)(10(126'(75$163257(

DQRWDo}HVGHaula)HQ{PHQRVGHWUDQVSRUWHUHIHUHVHDRHVWXGRGDWUDQVIHUrQFLDGHTXDQWLGDGHGHPRYLPHQWRHQHUJLDHPDWpULD2WHPDLQFOXLDVGLVFLSOLQDVGHGLQkPLFDGRVIOXLGRVDWUDQVIHUrQFLDGHFDORUHDWUDQVIHUrQFLDGHPDVVD$SULPHLUDWUDWDGRWUDQVSRUWHGDTXDQWLGDGHGHPRYLPHQWRDVHJXQGDGRWUDQVSRUWHGHHQHUJLDHQTXDQWRTXHDWHUFHLUDGRWUDQVSRUWHWUDQVIHUrQFLDGHPDVVDHQWUHDVHVSpFLHVTXtPLFDV'(),1,d2(35235,('$'('26)/8,'26

'HILQLomR)OXLGRVVmRVXEVWkQFLDVFXMDVPROpFXODVVHPRYLPHQWDPXPDVHPUHODomRjVRXWUDVVREDDomRGHIRUoDV1mRSRVVXHPIRUPDSUySULDGHIRUPDPVHFRQWLQXDPHQWH)OXLGRpTXDOTXHUVXEVWkQFLDQmRVyOLGDFDSD]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

*iV

/tTXLGR

01

3UHVVmRGHYDSRUGHXPOtTXLGRpDSUHVVmRQDVXSHUItFLHTXDQGRROtTXLGRHYDSRUD$SUHVVmRGHYDSRUYDULDFRPDWHPSHUDWXUD$SUHVVmRGHYDSRUGDiJXDD&SRUH[HPSORpEDU$&pEDU$iJXDHYDSRUDD&DRQtYHOGRPDU$SUHVVmRDWPRVIpULFDDRQtYHOGRPDUpLJXDODEDU&RPSUHVVLELOLGDGHpDSURSULHGDGHTXHWHPRVFRUSRVGHUHGX]LUVHXVYROXPHVVREDDomRGHSUHVV}HVH[WHUQDV3(62(63(&),&20$66$(63(&),&$'(16,'$'(

3(62(63(&),&2

2SHVRHVSHFtILFRGHXPDVXEVWkQFLDpRSHVRGHVWDVXEVWkQFLDSHODXQLGDGHGHYROXPHTXHHODRFXSD

*9

JDPD SHVR HVSHFtILFR

* SHVR GDVXEVWkQFLD9 YROXPHRFXSDGRSHOD VXEVWkQFLD

$VXQLGDGHVPDLVXVXDLVVmRNJIPNJIGP1P6,OEIIW 0$66$(63(&),&$

$PDVVDHVSHFtILFDGHXPDVXEVWkQFLDpDPDVVDGHVVDVXEVWkQFLDSHODXQLGDGHGHYROXPHTXHHODRFXSD

P 9 P

U{ PDVVD HVSHFtILFDPDVVD GDVXEVWkQFLD

9 YROXPHRFXSDGRSHOD VXEVWkQFLD$VXQLGDGHVPDLVXVXDLVVmRNJP6,NJGPOEIW

5(/$d2(175(3(62(63(&),&2(0$66$(63(&),&$

&RPRRSHVRGHXPDVXEVWkQFLDpRSURGXWRGHVXDPDVVDSHODFRQVWDQWHDFHOHUDomRGDJUDYLGDGHUHVXOWDDVHJXLQWHUHODomRHQWUHSHVRHVSHFtILFRHPDVVDHVSHFtILFD

JJDPD SHVR HVSHFtILFR

U{ PDVVD HVSHFtILFD

J DFHOHUDomRGDJUDYLGDGH PV02

'(16,'$'(

'HQVLGDGHGHXPDVXEVWkQFLDpDUD]mRHQWUHRSHVRHVSHFtILFRRXPDVVDHVSHFtILFDGHVVDVXEVWkQFLDHRSHVRHVSHFtILFRRXPDVVDHVSHFtILFDGHXPDVXEVWkQFLDGHUHIHUrQFLDHPFRQGLo}HVSDGUmR3DUDVXEVWkQFLDVHPHVWDGROtTXLGRDVXEVWkQFLDGHUHIHUrQFLDpDiJXDFRP SHVR HVSHFtILFR LJXDO D NJIP 3DUD VXEVWkQFLDV HP HVWDGR JDVRVR DVXEVWkQFLDGHUHIHUrQFLD p RDUD&

G IOXLGRG IOXLGR

IOXLGRSDGUmR IOXLGRSDGUmR 2EV $GHQVLGDGHpXPQDGLPHQVLRQDO

(PDOJXQV UDPRVGD LQG~VWULDSRGHVHHQFRQWUDUDGHQVLGDGHH[SUHVVDHPJUDXV WDLVFRPRRVJUDXV$3,,QG~VWULD3HWURTXtPLFDRVJUDXV%$80e,QG~VWULD4XtPLFDHRJUDXV%5,;,QG~VWULDGH$oXFDUH$OFRRO(VWHVJUDXVSRGHPVHUFRQYHUWLGRVHPGHQVLGDGHDWUDYpVGHWDEHODV$V JUDQGH]DV DFLPD GHSHQGHP GR Q~PHUR GH PROpFXODV GR IOXtGR QD XQLGDGH GHYROXPH3RUWDQWRGHSHQGHPGDWHPSHUDWXUDGDSUHVVmRHGRDUUDQMRHQWUHDVPROpFXODV

