0510820 2010 postextual - puc-rio · savidge, j. l. aga10 sound speed equations: background,...
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Referências Bibliográficas
ABRAMOWITZ, M.; STEGUN, I. A. Handbook of mathematical functions.
Nova York: Dover Publications, 1965.
AGA 3.1: Natural gas fluids measurement: Concentric, square-edged orifice
meters: General equations and uncertainty guidelines. American Gas Association,
1993.
AGA 3.2: Natural gas fluids measurement: Concentric, square-edged orifice
meters: Specification and installation requirements. American Gas Association,
2000.
AGA 7: Measurement of gas by turbine meters. American Gas Association, 1996.
AGA 9: Measurement of gas by multipath ultrasonic meters. American Gas
Association, 2007.
AGA 10: Speed of sound in natural gas and other related hydrocarbon gases. 2 sd.
American Gas Association, 2003.
AGA M-96-2-3: Ultrasonic Flow Measurement for Natural Gas Applications,
American Gas Association: Engineering Technical Note, 1996.
ANSI/ASME MFC-2M : Measurement uncertainty for fluid flow in closed
conduits. American Society of Mechanical Engineers, 1983.
ANSYS, CFX Release 12.0, ANSYS, 2009.
ANTUNES, B. C., Ultrasonic transit-time on heavy, high viscosity oils,
Proceedings of HEAVY OIL WORKSHOP, Rio de Janeiro, 2009.
API 4.8: Proving systems: Operation of proving systems. American Petroleum
Institute, Manual of Petroleum Measurement Standards, 2002.
API 5.3: Metering: Measurement of liquid hydrocarbons by turbine meters.
American Petroleum Institute, Manual of Petroleum Measurement Standards,
2005.
![Page 2: 0510820 2010 postextual - PUC-Rio · SAVIDGE, J. L. AGA10 sound speed equations: background, thermodynamic relations, ideal gas and equation of state methods, uncertainty analysis,](https://reader031.vdocuments.net/reader031/viewer/2022011800/5ad69f8c7f8b9a6b668bf13a/html5/thumbnails/2.jpg)
225
API 5.8: Metering: measurement of liquid hydrocarbons by ultrasonic flow
meters using transit time technology. American Petroleum Institute, Manual of
Petroleum Measurement Standards, 2005.
API 12.2.3: Calculation of petroleum quantities using dynamic measurement
methods and volumetric correction factors: Proving reports. American Petroleum
Institute, Manual of Petroleum Measurement Standards, 2002.
API 13.1: Statistical aspects of measuring and sampling: statistical concepts and
procedures in measurements. American Petroleum Institute, Manual of Petroleum
Measurement Standards, 2006.
ARANTES, W. F., Avaliação metrológica da comparação inter-laboratorial
da calibração de medidores ultrassônicos. 2007. Dissertação (Mestrado em
Metrologia para Qualidade e Inovação) – Pontifícia Universidade Católica do Rio
de Janeiro, Rio de Janeiro, 2007.
BOGUE, D.C.; METZNER, A.B. Velocity profiles in turbulent pipe flow –
Newtonian and non-Newtonian fluids, Industrial & Engineering Chemistry
Fundamentals (I&EC Fundamentals), v.2, n.2, 1963.
BRASSIER, P. Débitmétrie par technique ultrasonore en milieu gazeux
industriel . 2000. Tese (Doutorado) – École Doctorale de Sciences Physiques e de
L’Ingenieur, L’Université Bordeaux I, Bordeaux., 2000.
BROWN G.; AUGENSTEIN D.; COUSINS T. Velocity profile effects on
multipath ultrasonic meters. Proceedings of INTERNATIONAL SYMPOSIUM
ON FLUID FLOW MEASUREMENT, 6., Querétaro, 2006a.
BROWN, G.; AUGENSTEIN, D.; COUSINS, T. The relative merits of ultrasonic
meters employing between two and eight paths. Proceedings of
INTERNATIONAL SOUTH EAST HYDROCARBON FLOW
MEASUREMENT WORKSHOP, 5., Kuala Lumpur, 2006b.
