYHOLLQHYUHGQRVWL

%U]LQDVHL]UDXQDYDSUHNRMHGQDLQHNRQWLQXLWHWDLOLVHRGUHXMHSRPRXSRGDWDNDL]WDEHOD

$UPDWXUHVSRMHYLUH]HUYRDULDSDUDWLLVOSURX]URNXMXgubitke usled trenja, odnosno gubitke usled promene

SUDYFD SURWLFDQMD L PRJX ELWL ]DMHGQLNL REXKYDHQLSUHNRNRHILFLMHQWDRWSRUD3RUHGWRJDPRUDELWLX]HWDX RE]LU EU]LQD VWUXMDQMD YLGHWL WDEHOX NRHILFLMHQWDORNDOQLKRWSRUDXSULORJX

,]SUDNWLQLKUD]ORJDXWDEHODPDVXQDYHGHQHSULEOLQHYUHGQRVWLRWSRUD

Nekoliko primera sistema sa lokalnim otporima

D'LVNRQWLQXLWHWSRSUHQRJSUHVHND

3DG SULWLVND VH X RVQRYL GHDYD SRG ]DMHGQLNLP

XWLFDMHP UD]OLLWLK EU]LQD NUHWDQMD IOXLGD L UD]OLLWLKSUDYDFDNUHWDQMDIOXLGQLKGHOLD

3UL L]UDXQDYDQMX JXELWDND SULWLVND PRUD VH REUDWLWLSDQMD QD NRML VH GLQDPLNL SULWLVDN RGQRVL YUHGQRVWkoeficijenta; na brzinu strujanja wLVSUHGUDYHLOLQD

brzinu strujanja wA XUDYL

3ULOLNRPVDELUDQMDSURWRNDYUHGQRVWLNRHILFLMHQWDPRJXELWLDNLQHJDWLYQHWRMHVWDNRVHSURWRNQDXOD]XVDVWRMLRGSURWRNDVDYHOLNRPHQHJLMRP*XELFLXUDYLmogu biti umanjeni konusnim prelazom i dodatno,

EROMLP]DREOMHQMHPVSRMDFHYLLUDYH5D]GHOMLYDQMHSURWRNDUDYRPXREOLNXNULYLQHNROHQD]DUD]OLNXRGUDYLSRGXJORPRGUH]XOWXMHXPDQMHQLPJXELFLPD

3RG QRUPDOQLP XVORYLPD YUHGQRVWL PRJX ELWLRGUHLYDQH VD VOLNH =D JXELWNH X UD]YRGQLNXNRHILFLMHQW]DVDELUQLNROHNWRUPRHVHXVYRMLWLGDMHGRNHRGJRYDUDMXLSRSUHQLSUHVHNELWLRGUHHQLWHUDFLMRP

*GHVX

Slika 1-5 Otpor usled proirenja cevi

1.2.8 Pad pritiska usled otpora trenja ucevovodu

Z

Z

Z

Z

Z

Z

Z

Z

$p Z wE ZR2

2

'pE Pa Pad pritiskausled lokalnih otpora (Z)

Z - Koeficijent otporaR kg.m-3 Gustina (za vodu R|1.000 kg.m-3)w m.s-1 Brzina

x 2d oblika poprenog preseka ceYi

x

kruni ili praYougaoni,x Karakteristika poprenog presekaA/AA odn A/AD,x Brzinske karakteristikew/wA odn w/wD,x Ugla raYanja B

2blika raYe npr konusna

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R



Strana 16

c) Kalorimetar:

Za merenje utroka toplotne energije koriste seNDORULPHWULNRMLVHXJUDXMXNRGSRWURDD3UHVYDNRJ

NDORULPHWUDXJUDXMHVHKYDWDQHLVWRDQD UDVWRMDQMXRG'GR'DL]DQMHJD'GR'$NRMHPRJXHSULOLNRP SRVWDYOMDQMD VHQ]RUD NRULVWLWL OXN VDSRWRSOMHQRP DXURP SRVWDYOMHQ VXSURWQR RG VPHUDVWUXMDQMD JUHMQRJ PHGLMXPD *XELWDN SULWLVND QDNDORULPHWUXGHNODULVDQMHXVSHFLILNDFLMLSURL]YRDD

d) Grejna tela:

=DSDGSULWLVNDQDFHYDVWLPLOLSORDVWLPJUHMQLPWHOLPDNRQYHNWRULPD VD PDORP EU]LQRP VWUXMDQMD JUHMQRJPHGLMXPDXVYDMDVHYUHGQRVW 3DGSULWLVNDQDJUHMQLPWHOLPDX3DL]QRVL

e) Cevi za podno i zidno grejanje3DG SULWLVND QD FHYQRM PUHL GXLQH O PRH ELWLL]UDXQDW9UHGQRVWL5 GDWH VX WDEHODUQR X WHKQLNRMGRNXPHQWDFLMLSURL]YRGD.

I,]PHQMLYDLWRSORWHNDORULIHULLVRODUQLNROHNWRUL

8RSWHQRYDL

3DGSULWLVND VHRGUHXMHL]WHKQLNHGRNXPHQWDFLMH

QD RVQRYX QRPLQDOQRJ ]DSUHPLQVNRJ SURWRND qN

6WYDUQL SDG SULWLVND SURSRUFLRQDODQ MH NYDGUDWXNROLQLND]DSUHPLQVNLKSURWRNDqv2

MHEU]LQDYRGHQDXOD]QRPSUHVHNXQSU'1SUHPD g1250 0 ]D FHYL VUHGQMH WYUGRH VDQDYRMHP D QH EU]LQD VWUXMDQMD X FHYL =D LVSUDYQRL]YRHQMH SURUDXQD SRWUHEQR MH SRVHEQR UD]PRWULWLVYDNLJUHMQLHOHPHQW*UHMQLHOHPHQWLVDL]X]HWQRPDOLPSRSUHQLP SUHVHNRP QDPHVWLPD SURWLFDQMDPHGLMXPDPRUDMXELWLX]HWLXRE]LUSDOMLYRQDRVQRYXGLMDJUDPDSURL]YRDD

Z

2

Hw.2.p

RZ'

wH

lRpFB '

'pN

vN

vN

q

qpp $$

6OLND.RHILFLMHQWRWSRUDUDYDNROHNWRU]DSUDYH7ILWLQJH

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Strana 17


R

,]PHQMLYD WRSORWH SUHPD SURL]YRDNRM VSHFLILNDFLMLL]D]LYDSDGSULWLVNDRGPSULQRPLQDOQRPSURWRNXRGPK3URQDLJXELWDNSULWLVNDQDL]PHQMLYDXSUL

SURWRNXRGP

/h.