9,6&26,'$'(

4XDQGR XP IOXLGR HVFRD YHULILFDVH XP PRYLPHQWR UHODWLYR HQWUH DV VXDV SDUWtFXODVUHVXOWDQGRXPDWULWRHQWUHDVPHVPDV$WULWRLQWHUQRRXYLVFRVLGDGHpDSURSULHGDGHGRVIOXLGRV UHVSRQViYHO SHOD VXD UHVLVWrQFLD j GHIRUPDomR SHOD VXD UHVLVWrQFLD DRFLVDOKDPHQWRLQWHUQRLVWRp DTXDOTXHUIRUoDTXHWHQGDDSURGX]LURHVFRDPHQWRHQWUHVXDVFDPDGDV$YLVFRVLGDGHpGLUHWDPHQWHUHODFLRQDGDFRPDFRHVmRHQWUHDVSDUWtFXODVGRIOXLGR$YLVFRVLGDGHWHPXPDLPSRUWDQWHLQIOXrQFLDQRIHQ{PHQRGRHVFRDPHQWRQRWDGDPHQWHQDV SHUGDV GH SUHVVmR GRV IOXLGRV$PDJQLWXGH GR HIHLWR GHSHQGH SULQFLSDOPHQWH GDWHPSHUDWXUDHGDQDWXUH]DGRIOXLGR$VVLPTXDOTXHUYDORULQGLFDGRSDUDDYLVFRVLGDGHGHXPIOXLGRGHYH VHPSUH LQIRUPDUD WHPSHUDWXUDEHPFRPRDXQLGDGHTXHDPHVPDpH[SUHVVD1RWDUTXHQRVOtTXLGRVDYLVFRVLGDGHGLPLQXLFRPRDXPHQWRGDWHPSHUDWXUD /(,'(1(:721

1HZWRQ GHVFREULX TXHHPPXLWRV IOXLGRV D WHQVmRGH FLVDOKDPHQWRpSURSRUFLRQDO DRJUDGLHQWHGHYHORFLGDGHFKHJDQGRDVHJXLQWHIyUPXOD

03

FRHILFLHQWHGHYLVFRVLGDGHGLQkPLFD

(A)

2FRHILFLHQWH pFDUDFWHUtVWLFRGRIOXLGRHPGHWHUPLQDGDWHPSHUDWXUDHSUHVVmRTXHVHGHQRPLQDFRHILFLHQWHGHYLVFRVLGDGHGLQkPLFDRXYLVFRVLGDGHGLQkPLFDRXDEVROXWD23DVFDOVHJXQGR3DVpXPDXQLGDGHQRVLVWHPD6,GRFRHILFLHQWHGHYLVFRVLGDGHGLQkPLFDHR3RVH3pXPDXQLGDGHQRVLVWHPD0.63DUDiJXDD&HDWP -3 N.s/m2 = -3 Pas = 1centepoise (cP) = 0,01 P.2VIOXLGRVTXHREHGHFHPDHTXDomRDFLPDVmRRVFKDPDGRVIOXLGRV1HZWRQLDQRVHRVTXHQmRREHGHFHPVmRRVFKDPDGRVQmR1HZWRQLDQRV2VIOXLGRVQmR1HZWRQLDQRVDSUHVHQWDPXPDUHODomRQmROLQHDUHQWUHRYDORUGDWHQVmRGHFLVDOKDPHQWRDSOLFDGDHDYHORFLGDGHGHGHIRUPDomRDQJXODU(VWmRLQFOXtGRQRVIOXLGRVQHZWRQLDQRVDiJXDOtTXLGRVILQRVDVVHPHOKDGRVHRVJDVHVGHPDQHLUDJHUDO1RVQmRQHZWRQLDQRVRVORGRVHPJHUDO

5.2) COEFICIENTE DE VISCOSIDADE CINEMTICA (ou Viscosidade Cinemtica)eGHILQLGDFRPRRTXRFLHQWHHQWUHDYLVFRVLGDGHGLQkPLFDHDPDVVDHVSHFtILFDRX VHMD

YLVFRVLGDGH FLQHPiWLFD YLVFRVLGDGH GLQkPLFDPDVVDHVSHFtILFD

2VtPERORQRUPDOPHQWHXWLOL]DGR SDUDLQGLFiODp OHWUD $VXQLGDGHVPDLVXVXDLVVmRRFHQWL6WRNHF6W R6WRNH6W FPV0.6RPV6,6) LQUIDO PERFEITOeXPIOXLGRVHPYLVFRVLGDGHHLQFRPSUHVVtYHO(VVDVGXDVFRQGLo}HVGHILQHPROtTXLGRSHUIHLWR8POtTXLGRSHUIHLWRQmRH[LVWHQDSUiWLFDRXVHMDQDQDWXUH]DVHQGRSRUWDQWRXPDDEVWUDomRWHyULFD(PDOJXQVSUREOHPDVSDUWLFXODUHVSRGHVHXViORVHPJUDYHHUUR

