KOEFICIJENT TRENJAPRVA OBLAST ODGOVARA PRAVOJ I-I I ODNOSI SE NA LAMINARNO KRETANJE TENOSTI.1932. godine J. D. Nikuradze

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DRUGA OBLAST SE ODNOSI NA TURBULENTNO KRETANJE TENOSTI U HIDRAULIKI GLATKIM CIJEVIMA. =f(Re)

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0.04558946323202320232023200.0474740910.05515863330.1128664143

0.0452047080.041124242400240024000.04700299390.0544783550.1115592256

0.0427519730.0388110430000.04415722430000.04403155070.05029912830.1034953348

0.0397851940.036048440.0410151230.04026195240000.04051280910.04558483420.0943275729

0.031640.0286823260.03156250.030778701100000.0313108180.03429355280.0720324969

0.0211589430.0197659840.0211015660.020654416500000.02061501780.02255762490.0482731502

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20000000.010150260.0101342710.0103239560.0102965650.00995503790.0109833410.0240858687

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1000000001000000001000000000.0060092540.0060079690.00674571130.00629881580.0140053134

Blasius

Hermann

Kassatkin

Konakow

Nikuradse

Mudijeva formula

empirijska formula (8.28)

Altua-Colebrook-ova formula

Re

Koeficijent trenja

Sheet1

Mudijeva formulaempirijska formula (8.28)Altua-Colebrook-ova formula

23200.0474740910.05515863330.1128664143

100000.0313108180.03429355280.0720324969

1000000.01750711250.01929012350.0415315982

10000000.01110.0123456790.0269810834

100000000.00812608180.00857338820.0189259603

BlasiusHermannKassatkinKonakowNikuradseMudijeva formulaempirijska formula (8.28)Altua-Colebrook-ova formula

23200.0455894630.0474740910.05515863330.1128664143

24000.0452047080.041124240.04700299390.0544783550.1115592256

30000.0427519730.038811040.0441572240.04403155070.05029912830.1034953348

40000.0397851940.036048440.0410151230.0402619520.04051280910.04558483420.0943275729

100000.031640.0286823260.03156250.0307787010.0313108180.03429355280.0720324969

500000.0211589430.0197659840.0211015660.0206544160.02061501780.02255762490.0482731502

1000000.017792480.0170688050.0180674290.0177777780.0176341850.01750711250.01929012350.0415315982

20000000.010150260.0101342710.0103239560.0102965650.00995503790.0109833410.0240858687

60000000.0084439030.008733290.0086697870.00860428270.0092443670.0203677811

1000000000.0060092540.0060079690.00674571130.00629881580.0140053134

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00000000

00000000

00000000

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00000000

Blasius

Hermann

Kassatkin

Konakow

Nikuradse

Mudijeva formula

empirijska formula (8.28)

Altua-Colebrook-ova formula

Re

Koeficijent trenja

Sheet2

Sheet3

ZA ODREIVANJE KOEFICIJENTA TRENJA U OVOJ ZONI U LITERATURI JE PREDLOEN VELIKI BROJ EKSPERIMENTALNIH ZAVISNOSTI OD KOJIH MOEMO IZDVOJITI OBRASCE COLEBROOK-A I ALTUA:

DRUGA PRELAZNA ZONA U OVOJ ZONI KOEFICIJENT TRENJA JE U FUNKCIJI Re BROJA I RELATIVNE HRAPAVOSTI CJEVOVODA:=f(Re,n)

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TREA OBLAST

U OVOJ OBLASTI GUBICI PRITISKA PREKO KOEFICIJENTA TRENJA NE ZAVISE OD Re BROJA VE OD RELATIVNE HRAPAVOSTI.

=f(n)

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Zavisnost koeficijenta trenja od relativne hrapavosti prema formulama iz tabele 8.4

Chart2

0.02091901590.01053925840.00933395020.01054087680.01

0.02324840320.01197365150.01110.01197561130.0118920712

0.02598968630.01372211960.0132001990.0137245240.0141421356

0.02924602580.01588352450.01569777050.01588651890.0168179283

0.03144277070.01739327750.01737243880.01739670880.0186120972

0.0331550230.0185989240.01866790040.01860271820.02

0.03458133980.01962257140.01973890150.01962668320.0211474253

0.03965082840.02340369930.0234736420.02340905520.0251486686

0.04592261720.02839311370.02791502210.02840027060.0299069756

0.0503066040.03208862030.03089305030.03209721920.0330975092

0.05380928130.03516634410.03319674290.03517620930.0355655882

0.05678438740.03786913530.0351012820.03788015960.0376060309

0.06286030670.04364676130.03884595420.04366040260.0416179145

0.06778269220.04858723750.04174269430.04860325950.0447213595

0.07576495990.05710994650.04619588510.05713036440.04949232

0.08231559190.06459407440.04964070910.06461863510.053182959

0.08799996410.07146101950.05248865930.07148959930.0562341325

koef. trenja prema Teplovu

koef. trenja prema Karmanu

koef. trenja prema Schifrinsonu

koef. trenja prema Herning-Prandtlu

koef. trenja prema Nikuradseu

Relativna hrapavost, n

Koeficijent trenja, l

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koef. trenja prema Teplovukoef. trenja prema Karmanukoef. trenja prema Schifrinsonukoef. trenja prema Herning-Prandtlukoef. trenja prema Nikuradseu