3URPHQD SURWRND YRGH NUR] VLVWHP WDNRH L]D]LYDSURPHQXJXELWDNDSULWLVND3DGSULWLVNDQDUHJXODFLRQLPYHQWLOLPDLOLYHQWLOLPDVDSUHWSRGHDYDQMHPPRHELWLJUDILNL SULND]DQ QD GLMDJUDPX OLQLMRP SDGD SULWLVND6OLND

.DUDNWHULVWLNDYHQWLOD kvSULND]XMH]DSUHPLQVNLSURWRNYRGHqvXP.hSULNRPHGROD]LGRSDGDSULWLVND]DEDUSUHPD9',9'(

3DG SULWLVND QD YHQWLOX PRH ELWL L]UDXQDW SUHNRNRHILFLMHQWD RWSRUD VYHGHQRJ QD SRSUHQL SUHVHNRWYRUDYHQWLODNDR

3DG SULWLVND QH ]DYLVL RG SRSUHQRJ SUHVHND RWYRUDYHQWLODSULILNVQRMYUHGQRVWLNDUDNWHULVWLNHYHQWLODkvs.

Slika 1-7 Linija pada pritiska

1.2.9 Pad pritiska na regulacionim

ventilima i izvrnim elementima XSUDYOMDNRJVLVWHPD

Z

rimer 3 3DGSULWLVNDQDL]PHQMLYDXWRSORWH

22

vN

2vN2

2,3

52,1

q

qpp '' 2,93 m

V

v

v

p

qk

'

SUi 000zR nSU.OaNRXOje

V

vv

p

qk

'

R

kv -vrednost predstavlja protok krozregulacioni element u m3/h, koji priRGUHHQRMRWYRUHQRVWLYHQWLOD

(nominalna otvorenost H) izaziva padpritiska od 1 bar = 100 kPa.

kvs-vrednost se odnosi na otvorenostH100 ,to jest pri 100% otvorenosti ventila.

Zaqv=kvsi' p=EaUSaGSUiWiVNanavenWiOimaEiH

v

v

q

q

p

p

$$

SUiemXje

vs

vV

k

qp$ EaUJGejeqv X m/h iOi

'p qkV

v

vs

00

N3aVaqv X m/h

$p wq

kVv

vs

Z

R

0 X3a

GGeVX Z - Koeficijent otporaR kg.m-3 Gustinaw m.s-1 Brzina na ulazuqv m

3.h

-1Zapreminski protok

kvs m3.h

-1Karakteristika potpuno otvorenog ventila

'pV bar Pad pritiska na ventilu

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Strana 18

rimer :P Dimenzionisanje regulacionog ventila

rimer :P Pad pritiska na radijatorskim ventilima

Potrebno je izvriti izbor regulacionog ventila za padpritiska , pri protoku od qv.

Pad pritiska na ventilu = 5 kPa = 5.10-2 bar, protokqv= 1,5 m3/h

izabrana vrednost kvs = 6 (pogledati dijagram)

8NXSQLSDGSULWLVNDQDRGDEUDQRPYHQWLOXL]UDXQDYDse kao:

Odrediti pad pritiska radijatorskim ventilima za brzinustrujanja vode w u srednje mekim cevima prema DIN2440 (NORM M 5611).

$NRMHPHGLMXPYRGDRQGDYDL

=D GUXJH WLSRYH SULNOMXDND QSU RG SODVWLNH SDGpritiska se mora odrediti preko kv-vrednosti.

2LWDQHYUHGQRVWLSRMHGLQDQLKRWSRUDXRYRPVOXDMXne mogu biti primenjene.

3URUDXQ]Dqv = 500 l/h = 0,5 m3/h: pad pritiska naventilu iznosi:

3DGSULWLVNDQDGHRQLFLVDNRQVWDQWQLPSRSUHQLPpresekom.

3DG SULWLVND QD GHRQLFL GXLQH l sastoji se od padapritiska usled trenja fluida u cevi i lokalnih otpora.

1DSULPHU]DYLVQRVWPRHPRLVND]DWLSUHNRMHGQDLQH

$pV

$pV

7,610.5

5,1

p

qk

2V

vV '

m3/h

7,53,6

5,1

100k

q

100p

22

vs

v

V

' kPa

22

Vw.500w

2p Z

RZ ' u Pa

Herz AS; Nr. 6823 dimenzija 1 = DN 25kvs = 8,2

37,02,8

5,0100

k

q100p

22

vs

vV

' kPa

=DVYDNXGHRQLFXFHYRYRGDYDLGDMHSUL

LVWRPSUHQLNXFHYLMHGQDNSURWRN

Padovi pritiska su proporcionalnikvadratu zapreminskih protoka

22

E21

w2

w2

.D

l

pl.Rppp

RZ

RL

''

Ovde su:

L - Koeficijent trenja cevil m Duina ceviD m Unutranji prenik ceviR kg.m-3 Gustinaw m.s-1 BrzinaZ - Koeficijent otporaR Pa . m

-1Pad pritiska po metru cevi

$p Pa Pad pritiska'pE Pa Pad pritiska usled lokalnih otpora

2

1v

2v

1

2

q

q

p

p

'

'

Gde su:

'p Pa Pad pritiskaqv1 m

3.s

-1Zapreminski protok pri ' p1

qv2 m3.s

-1Zapreminski protok pri p2

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Strana 19


R

Ovde su:

$p Pa Pad pritiskaR kg.m-3 Gustinaw m.s-1 BrzinaZ - Koeficijent otporaL - Koeficijent trenja cevil m Duina cevi

A m2

Povrina poprenog preseka

D m Unutranji prenik ceviqv m

3.s


K Pa.s2.m

-6Konstanta cevne mree

'pV Pa Pad pritiska na regulacionom ventilu$pst Pa Hidrostatiki pritisak

g m.s-2

Ubrzanje zemljine tee = 9,81 m.s-2

H0 mWS Visina vodenog stuba

1.2.10 Karakteristika cevovoda(Karakteristika deonice)

Karakteristika cevovoda je kriva koja prikazuje vezuL]PHXSDGDSULWLVNDLRGJRYDUDMXHJSURWRND7RVOHGL

iz %HUQXOLMHYHMHGQDLQHRGUDQMDHQHUJLMH

3ULRGUHHQRPSRYHDQMXSURWRNDQHPLQRYQRGROD]LGRSRGL]DQMD QLYD YRGH X VLVWHPX 2YR L]D]LYD SRUDVWKLGURVWDWLNRJSULWLVNDNRMLPRUDELWLVDYODGDQGRYLVLQH

H0SRUHGRVWDOLKRWSRUDXVLVWHPX

.DUDNWHULVWLND VLVWHPD ]D RWYRUHQL VLVWHP SRND]XMHNRPSRQHQWX KLGURVWDWLNRJ SULWLVND NRMD PRUD ELWLVDYODGDQDSXPSRP]DYLVLQXYRGHQRJVWXEDHo