PRESSO3UHVVmRpDIRUoDH[HUFLGDSRUXQLGDGHGHiUHDVREUHDTXDODIRUoDDWXD

) 33 )

$ $UHD

8QLGDGHVXVXDLVNJIFPEDUSVL3DVFDO 3D6,

3UHVVmR)RUoD)RUoD

$GSH

S$SDK

2EHOH&SR$

GLIHUHQoDVRHVSHFt

S$

$DWP

EVHUYDomR3DUDGHWHHVPDVVLP&RPRFRQVQWRVTXH$SUHVVmR

GHSUHVVmtILFRGRIOX

$K%

$ SDWP

SUHVVmRSUHVVmR D

GLIHUHQoDQtYHO GRI

SHVR HVS

RHUPLQDUDGPDGLIHUHVHTXrQFLDHVWHMDPQ

RLQGHSHQG

&$

mRHQWUHGLGRSHODG

K

QRSRQWRDWPRVIpULGHFRWDVIOXLGR QRUSHFtILFRGR

GLIHUHQoDHQoDGHFRDGDOHLGHQDPHVPDGHGRIRUP

K

7(25(RLVSRQWRVLIHUHQoDG

S$S%K

$FDORFDOV HQWUHR VUHVHUYDWyR IOXLGR

GHSUHVVmRWDVHQWUHH6WHYLQHDFRWDWHPPDWRGRUHFLSLHQWHSDUDTXDOTXHUSRQWRGRUHFLSLHQWH

'%

(0$'(VGHXPIOGHFRWDHQW

$%

S%SUSU

GL

SH

VSRQWRV $yULR

mRHQWUHGHOHVHPXPOtTXPDPHVP

67(9,1OXLGRHPHWUHRVGRLV

S$

UHVVmR QRUHVVmR QRIHUHQoDGHVR HVSHF

$HR

GRLVSRQWR

XLGRHPHPDSUHVVmR

S$ S%

S& S'

S$S&

1HTXLOtEULRpVSRQWRVR

K

RSRQWR $RSRQWR %GHFRWDVHFtILFRGRI

VQmRLPS

TXLOtEULRDR

%

'

S%S'

pLJXDODRRXVHMD

S% HQWUHRVSIOXLGR

SDWP

K$

SRUWDDGLV

DSUHVVmR

' K

RSURGXWRG

KS$SRQWRV$H

VWkQFLDHQ

RGHGRLV

GR

H%

QWUH

05

/(,'(3$6&$/

$SUHVVmRDSOLFDGDHPXPSRQWRGHXPIOXLGRHPUHSRXVRFRQWLGRHPXPUHFLSLHQWHpDPHVPDHPWRGDVDVGLUHo}HVGRIOXLGR

S

35,1&,3,2'(3$6&$/&RQVLGHUHPRVXPOtTXLGRHPUHSRXVRGHQWURGHXPUHFLSLHQWH8PDSUHVVmRDSOLFDGDHPXPSRQWRGHVVHOtTXLGRpWUDQVPLWLGDLQWHJUDOPHQWHSDUDWRGRVRVSRQWRVGDOtTXLGR(VVDSURSULHGDGHIRLDSUHVHQWDGDSHODSULPHLUDYH]SHORItVLFRHPDWHPiWLFRIUDQFrV%ODLVH3DVFDO

(VVHSULQFtSLRpXVDGDIUHTXHQWHPHQWHQRVPHFDQLVPRVKLGUiXOLFRVXVDGRVSDUDDXPHQWDULQWHQVLGDGHVGHIRUoD

1DILJXUDDEDL[RXPOtTXLGRHVWiHPXPUHVHUYDWyULRYHGDGRSRUSLVW}HVPyYHLVGHiUHDV$H$VHQGR$$

6HDSOLFDUPRVXPDIRUoD)QRSLVWmRGHiUHD$VHUiSURGX]LGDXPDSUHVVmRS

S

06

$SUHVVmRSWUDQVPLWHVHDRSLVWmRGHiUHD$GHPRGRTXHHVWDILFDVXMHLWDDXPDIRUoD)

S DVVLPWHPVH

S HSRUWDQWR) .

&RQIRUPHDFLPDFRPR$!$WHUHPRV)!)3RUWDQWRDIRUoD)VHUiWDQWDVYH]HVPDLRUTXHDIRUoD)TXDQWDVYH]HVIRUDiUHD$PDLRUTXHDiUHD$3RUH[HPSORVH$pYH]HVPDLRUTXH$FRQVHJXHVHPXOWLSOLFDUDIRUoD)SRU) $