0.000050.02091901590.01053925840.00933395020.01054087680.01

0.00010.02324840320.01197365150.01110.01197561130.0118920712

0.00020.02598968630.01372211960.0132001990.0137245240.0141421356

0.00040.02924602580.01588352450.01569777050.01588651890.0168179283

0.00060.03144277070.01739327750.01737243880.01739670880.0186120972

0.00080.0331550230.0185989240.01866790040.01860271820.02

0.0010.03458133980.01962257140.01973890150.01962668320.0211474253

0.0020.03965082840.02340369930.0234736420.02340905520.0251486686

0.0040.04592261720.02839311370.02791502210.02840027060.0299069756

0.0060.0503066040.03208862030.03089305030.03209721920.0330975092

0.0080.05380928130.03516634410.03319674290.03517620930.0355655882

0.010.05678438740.03786913530.0351012820.03788015960.0376060309

0.0150.06286030670.04364676130.03884595420.04366040260.0416179145

0.020.06778269220.04858723750.04174269430.04860325950.0447213595

0.030.07576495990.05710994650.04619588510.05713036440.04949232

0.040.08231559190.06459407440.04964070910.06461863510.053182959

0.050.08799996410.07146101950.05248865930.07148959930.0562341325

Sheet1

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

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00000

00000

00000

00000

koef. trenja prema Teplovu

koef. trenja prema Karmanu

koef. trenja prema Schifrinsonu

koef. trenja prema Herning-Prandtlu

koef. trenja prema Nikuradseu

Relativna hrapavost, n

Koeficijent trenja, l

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Sheet3

OSNOVNI POJMOVI IZ MEHANIKE FLUIDAVRSTE STRUJANJA

HIDROSTATIKI PRITISAK NA RAVNIM POVRINAMAPritisak na dno akumulacije iznosi ; (Pa) -zapreminska masa tenosti (kg/m3),h-visina stuba tenosti (m),g-ubrzanje zemljine tee (m/s2),=g- zapreminska teina tenosti (kN/m3).

PRITISAK NA BONE STRANE

Ukoliko je bona strana rezervoara pod uglom (, prema horizontu elementarna sila pritiska je :

(5.2)

(5.3)

_1236434630.unknown

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(5.3)

Kako je: h=y sin(, a (=const.

(5.4)

(y dA-zbir stkih momenata svih elementarnih povrina za osu (x), i moe se predstaviti kao:

(5.5)

(5.6)

"yc" je odstojanje teita (C) povrine (A) od ose (x).

_1236434667.unknown

_1236434697.unknown

_1236434700.unknown

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(N)

Ovaj obrazac slui za odreivanje sile pritiska na vertikalnom zidu.

Sila pritiska mijenja sa dubinom, i napadna taka sile pritiska nee leati u teitu povrine, ve ispod teita

_1236434726.unknown

yo-ordinata napadne

; (cm)

(5.9)

Ix-momenat inercije povrine (cm4).

Prema teoremi tajnera:

(5.10)

Ic-sopstveni momenat inercije(cm4).,

Ayc2-poloajni momenat inercije(cm4).

Prema navedenom:

; (cm)

_1236434805.unknown

_1236434810.unknown

_1236434820.unknown

_1236434775.unknown

PRITISAK NA KRIVOJ POVRININa elementu krive povrine djeluje sila pritiska:

Projekcija sile na horizontalnu osu x-x:

Za cijev prenika (D) imamo sluaj da je kritina osa loma, osa (x-x).

l-duina cijevi konstantnog prenika (D).

JEDNAINA KONTINUITETA; (m3/s)

v1 i v2 su srednje brzine.

BERNULIJEVA JENAINA

Moe se rei da je cijela hidraulika zasnovana na primjeni Bernulijeve jednaine, ali treba strogo voditi rauna o uslovima pod kojima je jednaina izvedena.

Prvi lan Bernulijeve jednaine predstavlja kinetiku energiju sraunatu za jedinicu mase, drugi lan potencijalnu energiju, a trei lan energiju pritiska.

=const. (m) V.S.

1 m V.S. odgovara veliini od 10 kPa.

BRZINSKA VISINA

PIJEZOMETARSKA VISINA

VISINA POLOAJA-GEODETSKA VISINA

PIJEZOMETARSKA LINIJA

ENERGETSKA LINIJA-VISINA UKUPNE ENERGIJE

_1233123756.unknown

U tehnikoj primjeni, ako je referentni nivo od koga posmatramo stanje energije pri kretanju fluida, stanje (1), onda je Bernulijeva jednaina:

hw 1,2-zbir otpora u cijevi, koji se suprostavljaju kretanju tenosti; (m) V.S. ili (kPa) Poto se brzina mijenja od v1 do v2 ; za odrivanje otpora kretanju, mjerodavna je srednja brzina:

-koeficijent trenja u cijevi,L-duina cijevi (m),D-unutranji prenik cijevi (m),l-pojedinani koeficijent otpora za elemente armature cjevovoda.

Primjeri primjene Bernulijeve jednaine

Uporeujemo stanje na osi (x-x). Uz predpostavku da je cijev za isticanje relativno kratka: hw0.Takoe uz predpostavku da je H=const Bernulijeva jednaina za ova dva nivoa glasi:

Za nivo 11 do 33 imali bi slijedee stanje:

Brzinu (v1), bi dobili postavljanjem Bernulijeve jednaine za nivoe: (0-0) i (1-1).