1DVOLFLSULND]DQDMHOLQLMDNDUDNWHULVWLNHRWYRUHQRJVLVWHPD 3DUDEROLNL REOLNNULYH ]D UD]OLLWH YDULMDQWHSRGHDYDQMD SULJXHQMD RG SRLQMH VWDWLNRPNRPSRQHQWRPSULWLVND

6LVWHP JUHMDQMD X ]DWYRUHQRPVLVWHPX FLUNXODFLMH QDSULPHULPDNRQVWDQWQXNROLLQXYRGHNRMDVHSRPRXSXPSHNUHHNUR] VLVWHPRGERMOHUDGRJUHMQLK WHODD]DWLPSUHNRVLVWHPDFHYLYUDDL]JUHMQLKWHODXERMOHU

stv

2ppw

2D

l.p '''

RZ

L

0stH.g.p '' R

3DGSULWLVNDXFHYQRMPUHL

*XELFL SULWLVND X FHYQRM PUHL PRJX VH RGUHGLWL QDRVQRYXRSRUDWUHQMDXFHYRYRGXLSR]QDYDQMDORNDOQLKSDGRYDSULWLVNDQDUHJXODFLRQLPYHQWLOLPD

-HGQDLQDNRMDRSLVXMH]DWYRUHQLVLVWHPJODVL

.ULYD MH SDUDEROD GUXJRJ UHGD L YUHGQRVWL PRJX ELWLRLWDQHVDGLMDJUDPDQDVOLFL

Slika 1-8 Karakteristika sistema

Slika 1-9 Karakteristika otvorenog sistema

2

v2

2v

22

q.KA

q

2D

l

w.2

w.2D

lp

RZL

RZ

RL'

$Ho

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Strana 20

1.2.11 Paralelna veza grana cevovoda

.UR] VLVWHP SUROD]L WDQR RQROLNR YRGH NROLNRLVSRUXXMH SXPSD 1LMH RG ]QDDMD SRYHDQMH QLYRDYRGH X VLVWHPX MHU H YLVLQVND UD]OLND VLJXUQR ELWLVDYODGDQD 3RG XWLFDMHP JUDYLWDFLRQH VLOH RKODHQDYRGDVHXERMOHUYUDDWHHVDPQRJRYLHRWSRUDQHJR

WRYUXDYRGDGROD]LGRJUHMQLKWHOD

8WLFDM VLOH ]HPOMLQH WHH X]LPD VH X RE]LU VDPR DNR]QDDMQRXWLHQDQDSRUSXPSH7DNDYVOXDMVHPRHMDYLWL SUL YUOR QLVNRP UDGQRP SULWLVNX SXPSH LOL XVLVWHPLPD ]D JUHMDQMH YLVRNLK ]JUDGD 8 ]DWYRUHQLPVLVWHPLPDNDUDNWHULVWLNDPUHHSUROD]LNUR]QXOWXWDNX0RHELWLQLDSULPDQMHPSULWLVNXSXPSHLNRGVLVWHPDXYLVRNLP]JUDGDPD

=D]DWYRUHQLVLVWHPSDUDEROLQDNDUDNWHULVWLNDVLVWHPDSUROD]LNUR]QXOWXWDNX2YRMHSULND]DQRQDVOLFL.DUDNWHULVWLNDFHYRYRGDSRND]XMHX]DMDPQX]DYLVQRVW

L]PHXSULWLVNDL]DSUHPLQVNRJSURWRNDXFHYQRMPUHL3ULVQDEGHYDQMDVLVWHPDVDPRMHSULWLVNDSRWUHEQRDSULNROLLQHSRWUHEQRMHVDPRLWG

8 UDGQLP GLMDJUDPLPD SURL]YRDD SXPSL YHRPDHVWRVXNDUDNWHULVWLNHFHYRYRGDSULND]DQHNDRIDPLOLMDNULYLKLOLVXSUHGVWDYOMHQHNDRSUDYHOLQLMHXORJDULWDPVNRPNRRUGLQDWQRPVLVWHPX

6LVWHP ]D JUHMDQMH IXQNFLRQLHSRG UD]OLLWLPUDGQLPXVORYLPD WRNRP JUHMQH VH]RQH6YDNRP RG XVORYDSULSDGDRGJRYDUDMXDNDUDNWHULVWLNDPUHH.DUDNWHULVWLNDSRND]XMHRWSRUHRWYRUHQRJYHQWLODSULSURPHQOMLYRPSURWRNX8VLVWHPLPD]DJUHMDQMHMHXRELDMHQR

GDUDGHLVSRGQRPLQDOQRJRSWHUHHQMDQSUSULXSRWUHELWHUPRVWDWVNLKYHQWLOD7DGDGROD]LGRSRYHDQMDRWSRUD

6LVWHP ]D JUHMDQMH IXQNFLRQLHSRG UD]OLLWLPUDGQLPXVORYLPD WRNRP JUHMQH VH]RQH 6YDNRP RG XVORYDSULSDGDRGJRYDUDMXDNDUDNWHULVWLNDPUHH

.DUDNWHULVWLNDSRND]XMHRWSRUHRWYRUHQRJYHQWLODSULSURPHQOMLYRP SURWRNX 8 VLVWHPLPD ]D JUHMDQMH MHXRELDMHQMHUDGLVSRGQRPLQDOQRJRSWHUHHQMDQSUSULXSRWUHEL WHUPRVWDWVNLK YHQWLOD 3UL WRPH GROD]L GRSRYHDQMDRWSRUD

3ULUDWDMNULYHHVHSRYHDYDWLVDSRUDVWRPSURWRNDWMVD XGDOMDYDQMHPRG QXOWH YUHGQRVWL L WHL YHUWLNDOQRMOLQLML

8 KLGUDXOLNL SDUDOHOQR SRYH]DQLP JUDQDPD SURWRNYRGHVHPRHSRGHOLWLQDGYHNRPSRQHQWHSURWRNDqm1 iqm2 5DVSRGHOD VH YUL SURSUFLRQDOQR X VNODGX VD

SDGRP SULWLVND QD GHRQLFL RGQRVQR 5D]OLFLSULWLVDNDRGJRYDUD UD]OLNDSULWLVDNDXYRUX.''$RGQRVQR%

,]MHGQDDYDMXL RYH YUHGQRVWL UD]OLNH SULWLVDND QDGHRQLFDPDMHGQDLQDJODVL

2YD UDYQRWHD LPD SRWSXQX DQDORJLMX VD HOHNWULQLPVLVWHPLPD

1DVYDNRMRGGHRQLFDYDL

Slika 1-9 Karakteristika otvorenog sistema

$

$

p K q

p K q

m

m

KDD p K q K qm m $

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Strana 22

rimer :P Paralelno vezivanje grejnih tela

Vezivanje dva grejna elementa izvreno je kao to jeSULND]DQRQDVOLFL 'YDJUHMQDWHODVXSULNOMXHQDparalelno i odnos pritisaka se regulie preko regulacionihventila.