07

&$5*$'(35(662$/785$'(&2/81$'(/48,'2 K FDUJDGHSUHVVmR RXDOWXUDGHFROXQDGHOtTXLGR P

K 3

S SUHVVmR NJIP SHVRHVSHFtILFR NJIP

,QIOXrQFLDGR3HVR(VSHFtILFRQDUHODomRHQWUHSUHVVmRHDOWXUDGHFROXQDGHOtTXLGR D3DUDXPDPHVPDDOWXUDGHFROXQDGHOtTXLGROtTXLGRVGHSHVRVHVSHFtILFRVGLIHUHQWHVWHPSUHVV}HVGLIHUHQWHV

iJXDF

P OtTXGRFRP

P OtTXLGRF

P

NJIFP NJIFP NJIFP E3DUDXPDPHVPDSUHVVmRDWXDQGRHPOtTXLGRVFRPSHVRVHVSHFtILFRVGLIHUHQWHVDVFROXQDVOtTXLGDVVmRGLIHUHQWHV

iJXDF

P

OtTXLGRF

P

OtTXLGRF

P

NJIFP NJIFP NJIFP

(t/m3) (t/m3) (t/m3)

(t/m3)

(t/m3)

(t/m3)

(= 100000kgf/m2) (= 120000kgf/m2) (= 75000kgf/m2)

(= 100000kgf/m2) (= 100000kgf/m2) (= 100000kgf/m2)

(= 1000 kgf/m3)

(= 1200 kgf/m3)

(= 750 kgf/m3)

(= 1000 kgf/m3)

(= 1200 kgf/m3)

(= 750 kgf/m3)

08

(6&$/$6'(35(662

3DWP DUKDUKDURQGH7(55$KDUDOWXUDGDFDPDGDDWPRVIpULFDDUSHVRHVSHFtILFRGRDUNJIPD&([SHULrQFLDGH7RUULFHOOL$FDUJDGHSUHVVmRK PPGDFROXQDGHPHUF~ULRPXOWLSOLFDGDSHORSHVRHVSHFtILFRGRPHUF~ULR+JHTXLOLEUDDSUHVVmRDWPRVIpULFD

3DWP +JK+J 3DWPPP+J&RPR +J .JIPHK+J PP P3DWP .JIP .JIFP 3DWP DWP PP+J 1P3DWP .JIFP PFDPHWURVGHFROXQDGiJXD2EV$3DWPYDULDFRPDDOWLWXGHHGHSHQGHGDVFRQGLo}HVPHWHRUROyJLFDVVHQGRTXHDRQtYHOGRPDUHPFRQGLo}HVPHUF~ULR+JSDGURQL]DGDVDSUHVVmRpNJIFP

D(VFDODGHSUHVVmRDEVROXWD3DEVeDTXHODTXHDGRWDFRPRUHIHUrQFLDDSUHVVmRGRYiFXR3Y RX]HURDEVROXWR7RGRVRVYDORUHVTXHH[SUHVVmRSUHVVmRDEVROXWDVmSRVLWLYRVE(VFDODGHSUHVVmRHIHWLYD3HIeDTXHODTXHDGRWDFRPRUHIHUrQFLDDSUHVVmRDWPRVIpULFD3DWP

3HI

3DEV3DWP33DEV3DWP]HURDEVROXWR3DEV

3DEV 3HI3DWP([HPSORVD6HMDXPDFDQDOL]DomRFXMRSRQWRILJXUDDFLPDDSUHVVmRPHGLGD3HIHPUHODomRDSUHVVmRHIHWLYD3DWPpLJXDODPGHFROXQDGHiJXDYDORUSRVLWLYRFKDPDGDGHSUHVVmRPDQRPpWULFDHWDPEpPGHSUHVVmRHIHWLYDRXUHODWLYD6HDSUHVVmRDWPRVIpULFDORFDOFRUUHVSRQGHUDPFDDSUHVVmRDEVROXWD3DEVQDTXHOHSRQWRVHUiGHPFD3DEVE2SRQWRILJXUDDFLPDVLWXDGRDEDL[RGD3DWPHVWiVREYiFXRSDUFLDO$SUHVVmR3pLQIHULRUDSUHVVmRDWPRVIpULFDORFDOHVHULDQHJDWLYD(QWUHWDQWRQHVVHSRQWRDSUHVVmRDEVROXWD3DEVpSRVLWLYD

09

0(','25(6'(35(662D3LH]{PHWUR

K3$ K 3DWP 'HVYDQWDJHQV 3$1mRVHUYHSDUDGHSUHVV}HV1mRVHUYHSDUDJDVHV1mRVHUYHSDUDSUHVV}HVHOHYDGDVE0DQ{PHWURFRPWXER HP8 K

3$3$ KK K

3HF0DQ{PHWUR0HWiOLFR 7XERGH%RXUGRQ 3P 3L3HRQGH3L SUHVVmRLQWHUQD3HSUHVVmRDWPRVIpULFD3PSUHVVmRGRPDQ{PHWUR*HUDOPHQWH3H HVFDODHIHWLYDHQWmR