BROWN, G. J.; COUSINS T., AUGENSTEIN, D. R., ESTRADA, H. The
performance of ultrasonic meters in heavy oil applications, Proceedings of
HEAVY OIL WORKSHOP, Rio de Janeiro, 2009.
![Page 3: 0510820 2010 postextual - PUC-Rio · SAVIDGE, J. L. AGA10 sound speed equations: background, thermodynamic relations, ideal gas and equation of state methods, uncertainty analysis,](https://reader031.vdocuments.net/reader031/viewer/2022011800/5ad69f8c7f8b9a6b668bf13a/html5/thumbnails/3.jpg)
226
BUTKUS, J.; JAKEVICIUS, L.; VLADISAUKAS, A. Control of directivity
patterns of electroacoustical transducers when measuring gas flow parameters,
Ultragarsas, Kaunas, v. 52, p. 13-17, 2004.
CALDON. LEFM 240C: Installation, Operation and Maintenance Manual, 2005.
CALOGIROU, A.; BOEKHOVEN, J.; HENKES, R.A.W.M. Effect of wall
roughness changes on ultrasonic gas flowmeters, Flow Measurement and
Instrumentation , v.12, pp. 219-229, 2001.
DIAS, J. L. Metodologia para avaliação metrológica e determinação da
periodicidade de calibração em sistemas de medição fiscal e apropriação de
gás. 2007. 110p. Dissertação (Mestrado em Metrologia para Qualidade e
Inovação) – Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro,
2007.
ESTRADA, H.; COUSINS, T.; AUGENSTEIN, D. Installation effects and
diagnostic interpretation using the Caldon ultrasonic meter. Proceedings of
NORTH SEA FLOW MEASUREMENT WORKSHOP, 22., St. Andrews, 2004.
p. 1-14.
FERREIRA, A. L. A. S.; ORLANDO, A. F. Influence of the entrance flow field
on the development of the velocity profile in a straight pipe flow. Anais do
INTERNATIONAL CONGRESS OF MECHANICAL ENGINEER, 20.,
Gramado, 2009.
FRASIER, W. E. Applications for ultrasonic meters. Pipeline and Gas
Technology. 2008.
FOX, R. W.; MCDONALD, A. T. Introdução à Mecânica dos Fluidos. 5. ed.
Livros Técnicos e Científicos Editora, 2001.
GRIMLEY, T. A. Ultrasonic meter installation configuration testing. Proceedings
of AGA 2000 OPERATIONS CONFERENCE, Denver, 2000.
HINZE, J. O. Turbulence, McGraw-Hill Publishing Co., New York, 1975.
HOGENDOORN, J.; TAWACKOLIAN, K.; BRAKEL, P.; KLOOSTER, J.;
DRENTHEN, J. High viscosity hydrocarbon flow measurement, a challenge for
ultrasonic flow meters?. Proceedings of HEAVY OIL WORKSHOP, Rio de
Janeiro, 2009.
![Page 4: 0510820 2010 postextual - PUC-Rio · SAVIDGE, J. L. AGA10 sound speed equations: background, thermodynamic relations, ideal gas and equation of state methods, uncertainty analysis,](https://reader031.vdocuments.net/reader031/viewer/2022011800/5ad69f8c7f8b9a6b668bf13a/html5/thumbnails/4.jpg)
227
INMETRO. GUIA : Guia para a expressão da incerteza de medição. 3. ed. 2003.
INMETRO. EA-4/02: Expressão da incerteza de medição na calibração. 2010.
INMETRO. VIM : Vocabulário internacional de metrologia: conceitos
fundamentais e gerais e termos associados. 2009.
ISO 3534-2: Statistics: Vocabulary and symbols: Applied statistics. International
Organization for Standardization, 2006.
ISO 5168: Measurement of fluid flow: procedures for the evaluation of
uncertainties. International Organization for Standardization, 2005.
ISO 12765: Measurement of fluid flow in closed conduits: methods using transit-
time ultrasonic flowmeters. International Organization for Standardization,
Technical Report, 1998.
ISO ISO/GUM: Uncertainty of measurement: guide to the expression of
uncertainty in measurement (ISO/IEC Guide 98-3). International Organization for
Standardization, 2008.