,]UDXQDYDQMH]DSUHPLQVNRJSURWRND

Odabran je radijatorski ventil HERZ TS 98V, dimenzije ".Pad pritiska na radijatorskom ventilu na grejnom telu 1:

0RH VH XRLWL GD H SDG SULWLVND UH]XOWRYDWLprekomernim zagrevanjem elementa 1 za razliku odHOHPHQWDWDNRGDH]DSRWUHEHSURUDXQDELWLXVYRMHQRda je ventil 1 potpuno otvoren. Radijatorski ventil 2 je

potrebno podesiti prema razlici pritisaka u granama A i A'

Grejni element 1:Snaga grejnog tela = 1600WPad pritiska pri prolasku medijuma kroz grejno teloA-A ' = 250Pa

Grejni element 2:Snaga grejnog tela = 800WPad pritiska pri prolasku medijuma kroz grejno teloA-A ' = 60Pa

Temperaturna razlika 10 K

Dva radijatorska ventila dimenzije " potrebno jepodesiti tako da padovi pritiska na deonicama budupodjednaki.

Slika 1-13 Dva paralelno vezana grejna tela

&1

2

11

1

1

1

1v

h.kg8,136s.l038,0

s.kg038,010.kg.s4200

1600

.cq

Q')

11

1

1

2

2v

h.kg4,68s.l019,0

s.kg019,010.kg.s4200

800

.cq

Q')

15001 ' HRvp Pa pri potpunootvorenom ventilu.

Pad pritiska na radijatorskim ventilima:

$pHRv 2 : 21 pp $$

250 Pa + 1500 Pa =60Pa+ $pHRv2

$pHRv2 = 1690 Pa

VE = 5

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Slika 1-14 HERZ TS-98-V "

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Strana 24

2.1.1 Kapacitet pumpe

2.1.3 Kapacitet centrifugalne pumpe

(OHNWULQDVQDJDSXPSHPel i VWHSHQLVNRULHQMD

3RWLVQDYLVLQD+

Cirkulaciona pumpa za grejanje ima ulogu transportatople vode u zatvorenom sistemu grejanja, npr. topla vodaL]NRWODGRYRGLVHGRJUHMQLKWHODD]DWLPVHRKODHQDYUDDQD]DGXNRWDR

Kapacitet centrifugalne pumpe je koristan protokostvaren radom pumpe.

.DSDFLWHWSXPSHMHNRULVWDQSURWRNLVSRUXHQNUR]L]OD]QLSRSUHQLSUHVHNRGYRGDSXPSH.DSDFLWHWSXPSHXVLVWHPXVHL]UDXQDYDSUHPDHPLVLMLtoplote na strani korisnika i toplotnim gubicima pridistribuciji.

Napomena:8 LQHQMHUVNLP SURUDXQLPD PRH VH XVYRMLWL GD MHgustina vode 1000 kg/m3.

3RWLVQDYLVLQD+MHYLVLQDGRNRMHMHSXPSDXPRJXRVWLda podigne vodeni stub, odnosno, slobodnu povrinuWHQRVWL-HGLQLFDPHUHMHPHWDUYRGHQRJVWXED

(OHNWULQDVQDJDSRJRQDSXPSH

=DHOHNWULQLSRJRQFLUNXODFLRQHSXPSHYDL

2. Cirkulacione pumpe

QR '))

..c

q VHv

Gde su:

H) W Predat toplotni f luks

V) W Toplotni gubiciQ' K Razlika temperatura u potisnom

i povratnom vodu

c kJ.kg-1

K-1

spec. toplotni kapacitet

(voda c= 4,196 kJ . kg-1K-1)R kg.m-3 gustina (Voda pri 80C ima

gustinu R = 971,6 kg.m-3)

g

ZRlH

.

).(

R

Gde su:

l m Duina cevovodaR [Pa/m] Pad pritiskaZ [Pa] Lokalni otpor cevovoda

R kg.m-3 gustina (Voda pri 80CR = 971,6 kg.m-3)

g m.s-2

Ubrzanje Zemljine tee = 9,81 m.s-2

P g q Hv R. . .

Ovde su:

qv m3.s

-1Zapreminski protok (V

x

)P W Snagag m.s

-2Ubrzanje Zemljine tee = 9,81 m.s-2

R kg.m-3 GustinaH mWS Potisna visina

pH

Pq p

el

v p

ges

.'

H

Hges

= HM . HP0,40 ... 0,60 male pumpe0,60 ... 0,75 srednje pumpe0,75 ... 0,85 velike pumpe

0,50 ... 0,60 E-motor

Ukupan- stepen iskorienja pumpe

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Strana 25


R

.DYLWDFLRQD UH]HUYD KLGURVWDWLNRJ SULWLVND + 136+1HW 3RVLWLYH6XFWLRQ+HDG MHGQDND MHKLGURVWDWLNRPSULWLVNX YRGHQRJ VWXED VYHGHQRJ QD SRSUHQL SUHVHNL]OD]QHJUDQHSXPSH

8]RGJRYDUDMXHDSURNVLPDFLMH]DVYDNXSXPSXPRJXHMHSULPHQLWLVOHGHL]DNRQ]DNRQSURSRUFLRRQDOQRVWLLOLVOLQRVWL

$SVROXWQDYLVLQDXOD]QHJUDQHPRUDELWLYLDRG136+SUHPD SUHSRUXNDPD SURL]YRDD SXPSH NDNR EL VHL]EHJODNDYLWDFLMDSXPSH

6OLND8NXSDQVWHSHQLVNRULHQMD

2.1.5 Kavitaciona rezerva KLGURVWDWLNRJSULWLVND

=DNRQLVOLQRVWLOvde sX:

qv m3.s


'pp Pa Ukupni pritisak 1mVS = 10 kPaHges - Stepen iskorienja = H HM P

sd2

s

2

dstd hhg2

ww

g.

ppH

R

Ovde sX:

pd Pa Dinamiki pritisakpst Pa Statiki pritisakR kg.m-3 Gustinag m.s

-2Ubrzanje Zemljine tee = 9,81 m.s

-2

wd m.s-1

Brzina u izlaznoj grani

ws m.s-1

Brzina u ulaznoj grani

hd m Geostacionarna visina izlazne granehs m Visina ulazne grane

3rotoN Me SroSorcionalan EroMX oErta:

2

1

2

1

n

n

V

V

3otisna visina Me SroSorcionalna NvadratXEroMa oErta:

2

2

1

2

1

n

n

H

H

EleNtrino oStereenMe Me SroSorcionalnotreeP steSenX EroMa oErta:

3

2

1

2lE

1lE

n

n

P

P

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Strana 26

Slika 2-2 Karakteristika pumpe

6OLND5DGQDWDND

Slika 2-4 Karakteristika pumpe sa tri brzine rada

Linija karakteristike pumpe SRND]LMH YH]X L]PHXprotoka i pritiska pri konstantnom broju obrta pumpe.2GUHXMH VHSULOLNRP LVSLWLYDQMDQDSUREQLPVWRORYLPD

priguivanjem protoka i unosi na krivu priguenja.Zatvaranjem ventila ostvaruje se protok jednak nuli, aSULWLVDNLPDPDNVLPDOQXYUHGQRVWLWDGDVHSRVWLHQXOWDSRWLVQDYLVLQD2YDYUHGQRVWMH YUORHVWRR]QDHQDQDSXPSL ,VSRG UDGQH WDNH VH QDOD]L SUHVHQD WDNDkarakteristike sistema i karakteristike pumpe.

U cilju jednostavnijeg podeavanja pumpe premaUD]OLLWLP FHYRYRGLPD LLOL UDGQLP XVORYLPD SXPSHLPDMXRGJRYDUDMXHIDPLOLMHOLQLMDNDUDNWHULVWLNH1DWDMQDLQVHVPDQMXMHEURMWLSRYDSXPSL6DYUHPHQHSXPSHLPDMXWULEU]LQHUDGDSULHPXMHQDMPDQMDEU]LQDMHGQDND

50% maksimalne brzine.

.DUDNWHULVWLNDSXPSHLUDGQDWDND

2.1.8 Familija linija karakteristike

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R

Slika 2-5 Strma i blaga linija karakteristike pumpe

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Strana 28

2.3.1 Redno i paralelno vezivanje pumpi

(OHNWULQDUHJXODFLMDUDGDSXPSH

7LSRYLUHJXODFLMH

7LSRYLUHJXODFLMH8] WR PRHPR XRLWL UHJXODFLMXSURPHQRP GLPHQ]LMDLPSHOHUDUHJXODFLMRPREUWDQMDLVNOMXLYDQMHPSXPSHXJUXSL YLH SXPSL LOL SDN NRQWLQXDOQR UHJXODFLMRPSURPHQRP IUHNYHQFLMH 8SUDYOMDQMH SUHNR SURPHQDIUHNYHQFLMHYULVHIUHNYHQWQLPUHJXODWRURP

8]UHODWLYQRPDOLSURWRNSRWLVQDYLVLQDVH NRULHQMHPGYHSXPSH ]QDDMQR SRYHDYD X ]DYLVQRVWLRGQDLQDSRYH]LYDQMD.DUDNWHULVWLNHVXSULND]DQHQDLOXVWUDFLML

6OLND1DLQLVSUH]DQMDGYHMXSXPSL

3UL L]ERUX WUHEDOR EL GRQHWL RGOXNX SUHPD NRMRM VHRVWYDUXMH RSWLPDOQD HILNDVQRVW X UDGQRP RSVHJX6YDNDNR VH PRUDMX REH]EHGLWL GRYROMQH SHUIRUPDQVHSRJRQVNRJPRWRUDNDNRELVHL]EHJORSUHRSWHUHHQMH

.DYLWDFLRQD UH]HUYD KLGURVWDWLNRJ SULWLVND PRUD ELWLGRYROMQR YHOLND NDNR EL VH L]EHJODNDYLWDFLMD SXPSH2YDNYLP QDLQRP XSRWUHEH SUL RGJRYDUXHPRSWHUHHQMXRVWYDUXMHVH]QDDMQDXWHGD7DNRHVHPRHL]EHLSRMDYDEXNH

HVWR PRH ELWL SRWUHEQD YHOLND SRX]GDQRVW X UDGXVLVWHPD LOL ]DKWHYDQD UH]HUYDVQDJHX VLVWHPX7DGD VHNDRUHHQMHQDPHHNRULUHQMHGYHMXLOLYLHSXPSL

3ULQXOWRMSRWLVQRMYLVLQL9QSUDNRVXGYHSXPSHVSUHJQXWHNDRWRMHSULND]DQRQDVOLFL]DWYDUDQMHPYHQWLODSRVWLHVHGYRVWUXNDSRWLVQDYLVLQD

5HJXODFLMDWLSDSF.RG UHJXODFLMH WLSDSF YUL VH NRQVWDQWQD NRQWURODGR]YROMHQRJ RSVHJD SURWRND SUHNR SRGHHQH YUHGQRVWLGLIHUHQFLMDOQRJSULWLVND+V

5HJXODFLMDWLSDSY3UL UHJXODFLML WLSD SY SURPHQD HOMHQH YUHGQRVWLGLIHUHQFLMDOQRJ SULWLVND YUL VH HOHNWURQLNRP SUL HPXPRHELWLRGUDQDOLQHDUQDNDUDNWHULVWLNDL]PHX+VL+VHOMHQDYUHGQRVWGLIHUHQFLMDOQRJSULWLVND+PHQMDVHVDSURPHQRPSURWRND4

3ULODJRDYDQMH SXPSH VLVWHPX ]D JUHMDQMH UHJXODFLMRPEU]LQHSRJRQVNRJPRWRUD8VLVWHPX]DJUHMDQMHVDPRMHWRNRPQHNROLNRGDQDX

JRGLQL SRWUHEQR SXQR DQJDRYDQMH SXPSH SD VWRJD X]DYLVQRVWLRGWLSDUHJXODFLMHSXPSDXRVWDORPSHULRGXPRH UDGLWLSUL VPDQMHQRPEURMXREUWD7DGDMH XOD]QDVQDJDGDOHNRPDQMD

'DQDVVHXSRQXGLPRJXSURQDLVDYUHPHQHNRPSDNWQHHOHNWURQLNLUHJXOLVDQHSXPSH6HWVHVDVWRMLRGSXPSHPRWRUD IUHNYHQWQRJ SUHWYDUDD NDR L VYHJD WR MHQHRSKRGQR ]D RSVOXLYDQMH =DGDYDQMH HOMHQLKRSHUDWLYQLK YHOLLQD RVWYDUXMH VH SUHNR NRQWUROQRJLQWHUIHMVD QD GLVSOHMX 2VQRYQD NDUDNWHULVWLND RYLKXUHDMDMHYLVRNDRSHUDWLYQRVW