3L3P 3L$ILJXUDDEDL[RLOXVWUDDOJXQVDVSHFWRVLQWHUQRVGHXPPDQ{PHWURPHWiOLFR

4XDQGRDSUHVVmRpPHQRUTXHDDWPRVIpULFDWHPRVSUHVVmRPDPRPpWULFDQHJDWLYD2PDQ{PHWURUHJLVWUDYDORUHVGHSUHVVmRPDQRPpWULFDSRVLWLYD2YDFX{PHWURUHJLVWUDYDORUHVGHSUHVVmRPDQRPpWULFDQHJDWLYDHRPDQRYDFX{PHWURUHJLVWUDYDORUHVGHSUHVVmRPDQRPpWULFDSRVLWLYDHQHJDWLYD(VWHVLQVWUXPHQWRVVHPSUHUHJLVWUDP]HURTXDQGRDEHUWRVjDWPRVIHUDDVVLPWHPFRPRUHIHUrQFLD]HURGDHVFDODDSUHVVmRDWPRVIpULFDGRORFDORQGHHVWiVHQGRUHDOL]DGDDPHGLomRG%DU{PHWUR$SUHVVmRDWPRVIpULFDQRUPDOPHQWHpPHGLGDSRUXPLQVWUXPHQWRFKDPDGREDU{PHWUR

10

(48$d20$120e75,&$

3DUDDILJXUDDFLPDWHPRV3$$K$KKK%K% 3%

11

9$=2(9(/2&,'$'(1) VAZO VOLUMTRICA Vazo volumtrica definida como sendo o volume de fluido que passa por uma determinada seo por unidade de tempo.

Q

Q =

V t

vazo volumtrica

volume

tempo

E tambm: Q= v . A, onde: v= velocidade; A= rea As unidades mais usuais so: m3/h; l/s; m3/s; GPM (gales por minuto). 2) VAZO MSSICA Vazo mssica a massa de fluido que passa por determinada seo , por unidade de tempo.

Qm=

Qm vazo mssica

m massa

t tempo E tambm: Qm= . v . A, onde: v= velocidade; A= rea ; = massa especfica As unidades mais usuais so: kg/h; kg/s; t/h; lb/h.. 3) VAZO EM PESO Vazo em peso o peso do fluido que passa por determinada seo, por unidade de tempo.

Qp=

Qp vazo em peso

G peso t tempo

E tambm: Qp = . v . A, onde: v= velocidade; A= rea ; = peso especfico As unidades mais usuais so: kgf/h; kgf/s; tf/h; lbf/h. 4) VELOCIDADE Existe uma importante relao entre vazo, velocidade e rea da seo transversal de uma tubulao:

12

Co

Sepotem Cosutam

Q = v

rea dDcircular

onsiderem

e tivermosor no havmpo. A ma

omo Qm =a massa embm ser

A

tubulaomR

(48$d

mos o segu

A1

s um escover variaassa fluida

= Q (Q=especficar igual a v

velocid

QV =

A

A

2'$&2

uinte trech

oamento es das pa que entr

=vazo voa constavazo volu

X D

ade

A

= 4

217,18,'

o da tubulA

em regimropriedad

ra na se

Qm1

olumtricaante, temoumtrica q

Q1

D

Q v A D

2

'$'(3$

ao: A2

me permades do fluio 1 igua

1 = Qm2

), se tivermos que a vque sai na

1 = Q2

dime

vazovelocirea ddimet(pi) = 3

$5$5(*,

A1 A2 v1 v2

nente (figdo em cadl a massa

mos um fluvazo voluseo 2, o

etro

volumtridade do a tubulatro interno3,1416...

0(3(50

reada sna svelo

ura cima)da ponto, que sai na

uido incomumtrica qou seja:

rea

ica escoame

o o da tubu

0$1(17

a da seoseo 2 veseo 1 ocidade na

), que se c com o dea seo 2,

mpressveque entra n

ento

lao

(

o 1 rea elocidade

a seo 2

caracterizaecorrer do ou seja:

l e como ana seo 1

a o

a 1

13

Com a relao entre vazo e velocidade, Q = v . A (v=velocidade e A=rea), podemos escrever: Q1 = v1 . A1 = Q2 = v2 . A2 Se o fluido incompressvel a vazo em volume a mesma em qualquer seo. Essa equao valida para qualquer seo do escoamento, resultando assim uma expresso geral que a Equao da Continuidade para fluidos incompressveis. Q1 = Q2 = constante Pela equao acima, pode-se obter a relao de velocidades em qualquer seo da tubulao. Nota-se que para uma determinada vazo escoando atravs de uma tubulao, uma reduo de rea acarretar um aumento de velocidade e vice-versa.

(;3(5,1&,$'(5(

.REGIME LAMINAR: .REGIME TRANSITRIO:.REGIME TURBULENTO:Reynolds aps sua investigaes, concluiu que o melhor critrio para determinar estes regimes so, atravs da equao:

Re Nmero de Reynolds (n sem dimenso)

Re = v x D v velocidade de escoamento do fluido (m/s) D dimetro interno da tubulao(m)

viscosidade cinemtica do fluido(m2/s)

.LIMITES DO NMERO DE REYNOLDS PARA TUBOS

Re 2000 escoamento laminar

2000 Re 4000 escoamento transitrio

Re 4000 escoamento turbulento

Notar que o nmero de Reynolds um nmero adimensional, independendo portanto do sistema de unidades adotado, desde que coerente. No geral, na prtica, o escoamento da gua em canalizaes se d em regime turbulento. Exceo feita quando as velocidades so muito baixas ou fluidos tem alta viscosidade.