ISO ISO/VIM: International vocabulary of metrology: basic and general concepts
and associated terms (ISO/IEC Guide 99). International Organization for
Standardization, 2007.
JEANNEAY, H.; PIGUET, M. Pipe flow modeling for ultrasonic flow
measurement. Proceedings of FLOMEKO, Salvador, 2000.
JUNG, J.C., SEONG, P.H. Estimation of the flow profile correction factor of a
transit-time ultrasonic flow meter for the feedwater flow measurement in a nuclear
power plant. IEEE Transactions on nuclear science, vol.52, n.3, jun. 2005.
KAYS, W. M.; CRAWFORD, M. E. Convective heat and mass transfer,
Hightstown, NJ: McGraw-Hill, 1993.
KROHNE. UFM 3030 Technical Data Sheet, Krohne, 2005.
LANSING, J. Ultrasonic gas flowmeter diagnostic basics. Pipeline & Gas
Journal, 2001.
LAUNDER, B.E.; SPALDING, D.B. The numerical computation of turbulent
flows. Computer methods in applied mechanics and engineering, 3: p. 269-289,
1974.
![Page 5: 0510820 2010 postextual - PUC-Rio · SAVIDGE, J. L. AGA10 sound speed equations: background, thermodynamic relations, ideal gas and equation of state methods, uncertainty analysis,](https://reader031.vdocuments.net/reader031/viewer/2022011800/5ad69f8c7f8b9a6b668bf13a/html5/thumbnails/5.jpg)
228
MARCHETTI, C., Utilização de medidores ultrassônicos para medição fiscal
de vazão de gás natural. 2009. Dissertação (Mestrado em Metrologia para
Qualidade e Inovação) – Pontifícia Universidade Católica do Rio de Janeiro, Rio
de Janeiro, 2009.
MATTINGLY, G. E.;YEH, T. T. NIST's ultrasonic technology assessment
program to improve flow measurement. NIST Tech. Note Virgínia: NIST,
1999.
MOORE, P. I. Modelling of installation effects on transit time ultrasonic flow
meters in circular pipes. 2000. Tese (Doutorado) – Departament of Electronic
and Electrical Engineering, University of Strathclyde, Grã-Bretanha, 2000.
MOORE, P. I.; BROWN, G. J.; STIMPSON, B. P. Modelling of transit time
ultrasonic flowmeters in theoretical asymmetric flow. Proceedings of FLOMEKO,
Salvador, 2000a.
MOORE, P. I.; BROWN, G. J.; STIMPSON, B. P. Ultrasonic transit-time
flowmeters modeled with theoretical velocity profiles: methodology.
Measurement Science and Technology. Bristol, UK, v. 11, n. 11, 2000b.
MOORE, P; PIOMELLI, U.; JOHNSON, A. N.; ESPINA, P. I. Simulations of
ultrasonic transit time in a fully developed turbulent flow using a ray-tracing
method. Proceedings of NORTH SEA FLOW MEASUREMENT WORKSHOP,
20., St. Andrews, 2002.
MYLVAGANAM, K. S. High-rangeability ultrasonic gas flowmeter for
monitoring flare gas. IEEE Transactions on Ultrasonics, Ferroelectrics, and
Frequency Control, Aurora, v. 36, n. 2, 1989.
NEL, Long term evaluation of ultrasonic flowmeter. Flow Measurement
Guidance Note n. 25, Glasgow. 2000.
OBERKAMPF, W. L., TRUCANO, T. G., Verification and validation in
computational fluid dynamics. Progress in Aerospace Sciences Journal, 2002.
ref. SAND2002-0529.
OIML R-117-1: Measuring systems for liquids other than water: metrological and
technical requirements. International Organization of Legal Metrology, 2007.
![Page 6: 0510820 2010 postextual - PUC-Rio · SAVIDGE, J. L. AGA10 sound speed equations: background, thermodynamic relations, ideal gas and equation of state methods, uncertainty analysis,](https://reader031.vdocuments.net/reader031/viewer/2022011800/5ad69f8c7f8b9a6b668bf13a/html5/thumbnails/6.jpg)
229
OIML R-137-1: Gas Meters: Requirements. International Organization of Legal
Metrology, 2006.