)UHNYHQWQL NRQWUROHUL RGQRVQR IUHNYHQWQL SUHWYDUDLLPDMX SUHGQRVW MHU SUXDMX PRJXQRVW NRQWLQXDOQHUHJXODFLMH

(OHNWULQDHILNDVQRVW6PDQMHQMHP UDGD KLGUDXOLQRJ VLVWHPD VPDQMXMH VHDQJDRYDQD HOHNWULQD HQHUJLMD 2YR LPD XWLFDMD L QDVPDQMLYDQMHEXNHSULUDGX

0RJXQRVWLUHJXOLVDQMDVQDJH

x SUHNo SUomHQH SoOoYDx SUHNo SUomHQH NDOHmoYDx HOHNtUoQVNL, SomoX IDzQH NoQtUoOH

tLULVtoUD

x HOHNtUoQVND NoQtUoOD SomoX IUHNYHQtQoJSUHtYDUDD

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Strana 29


R

6D GUXJH VWUDQH SUL UDGXEH] RWSRUD + SXPSHQHPRJX ]DMHGQR RVWYDULWL PDNVLPDOQL SURWRN YH VDPRSRMHGLQDQR

$NRMHSRWUHEQRSRVWLLYHOLNLSURWRNVDUHODWLYQRPDORPSRWLVQRP YLVLQRP SUHSRUXOMLYR MH NRULHQMH YLHSDUDOHOQR YH]DQLK SXPSL 6SUH]DQMHP GYH LGHQWLQHSXPSH GRELMD VH VLVWHP VD SRWSXQR QRYLPNDUDNWHULVWLNDPDWRMHSULND]DQRQDVOLFL

6D GLMDJUDPD NDUDNWHULVWLNH JUHMQRJ WHOD YUHGQRVWL VHRLWDYDMX VDPR SUL SURWRNX EH] SULWLVND + NDGDGROD]L GR XGYRVWUXHQMD SURWRND 6OLQR VLWXDFLML VDUHGQRPYH]RPREHSXPSH]DMHGQRQHPDMXYHXSRWLVQXYLVLQXXGXJLPUDGQLPWDNDPD

.DNRVHHILNDVQRVWJUHMQRJHOHPHQWDPHQMDVDSURPHQRPSURWRNDNRML GROD]LGR JUHMQLKHOHPHQDWD SULND]DQR MHkarakteristikom efikasnosti SURPHQH SURWRNDL]D]LYDSURPHQHHILNDVQRVWLJUHMQRJWHODSRVPDWUDQRSUHNRWHPSHUDWXUH

1D VOLFL SULND]DQD MH WLSLQD NULYD SHUIRUPDQVLVREQRJJUHMDDJUHMQRJWHOD

Slika 2-8 Redna veza dve pumpe Slika 2-9 Paralelna veza dve pumpe

Slika 2-10 Karakteristika snage grejnog tela

,]ERUSXPSH LXSRWUHEDJUHMQLKHOHPHQDWD

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Strana 30

Ako se protok prepolovi (umanji za 50%) tada se prekoJUHMQRJWHODSUHGDMHNROLLQHWRSORWHZapreminski protok iznosi:

.RHILFLMHQWFHYQHPUHH 6YDND UDGQD WDND VH QDOD]L QD SDUDEROL NDUDNWHULVWLNHFHYQHPUHH

3RWLVQDYLVLQD+PRUDSRNULWLJXELWNHSULWLVNDXJUDQLVDQDMYHLPSDGRPSULWLVND

*XELWDNSULWLVNDX FHYQRMPUHLL]UDXQDYDVHNDR]ELUVOHGHLKNRPSRQHQWLRWSRUD

Pretpostavka:*XELWDN SULWLVND XVOHG QHHOMHQH FLUNXODFLMH QD GXLPGHRQLFDPDL]UDXQDYDVHNDR53DP

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Slika 3-2 Dijagram pritiska za dvocevni sistem sa Tihelmanovom jednakom raspodelom pritiska

Slika 3-3 Tihelmanov sistem - ema cevovoda

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xsistemi za grejanje sa toplotnom

pumpom - temperatura na ulazur 50 Cxsistemi za grejanje sa gasnim

bojlerima - temperatura u povratnom

vodu 35 Cxostali sistemi za grejanje temperatura

na ulazu = 75 C

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ploasti radijatori, konvektori ilikombinovana reenja)x Sistem snabdevanja toplotnom

energijom (npr bojler, izmenjivatoplote, toplotna pumpa, solarni

kolektori)x Tip sistema za optimizaciju korienja

energije (npr niskotemperaturnisistemi, iskoriavanje otpadnih voda)x Vrste i temperature medijuma za

distribuciju toplote

(1) Ploasti i lankasti radijatoriStandardne koliine toplote kojeodgovaraju grejnim telima stvarajuosnovu za dimenzionisanje. Faktoripromene moraju biti uzeti u razmatranje uzavisnosti od optereenja zaodgovarajui tip povezivanja, za obloeneili sa metaliziranom bojom. Promenasrednje temperature medijuma zadistribuciju toplote (temperature vode),korekcija standardnih koliina toplote zadruge ambijentalne temperature mora bitiizvrena u saglasnosti sa OENORM M

7513.

(2) KonvektoriPrilikom vrenja prorauna moraju seuzeti u obzir tehnike specifikacijeproizvoda na koje utie promena radnihparametara (npr. srednja korigovanatemperatura medijuma)

(3) (Integrisani) grejai - podnogrejanje

Dimenzionisanje sistema za podnogrejanje vri se standardnim proraunomna osnovu podataka iz tehnike

dokumentacije .

(4) (Integrisani) grejai - drugi sistemiZa relevantne podatke potrebne zadimenzionisanje geometrijskihparametara i temperature medijumaplafonskih panelnih grejaa u prostorijiboravka, neophodno je koristiti tehnikudokumentaciju i odgovarajuu tehnikuliteraturu.

(5) Ostali grejni elementiZa ostale grejne elemente kalkulacija sevri na osnovu tehnikih podataka izproizvoake dokumentacije ili unedostatku informacija koriste se podaciiz relevantne tehnike literature. Prilikom

korienja posebnih tipova elemenatanpr. fen-konvektora potrebno je odreditisledee uticaje: nivo buke, (pogledatiOENORM H 6000-3), strujanje vazduha,regeneracije toplote.