15

(42SD&RQmFRSUHSR

&R

$OLQ

48$d2

WHRUHPDGUWLFXODUGRRQVLGHUDQGR H[LVWHQVWDQWH DHVVmRSQWRGRIOXL

RQVLGHUDQG

QKDSLH]RP

(48$

2'(%(5

GH%HUQRR3ULQFtSLRGRVHXPYLVFRVLGD

D VRPDG DSRUXQLGRRXVHM

GRDILJXUD

YJ

S

=

PpWULFDpG

$d2'$

5128//,

XLOOLpXPRGD&RQVHHVFRDPH

DGH QmRDV HQHUJLLGDGHGHMD

DDEDL[R

Y

$

GHWHUPLQD

=

(1(5*,$

GRVPDLVHUYDomRGHHQWRHPUHKi GLVVLSDV SRWrQSHVRHF

S=

SODQRG

SODQRG

DGDSHODVR

S=

Y

$3$5$5

VLPSRUWDQH(QHUJLDHJLPHSHUSDomR GHQFLDO RX GLQpWLFDY

YJ

GHFDUJDWR

GHUHIHUrQ

RPDGRVWH

J

5(*,0(

QWHVGDKPDQHQWHHQHUJLD

GH SRVLomRJSRU

FRQVW

RWDO

QFLD

HUPRV =

S =

Y

$

Y

Y

3(50$1

LGUiXOLFDH

GHXPOtTGXUDQWHR = SRUXQLGDGHG

WDQWH

S

=

S=

S J

YFDUJD

WRWDO

1(17(

HUHSUHVH

XLGRSHUIHR VHXPXQLGDGHGHSHVR

J

S

=

SDUDFDG

HQWDXPF

HLWRRXLGRYLPHQWRGH SHVRHPTXDOT

GDVHomR

FDVR

HDO p GHTXHU

S Z = Posio p = Presso = Peso especfico v = Velocidade g = Acelerao da gravidade

16

$1GH3LQW

127$2WSRD

E

'$37$d

RLWHPDQWHHQHUJLDS

DUDRVOtTXURGX]LQGR

WHUPR+SpQWRSDUD

+SRQWR

+SRQWR

Y

S

2'27(

HULRUFRQVSRUDWULWRGLGRVUHDLVRVHXPDS

J

Y

=

pDHQHUJLDDRSRQWR

(25(0$

VLGHURXVHGROtTXLGRFVID]VHQSDUFHODUHS

Y

$

=

DSHUGLGD3RUWDQWR+!+VHQGR

=

=

S

'(%(51

HXPOtTXLGFRPDWXEXQHFHVViULDSUHVHQWDWL

SODQRGH

SODQRGH

SHOROtTXLG

S=

S=

Y

Y

9

128,//,3

GRSHUIHLWXODomRDYDDDGDSWDLYDGHVWDV

FDUJDWRWD

HUHIHUrQF

J =

GRUHDOSR

J

J

3$5$/4

RTXHQmYLVFRVLGDGDomRGR7VSHUGDVF

DO

FLD

S=

RUXQLGDGH

S +

S +

Y

$

Y

Y

Y

Y

48,'265

RFRQVLGHGHHWF7HRUHPDGFRQIRUPHD

+J

S

=

J

HGHSHVR

S J

S J

FDUJD

WRWDO

5($,6

HUDRHIHLWR

GH%HUQRXDEDL[R

+SJ

+S

QRHVFRD

RGDVSHUG

XLOOL

PHQWRGR

( H1 = H2 + Hp )

17

(TXDomRGH%HUQRXOOLSDUD)OXLGR3HUIHLWR,QFRPSUHVVtYHOFRPD3UHVHQoDGHXPD0iTXLQDQR(VFRDPHQWR

0iTXLQD %RPED% )RUQHFHHQHUJLDDRIOXLGR0

7XUELQD7 5HWLUDHQHUJLDGRIOXLGR

D%20%$

+ +

%

+ +% +

+% (QHUJLD IRUQHFLGD DRIOXLGR SHOD ERPED SRUXQLGDGHGHSHVR&DUJDRXDOWXUDPDQRPpWULFDGDERPED

E785%,1$

+ ! +

+ +7 +

7

+7 (QHUJLD UHWLUDGD GRIOXtGR SHOD WXUELQD SRUXQLGDGH GH SHVR &DUJDRX DOWXUD PDQRPpWULFD GDWXUELQD

*HQHULFDPHQWH

+P ! 0p%RPED+P +%

0

+P 0p7XUELQD+P +7

+ +P +

H1 H2

H2H1

H2H1

HM

HT

HB

18

P

P

P

Equao de Bernoulli para Fluido Real e Presena de uma Mquina no Escoamento.

a) Sem Mquina Perda de energia

(1) H1 > H2 (2)

H1 > H2

H1 = H2 + H

H

= Perda de energia de 1 para 2 por unidade de peso.