OLIVEIRA, T. B. V.; PINHEIRO, J. A.; MATA, J. D.; CHURRO, J. J. T.;
ORLANDO, A. F.; VAL, L. G. Medição de petróleo e diagnóstico em medidores
do tipo ultra-sônico em elevadas vazões e viscosidades, Anais do RIO PIPELINE
CONFERENCE, 2007.
ORLANDO, A.F.; PINHEIRO, J. A.; MATA, J. D. Heavy oil flow measurement
and diagnostics with ultrasonic flow meters. Proceedings of HEAVY OIL
WORKSHOP, Rio de Janeiro, 2009.
RTM-001/2000: Regulamento técnico metrológico de petróleo e gás natural.
ANP/INMETRO, 2000.
RTM-64: Regulamento técnico metrológico referente à medição dinâmica de
petróleo, derivados líquidos e álcool. INMETRO, 2003.
SAKARIASSEN, R.; SDUN, W.; VULOVIC, F.; VIETH, D. Long term
comparison of an ultrasonic meter and a turbine meter with an orifice meter at
EMS test loop. Proceedings of NORTH SEA FLOW MEASUREMENT
WORKSHOP, 18., St. Andrews, 2000.
SALAMI, L. A. Application of a computer to asymmetric flow measurement in
circular pipes. Transaction of Institute Measurement and Control, London, v.
6, n. 4, p. 197-206, 1984.
SAVIDGE, J. L. AGA10 sound speed equations: background, thermodynamic
relations, ideal gas and equation of state methods, uncertainty analysis, and
calculation flow diagram for natural gas measurement applications. Proceedings
of INTERNATIONAL SYMPOSIUM ON FLUID FLOW MEASUREMENT, 5.,
Washington, 2002.
SCHEID F. Theory and Problems of Numerical Analysis. Schaum’s Outline
Series, McGraw-Hill Book Company, 1968.
SCHLICHTING, H. Boundary-layer theory. McGraw-Hill Book, 1968.
SILVA, H. A. Análise metrológica do desempenho de medidores ultrassônicos
de vazão de líquidos como diagnóstico de calibração, instalação e operação.
![Page 7: 0510820 2010 postextual - PUC-Rio · SAVIDGE, J. L. AGA10 sound speed equations: background, thermodynamic relations, ideal gas and equation of state methods, uncertainty analysis,](https://reader031.vdocuments.net/reader031/viewer/2022011800/5ad69f8c7f8b9a6b668bf13a/html5/thumbnails/7.jpg)
230
2008. 100p. Dissertação (Mestrado em Metrologia) – Pontifícia Universidade
Católica do Rio de Janeiro, Rio de Janeiro, 2008.
VATERLAUS, H. P. A new intelligent ultrasonic flowmeter for closed conduits
and open channels. Waterpower, p. 999-1008, 1995.
VATERLAUS, H. P.; HOSSLE, T.; GIORDANO, P.; BRUTTIN, C. Ultrasonic
flowmeters. In: WEBSTER, J. G. Measurement, Instrumentation and Sensors
Handbook. Flórida: CRC Press & IEEE, 1999. p. 28.74-28.89.
WHITE, F. M. Fluid mechanics. New York: McGraw-Hill, 1979.
YAKHOT, V.; ORSZAG, S. A., Renormalization group analysis of turbulence:
basic theory. Journal of Scientific Computing. 1(1): p. 3-50, 1986.
YEH, T. T.; MATTINGLY, G. E. Computer simulations of ultrasonic flow meter
performance in ideal and non-ideal pipeflows. Proceedings of ASME FLUIDS
ENGINEERING DIVISION SUMMER MEETING, Vancouver, 1997. p. 22-26.
ref. FEDSM97-3012.
YODER, J. Ultrasonic flow meters in the energy measurement spotlight. Pipeline
& Gas Journal, 2009.
ZAGAROLA, M.V.; SMITS, A.J. Mean-flow scaling of turbulent pipe flow, J.
Fluid. Mech., v.373, pp. 33-79, 1998.