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Strana 42

4.7.1 Nominalni toplotni fluks

4.7.2 Redukovano odavanjetoplote grejnog tela

7HPSHUDWXUQLYLDNMHUD]OLNDL]PHXSURVHQHWHPSHUD-WXUHYRGHLQRUPDOQHVWDQGDUGQHWHPSHUDWXUH

.DGDQLMHPRJXHL]UDXQDWLUWDGDVHSULLVSLWLYDQMXSUHPD g1250(1 PHUL DQJDRYDQMH JUHMQRJ

WHOD 1D RVQRYX VSHFLILQH SUHGDWH WRSORWH PRH ELWLRGUHHQ]DVYDNLHOHPHQW.DUDNWHULVWLNDJUHMQRJWHOD SULND]XMH SUHGDWX NROLLQX HQHUJLMH X IXQNFLMLSRUDVWDWHPSHUDWXUHSULNRQVWDQWQRPSURWRNX.DUDNWHU-LVWLNDMHIXQNFLMDVQDJHVDHNVSRQHQWRPn

1RPLQDOQL WRSORWQL IOXNV QRPLQDOQRM SUHGDWRMNROLLQLWRSORWHL SUHGVWDYOMDSUHGDWXNROLLQXHQHUJLMHNDGD VX LVSXQMHQL VOHGHL XVORYL X VDJODVQRVWL VDg1250(1

7HPSHUDWXUDQDXOD]X&7HPSHUDWXUDXSRYUDWQRPYRGX&6WDQGDUGQDWHPSHUDWXUDYD]GXKD&6WDQGDUGQLWHPSHUDWXUQLYLDNDULWPHWLNL.7HPSHUDWXUQLYLDNRGUHHQORJDULWDPVNL.

6WYDUQL WRSORWQL IOXNV JUHMQRJ WHOD VH SRG RGUHHQLPXVORYLPD VPDQMXMH X RGQRVX QD VWDQGDUGQL WRSORWQLIOXNV 3UHGDWD NROLLQD WRSORWH X VOXDMX GD SURWRNJUHMQRJ PHGLMXPD QHPD XWLFDMD QD SUHGDMX WRSORWHL]UDXQDYDVHPQRHQMHPVWDQGDUGQRJWRSORWQRJIOXNVDVDXWLFDMQLPNRHILFLMHQWLPD

8WLFDMQLNRUHNFLRQLIDNWRULNRULJXMXVWDQGDUGQLSUHGDWLWRSORWQL IOXNV SUHPD VWYDUQLP UDGQLP XVORYLPDXWYUXMXVHLVSLWLYDQMHP

(NVSRQHQWQNDUDNWHULVWLNHDQJDRYDQMDVREQRJJUHMDDVHSULND]XMHXWHKQLNRMGRNXPHQWDFLMLSURL]YRDD]DSRVPDWUDQLWLSJUHMQRJHOHPHQWD

1DMHHNRULHQHYUHGQRVWLHNVSRQHQWDQ

1HRSKRGQD NDUDNWHULVWLND MH RGUHHQD QD RVQRYXSUHGDWHNROLLQHHQHUJLMH

0DVHQLSURWRNMH

Slika 4-4 Karakteristika grejnog tela

.RQYHNWRUL Q5DGLMDWRUL Q3ORDVWLUDGLMDWRUL Q3RGQRJUHMDQMH Q

& N

& $ K Tmn

Qi C q2

q cm V R

& Q Q

GGe Vu

QV C Temperatura na ulazuQ

R C Temperatura u povratnom vodu

& W predata koliina toplote prekogrejnih povrina

qm kg.s

-1

Maseni protok

c kJ.kg-1

.K-1

spec. toplotni kapacitet = 4,2- -

&

&N

& & & N N gf f f f f f 2 4

f f f f f fg 2 4

Tabela 7-1: Uticajni faktori

UtiFajf1 Temperaturaf2 Vezef OElRJe, UGuEljenjaf4 Metalizirani premazf OJranien raGfJ Ukupan IaktRr

4.7 Predavanje toplotepreko grejnih tela

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Strana 43


R

fNTF

Tn

1

1

49 83

',

4.7.2.1 f1 - Temperaturni faktor

3RMHGQRVWDYOMHQSRVWXSDNSURUDXQD

prema NORM M 7513

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.RG RYH SURUDXQVNH PHWRGH NRULVWL VH DULWPHWLNLWHPSHUDWXUQLYLDN

=DL]DEUDQHWHPSHUDWXUHL]WDEHOHMHPRJXHRGUHGLWL1LVNRWHPSHUDWXUQHIDNWRUH17)

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/RJDULWDPVNLWHPSHUDWXUQLYLDNL]QRVL

$TV R

i

Q QQ

f

NTF

Tn

1

1

50

'

' 'T T ln

AritPetiNi tePSeratXrni viaN 'T iPa linearni rast

6liNa 7-5a ova se SoMednostavlMenMa odnose na

cR i

V i

t

Q QQ Q

0 7,

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Strana 44Tab. 4-2 Temperaturni faktor NTF za n = 1,3 pri normalnim uslovima 75/65/20C, NTF = 1,0

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Strana 45


R

4.7.2.3 f2IDNWRUQDLQDXJUDGQMH

4.7.2.4 f33UHSUHNHQLH

1DYHGHQHYUHGQRVWLIDNWRUDVXSULEOLQH

a) Pri ispitivanju pod normalnim uslovima grejniHOHPHQWL VX SRVWDYOMHQL SUHPD SUHSRUXFL SURL]YRDD(100 mm slobodnog prostora ispod i 50 mm iza grejnog

WHOD=DRYDNRSRVWDYOMHQJUHMQLHOHPHQWf3

E=DLQVWDODFLMXJUHMQLKWHODXQXWDUQLDUD]PRWUHQHVXPLQLPDOQH YUHGQRVWL XWYUHQH VWDQGDUGLPDSRWRYDQMHP VWDQGDUGD REH]EHXMH VH XPDQMHQMHpredaje toplote za maksimalno 4%

Slobodan prostor (iznad 65mm, ispod 70 mm i iza,prema zidu 40 mm)f3

Slika 4-7 Postavljanje grejnog tela za f3= 1,0 usaglasnosti sa NORM M 7513

Slika 4-8: Insalacija grejnih tela prema NORM M of7513, minimalne dimenzije, f3= 0.99... 0.96

1DYHGHQH YUHGQRVWL VX SULEOLQH RGQRVQR HPSLULMVNHYUHGQRVWL

1,0 sa jednakim stranama sa gornjimizlazom

VDMHGQDNLPVWUDQDPDYHQWLORWYRUHQ100% protoka

VDMHGQDNLPVWUDQDPDYHQWLOSULprotoka

1,0 suprotan (do 2m) XOD]LL]OD]VDGRQMHVWUDQH VUHGQMLSULNOMXDNYHQWLOD VSHFLMDOQLYHQWLOL]DMHGQRFHYQHVLVWHPH VDSRWDSDMXRPFHYL

Slika 4-6 Korekcioni faktor f1 za n = 1,3 i

$Tn = 50 K lt NORM M 7513:1997

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Strana 46

c) Maskirano postavljanje grejnih tela ( npr. maskiranjeGUYHQRP LOL PHUPHUQRP SORRP ]D UD]OLNX RGVORERGQR SRVWDYOMHQRJ UDGLMDWRUD RSVWUXLUD SUHGDMXWRSORWH YD]GXKX X SURVWRULML SUL HPX MH XPDQMHQMHHILNDVQRVWLJUHMQLKWHODSULEOLQRDf3= 0.9... 0.85