H

= Perda de carga (m, cm, mm)

Observao Importante: Havendo o escoamento e devido HP, temos por exemplo:

(Trecho onde no existe mquina)

(1) (2)

Escoamento de (1) para (2): H1 > H2 Escoamento de (2) para (1): H2 > H1

b) Com Mquina

M

H1 + Hm = H2 + HP12 (1) (2)

H2H1

H2H1

H2H1HM

19

c) Resumo:

Fluido Perfeito Fluido Real

a) sem mquina: H1 = H2 a) sem mquina: H1 = H2 + HP12 b) c/ mquina H1 + Hm = H2 b) com mquina H1 + Hm = H2 + HP12Potncia (P0) Fornecida ou Retirada do Fluido na Passagem pela Mquina e Rendimento

.Potncia (P0) RXSRWrQFLDKLGUiXOLFDIRUQHFLGDRXUHWLUDGDGHSHQGHGRWLSRGHPiTXLQD

: Peso especfico do fluido que atravessa a mquina.

Q: Vazo volumtrica do fluido na passagem pela Mquina.

Hm : Energia fornecida ou retirada do fluido pela mquina por unidade de peso.

P0 = QHm

- M.K*.S -

kgf/m3 Q m3/s P0 = kgf . m/s (kgm/s) Hm m

- S.I.

N/m3

Q m3/s P0 = N m

J W

s s

Hm m

1C.V. = 75 kgf .m/s

1C.V. = 736 W = 0,736 kW

20

3

%

5HQGLPHQWR

D%20%$

% 3R%

3R3RWrQFLDIRUQHFLGDDRIOXtGR3%3RWrQFLDGD%RPED

3R3% % 3 4+%%

E785%,1$

377

3R3R3RWrQFLDUHWLUDGDGRIOXLGR

37 3RWrQFLDGDWXUELQD

37 3R 7 37 4+P 7

3

21

(6&2$0(1723(50$1(17('()/8'265($,6,1&2035(669(,6(0&21'8726)25d$'262FRQGXWRpGLWRIRUoDGRTXDQGRRIOXtGRTXHQHOHHVFRDRSUHHQFKHWRWDOPHQWHHVWDQGRHPFRQWDWRFRPWRGDDVXDSDUHGHLQWHUQDQmRDSUHVHQWDQGRQHQKXPDVXSHUItFLHOLYUH58*26,'$'(2VFRQGXWRVDSUHVHQWDPUXJRVLGDGHRXDVSHUH]DQDVSDUHGHVLQWHUQDV$UXJRVLGDGHRXDVSHUH]DSRGHVHUGHWHUPLQDGDDWUDYpVGHXPDSDUHOKRFKDPDGRUXJRVLPHWURTXHPHGHDDOWXUDPpGLDGDVDVSHUH]DVGDSDUHGHLQWHUQDGRVWXERV$UXJRVLGDGHUHODWLYDpDUHODomRHQWUHDUXJRVLGDGHDEVROXWDHHRGLkPHWUR'GDWXEXODomRUU BHB2QGHUU 5XJRVLGDGHUHODWLYD'H 5XJRVLGDGHDEVROXWDP' 'LkPHWURGRWXERP

&RQGXWRV/LVRVH5XJRVRV6XSHUItFLHOLVDQDYHUGDGHQmRKi(PXPHVFRDPHQWRGROtTXLGRSRUXPFRQGXWRRXWXERMXQWRDSDUHGHGRWXERHQFRQWUDVHXPDFDPDGDDGHUHQWHHLPyYHOGROtTXLGR2OtTXLGRHPPRYLPHQWRHVWiHPFRQWDWRFRPHVWDFDPDGDDGHUHQWHHLPyYHOHVWDFDPDGDGHOtTXLGRHVWDFLRQiULDpFKDPDGDILOPHODPLQDU3RUWDQWRD2HVFRDPHQWRVHUHDOL]DHPWXEROLVRTXDQGRDVDVSHUH]DVGDSDUHGHGRWXERVmRPHQRUHVTXHDHVSHVVXUDGRILOPHODPLQDU1HVWDFRQGLomRDQDWXUH]DGHVVDVDVSHUH]DVQmRLQIOXLQD]RQDWXUEXOHQWDE2HVFRDPHQWRVHUHDOL]DHPWXERUXJRVRTXDQGRDVDVSHUH]DVGDSDUHGHXOWUDSDVVDPDHVSHVVXUDGRILOPHODPLQDUHHQWUDPQD]RQDWXUEXOHQWDSURYRFDPRDXPHQWRGHVWDUHVXOWDQGRXPDSHUGDPDLVHOHYDGD