ZANKER, K. J. The effects of Reynolds number, wall roughness, and profile
asymmetry on single- and multi- path ultrasonic meters. Proceedings of NORTH
SEA FLOW MEASUREMENT WORKSHOP, 17., Noruega, 1999. 117-129.
ZANKER, K. J.; BROWN, G. J. The performance of a multi-path ultrasonic meter
with wet gas. Proceedings of NORTH SEA FLOW MEASUREMENT
WORKSHOP, 18., St. Andrews, 2000.
ZANKER, K. J. Diagnostic ability of the Daniel four-path ultrasonic flow meter.
Proceedings of SOUTH EAST ASIA HYDROCARBON FLOW
MEASUREMENT WORKSHOP, 2003.
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Apêndice A Curvas: Velocidade de 0D a 100D
Velocidade Média Normalizada (1C; beta = 0o)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-1: Velocidade adimensional para β = 0º (1C).
Velocidade Média Normalizada (1C; beta = 180o)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-2: Velocidade adimensional para β = 180º (1C).
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232
Velocidade Média Normalizada (1C; beta = 90o)
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
1,10
1,20
1,30
1,40
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais
4canais5canaisC8K5
XK3
Figura A-3: Velocidade adimensional para β = 90º (1C).
Velocidade Média Normalizada (1C; beta = 270o)
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
1,10
1,20
1,30
1,40
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-4: Velocidade adimensional para β = 270º (1C).
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233
Velocidade Média Normalizada (2C1P, beta = 0o)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-5: Velocidade adimensional para β = 0º (2C1P).
Velocidade Média Normalizada (2C1P; beta = 180o)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-6: Velocidade adimensional para β = 180º (2C1P).
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234
Velocidade Média Normalizada (2C1P; beta = 90o)
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
1,30
1,35
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais
4canais5canaisC8K5
XK3
Figura A-7: Velocidade adimensional para β = 90º (2C1P).
Velocidade Média Normalizada (2C1P; beta = 270o)
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
1,30
1,35
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-8: Velocidade adimensional para β = 270º (2C1P).
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235
Velocidade Média Normalizada (2C2P; beta = 0o)
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-9: Velocidade adimensional para β = 0º (2C2P).
Velocidade Média Normalizada (2C2P; beta = 180o)
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-10: Velocidade adimensional para β = 180º (2C2P).
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236
Velocidade Média Normalizada (2C2P; beta = 90o)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais
4canais5canaisC8K5
XK3
Figura A-11: Velocidade adimensional para β = 90º (2C2P).
Velocidade Média Normalizada (2C2P; beta = 270o)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura A-12: Velocidade adimensional para β = 270º (2C2P).
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237
Velocidade Média Normalizada (1C; beta = 0o)
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
X
V
XX
#
Figura A-13: Velocidade adimensional para β = 0 (1C).
Velocidade Média Normalizada (1C; beta = 90o)
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
1,30
1,35
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
X
V
XX
#
Figura A-14: Velocidade adimensional para β = 90 (1C).
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238
Velocidade Média Normalizada (2C1P; beta = 0o)
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
X
V
XX
#
Figura A-15: Velocidade adimensional para β = 0 (2C1P).
Velocidade Média Normalizada (2C1P; beta = 90o)
0,70
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
0 10 20 30 40 50 60 70 80 90 100
diâmetros
Vel
ocia
de M
édia
Nor
mal
izad
a 1canal
X
V
XX
#
Figura A-16: Velocidade adimensional para β = 90 (2C1P).
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239
Apêndice B Curvas: Fator de 0D a 100D.
Fator do Medidor (1C; beta = 0o)
0,86
0,88
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-1: Fator de velocidade para β = 0º (1C).
Fator do Medidor (1C; beta = 90o)
0,35
0,45
0,55
0,65
0,75
0,85
0,95
1,05
1,15
1,25
1,35
1,45
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-2: Fator de velocidade para β = 90º (1C).
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240
Fator do Medidor (1C; beta = 270o)
0,35
0,45
0,55
0,65
0,75
0,85
0,95
1,05
1,15
1,25
1,35
1,45
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-3: Fator de velocidade para β = 270º (1C).