SUL]D]RULPDSUHPDVOLFL

G 8 VOXDMX XJUDGQMHGHNRUDWLYQLKSUHJUDGQLK SORDkoeficijent f3 L]QRVLLL]YRGLVHXVNODGXVDVWDQGDUGRP g1250 0 3RPHQXWR VPDQMHQMHSUHGDYDQMD WRSORWHJUHMQLK WHODVHQHPRHSRLVWRYHWLWLSRGVYLPXVORYLPDVDJXELFLPDWRSORWHNUR]VSROMDQMH

]LGRYH

H6REQLUDGLMDWRUVDXJUDHQLPUHHWNDVWLPSRNORSFHPLPD VPDQMHQMH HILNDVQRVWL SUHGDYDQMD WRSORWH WRQDMYLH]DYLVLRGYHOLLQHRWYRUDNUR]NRMLVWUXMLYD]GXKLL]QRVLRNRf3

I3ULOLNRPSUHGDYDQMDWRSORWHSUHNRJRUQMLKLERQLKSRNULYQLKOLPRYDUDGLMDWRUDL]D]LYDVHVPDQMHQMH f3 =3RGDFLVXSULNXSOMHQLLREUDHQLSUHPD(1SRGNRQWUROLVDQLPXVORYLPD

J 6PDQMHQMHRGDYDQMDWRSORWH]UDHQMHPIURQWDOnim limovima.

*RUQML L GRQML XVLVQLFL YD]GXKD PRUDMX RGJRYDUDWLQDMPDQMHPQRUPDOQRPSRSUHQRPSUHVHNXNUR]NRMLVHYULVWUXMDQMHYD]GXKD[GXELQD[XNXSQDGXLQD3UHSUHNDL]D]LYDJXELWNHXVOHGNRQYHNFLMHDNXPXODFLMDWRSORWH DNR VX JRUQML GRQML L ERQL RWYRUL MHGQDNLGXELQLUDGLMDWRUDf3

K3UHEOL]XSRVWDYOMHQH]DYHVHLPDMXXWLFDMQDSUROD]DNWRSORJYD]GXKDXSURVWRULMXf3

0DOLP NRHILFLMHQWRP ]UDHQMD PHWDOQLK SRYULQDVPDQMXMHVHLRGDYDQMHWRSORWH

f4 2VQRYQDERMDg1250 &IDUED]DUDGLMDWRUHQHUHIOHNWLYQLVORM QH]DYLVQRRGERMH

f4 PHWDOL]LUDQLSUHPD]LEURQ]DQL SUHPD]DOXPLQLMXPVNLVMDM

6WDOQLSUHNLGLXUDGXVLVWHPDNDRWRMHQDSULPHUEU]R]DJUHYDQMH SURVWRULMD PRH ELWL UD]ORJ SRYHDQMDSUHGDWRJWRSORWQRJIOXNVDVDJUHMQRJWHOD

$NRMHSRHOMQRSUHGLPHQ]LRQLVDWLVLVWHPQDMEROMHMHWRXLQLWLSUHNRIDNWRUDf51DSULPHUNRGYHRPDEU]RJ]DJUHYDQMDf5

6OLND3UHSRUXHQRSRVWDYOMHQMHUDGLMDWRUDSUHPDg12500VDf3= 0.9... 0.85

6OLND3RVWDYOMDQMHJUHMQLKWHODXVDJODVQRVWLVD

g12500

4.7.2.5 f4 - Faktor metalnih povrina

4.7.2.6 f5 2JUDQLHQUDG

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Strana 47


R

rimer :P 3ORDVWLUDGLMDWRU

rimer :P 5DGLMDWRU

rimer :P *UHMDQMHSULPHQRPWRSORWQHSXPSH

NoPLQDlQD LzlDzQD VQDgD UDGLMDWoUD LzQoVL 112W So UHbUX.

&1N = 112 W SUL QV 75, QR 65, Qi 20C

PUoQDL VWvDUQo SUHGDWX kolLLQX WoSloWH Dko VXQ v = 80C. Q R = 60C, Q L =22C

D) THPSHUDWXUQL vLDkVH oGUHXMH kDo

'T K

80 60

222 48 , f1

1 348

500 948

,

,

VD GLMDgUDPD (VlLkD 4-6) SUL HPX MH 'T=48K,D WHPSHUDWXUQL koUHkcLoQL fDkWoU f1 = 0,93,

NTF = 1,07 Lz WDbHlH 4-2

PUL WoPH VPDQMHQL SUHGDWL WoSloWQL flXkV LzQoVL:

& = f1 . &1N = 0,93. 112 = 104 W.

b) IzUDXQDvDQMH Temperaturnog faktora f1SoPoX'TlQ

ToSloWQo oSWHUHHQMH MH fXQkcLMD VQDgH zDvLVQDoG logDULWDPVkog WHPSHUDWXUQog vLkD 'TlQ

KT

iR

iV

Rv 3,47

2260

2280lQ

6080

lQlQ

'

QQQQ

QQ

f1 2

1 347 3

49 830 934,

,,

,,

, NTF = 0707,1

1

2,1

f

.DYLWDFLRQD UH]HUYDKLGURVWDWLNRJ SULWLVND + 136+1HW 3RVLWLYH 6XFWLRQ +HDG MHGQDND MHKLGURVWDWLNRPSULWLVNX YRGHQRJ VWXED VYHGHQRJ QD SRSUHQL SUHVHN

L]OD]QHJUDQHSXPSH

6LVWHP ]D JUHMDQMH WUHED GD RVWYDUL WHPSHUDWXUH

XOD]QDSRYUDWQD L WHPSHUDWXUX DPELMHQWD RG20C.7RSORWQR RSWHUHHQMH X SURVWRULMDPD P3 VD VSHFWRSORWQLPRSWHUHHQMHPRG:P3,6WDQGDUGQR WRSORWQR RSWHUHHQMH & :UHEUX]DUDGLMDWRUH

7RSORWQRRSWHUHHQMHXSURVWRULMLL]QRVLW

7HPSHUDWXUQL IDNWRU MH XWLFDMQL NRHILFLMHQW UDGQHWHPSHUDWXUHLRGUHXMHVHNDR

HlLQL SloDVWL UDGLMDWoU LPD LzlDzQX VQDgX)

N 1300 W. PUoQDL WoSloWQL flXkV & ?SUL Q1 55C, Q2 45C, iQ 18C

c

!45 18

55 180 729 0 7, ,

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