D

e

22

e

3(5'$6'(&$5*$2VOtTXLGRVUHDLVQmRVmRSHUIHLWRV$YLVFRVLGDGHHRDWULWRVmRRVSULQFLSDLVUHVSRQViYHLVSHODVSHUGDVGHFDUJD2HVFRDPHQWRGROtTXLGRUHDOSRUXPFRQGXWRRXWXERSURYRFDSHUGDVGHFDUJDTXHGLVVLSDPQDIRUPDGHFDORUTXHRFRUUHPSULQFLSDOPHQWHGHYLGRDRDWULWRHQWUHDVSDUWtFXODVGROtTXLGRUHDOFRPDVSDUHGHVGRWXERRVFRQGXWRVDSUHVHQWDPDVSHUH]DVQDVSDUHGHVLQWHUQDVHGHYLGRDRDWULWRHQWUHDVSDUWtFXODVGROtTXLGRUHDO3RUWDQWRDSHUGDGHFDUJDpXPDSHUGDGHHQHUJLDRXGHSUHVVmR$VSHUGDVGHFDUJDSRGHPVHU'LVWULEXtGDV/RFDOL]DGDVRXVLQJXODUHVRXDFLGHQWDLV3HUGDGHFDUJDWRWDOpDVRPDGHWRGDVDVSHUGDVGHFDUJDGLVWULEXtGDVFRPWRGDVDVSHUGDVGHFDUJDORFDOL]DGDV3HUGDVGHFDUJD'LVWULEXtGDV6mRDTXHODVTXHRFRUUHPDRORQJRGRVFRQGXWRV2FRUUHPSHORPRYLPHQWRGDiJXDQDSUySULDWXEXODomR7DPEpPFKDPDGDVGHSHUGDVFRQWtQXDVSRLVDGPLWHVHTXHHVVDSHUGDVHMDXQLIRUPHHPTXDOTXHUWUHFKRGDWXEXODomRGHGLPHQV}HVFRQVWDQWHVLQGHSHQGHQWHGDSRVLomRGDPHVPD$WUDYpVGHH[SHULrQFLDVUHDOL]DGDVSRUSHVTXLVDGRUHVIRUDPGHVHQYROYLGDVIyUPXODVSDUDRFiOFXORGDSHUGDGHFDUJDGLVWULEXtGD$VSULQFLSDLVVmR)yUPXOD8QLYHUVDORXIyUPXODGH'DUF\:HLVEDFK )yUPXODGH+D]HQ:LOOLDPV)yUPXOD)DLU:KLSSOH+VLDR)yUPXOD)ODPDQW

Filme Laminar

Filme Laminar

e

e

Tubo Liso

Tubo Rugoso

23

3HUGDVGHFDUJD/RFDOL]DGDVRXVLQJXODUHVRXDFLGHQWDLV6mRDTXHODVRFDVLRQDGDVSHODSDVVDJHPGROtTXLGRSHORVGLYHUVRVSRQWRVVLQJXODUHVH[LVWHQWHQDFDQDOL]DomRRXWXEXODomRRXVHMDVmRDTXHODVRFDVLRQDGDVSRUSHoDVHVSHFLDLVFRQH[}HVYiOYXODVUHJLVWURVPHGLGRUHVPXGDQoDVGHGLUHomRFRWRYHORVFXUYDVWrVHWFPXGDQoDGHGLkPHWURUHGXo}HVHDPSOLDo}HVSRUREVWUXo}HVSDUFLDLVHHWFH[LVWHQWHVHPXPDGHWHUPLQDGDFDQDOL]DomRRXWXEXODomR3RUWDQWRGLYHUVRVWLSRVGHSHUGDVDFLGHQWDLVRXVLQJXODUHVRXORFDOL]DGDVSRGHPH[LVWLUQDVFDQDOL]Do}HVRXWXEXODo}HVHGHYHPVHUREVHUYDGDV$EDL[RDVSULQFLSDLVIyUPXODVHPpWRGRVSDUDFDOFXODUDVSHUGDVGHFDUJDORFDOL]DGDV)yUPXODJHUDOGDSHUGDGHFDUJDORFDOL]DGDRXPpWRGRGRN0pWRGRGRVFRPSULPHQWRVHTXLYDOHQWHVRXYLUWXDO,167$/$d2'(5(&$/48(eFRPSRVWDSRUWXEXODomRFRQMXQWRPRWRUHERPEDHDFHVVyULRVQHFHVViULRVSDUDWUDQVSRUWDUXPDYD]mRGHOtTXLGRGHXPORFDORXUHVHUYDWyULRQXPDFRWDLQIHULRUSDUDRXWURORFDORXRXWURUHVHUYDWyULRQXPDFRWDVXSHULRU$ERPEDpDPDTXLQDTXHIRUQHFHHQHUJLDGHQRPLQDGDFDUJDPDQRPpWULFDGDERPED+%2LQVWDODomRGHUHFDOTXHpGLYLGLGDHP7XEXODomRGHVXFomReDTXHODFRQVLGHUDGDFRPRDWXEXODomRDQWHVGDERPEDeDWXEXODomRTXHOLJDRUHVHUYDWyULRLQIHULRUjERPED,QFOXLSRUH[HPSORDFHVVyULRVWDLVFRPRYiOYXODGHSpFULYRYiOYXODFXUYDVUHGXo}HVHWF7XEXODomRGHUHFDOTXHeDTXHODFRQVLGHUDGDFRPRDWXEXODomRDSyVDERPEDeDWXEXODomRTXHOLJDDERPEDDRUHVHUYDWyULRVXSHULRU,QFOXLSRUH[HPSORDFHVVyULRVFRPRYiOYXODYiOYXODVGHUHWHQomRFXUYDVHWF

24

(Distribuda)

(Distribuda)

(Localizada)

(Distribuda)(Localizada)

(Localizada)

(Localizada)

(Localizada)

(Localizada)

25