Fator do Medidor (2C1P; beta = 0o)
0,88
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-4: Fator de velocidade para β = 0º (2C1P).
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241
Fator do Medidor (2C1P; beta = 90o)
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
1,30
1,35
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-5: Fator de velocidade para β = 90º (2C1P).
Fator do Medidor (2C1P; beta = 270o)
0,65
0,70
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
1,25
1,30
1,35
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-6: Fator de velocidade para β = 270º (2C1P).
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242
Fator do Medidor (2C2P; beta = 0o)
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-7: Fator de velocidade para β = 0º (2C2P).
Fator do Medidor (2C2P; beta = 180o)
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-8: Fator de velocidade para β = 180º (2C2P).
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243
Fator do Medidor (2C2P; beta = 90o)
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-9: Fator de velocidade para β = 90º (2C2P).
Fator do Medidor (2C2P; beta = 270o)
0,75
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
0 10 20 30 40 50 60 70 80 90 100
diâmetros
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura B-10: Fator de velocidade para β = 270º (2C2P).
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244
Apêndice C Curvas: Velocidade na Seção Transversal
Velocidade Média Normalizada (1C; 0D)
0,30
0,50
0,70
0,90
1,10
1,30
1,50
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-1: Velocidade adimensional na seção transversal a 0D (1C).
Velocidade Média Normalizada (1C; 5D)
0,70
0,80
0,90
1,00
1,10
1,20
1,30
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-2: Velocidade adimensional na seção transversal a 5D (1C).
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245
Velocidade Média Normalizada (1C; 20D)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-3: Velocidade adimensional na seção transversal a 20D (1C).
Velocidade Média Normalizada (1C; 80D)
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 45 90 135 180 225 270 315 360
graus
Vel
ocia
de M
édia
Nor
mal
izad
a
1canal2canais3canais4canais5canaisC8K5XK3
Figura C-4: Velocidade adimensional na seção transversal a 80D (1C).
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246
Velocidade Média Normalizada (2C1P; 0D)
0,60
0,70
0,80
0,90
1,00
1,10
1,20
1,30
1,40
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-5: Velocidade adimensional na seção transversal a 0D (2C1P).
Velocidade Média Normalizada (2C1P; 5D)
0,70
0,80
0,90
1,00
1,10
1,20
1,30
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais4canais5canaisC8K5XK3
Figura C-6: Velocidade adimensional na seção transversal a 5D (2C1P).
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247
Velocidade Média Normalizada (2C1P; 20D)
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais4canais5canaisC8K5XK3
Figura C-7: Velocidade adimensional na seção transversal a 20D (2C1P).
Velocidade Média Normalizada (2C1P; 80D)
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais4canais5canaisC8K5XK3
Figura C-8: Velocidade adimensional na seção transversal a 80D (2C1P).
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248
Velocidade Média Normalizada (2C2P; 0D)
0,65
0,75
0,85
0,95
1,05
1,15
1,25
1,35
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-9: Velocidade adimensional na seção transversal a 0D (2C2P).
Velocidade Média Normalizada (2C2P; 5D)
0,90
0,95
1,00
1,05
1,10
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais4canais5canaisC8K5XK3
Figura C-10: Velocidade adimensional na seção transversal a 5D (2C2P).
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249
Velocidade Média Normalizada (2C2P; 20D)
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais4canais5canaisC8K5XK3
Figura C-11: Velocidade adimensional na seção transversal a 20D (2C2P).
Velocidade Média Normalizada (2C2P; 80D)
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal2canais3canais4canais5canaisC8K5XK3
Figura C-12: Velocidade adimensional na seção transversal a 80D (2C2P).
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250
Swirl (1C; 0D)
-0,50
-0,40
-0,30
-0,20
-0,10
0,00
0,10
0,20
0,30
0,40
0,50
0 45 90 135 180 225 270 315 360
graus
W
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-13: Swirl na seção transversal a 0D (1C).
Swirl (2C2P; 0D)
-0,25
-0,20
-0,15
-0,10
-0,05
0,00
0,05
0,10
0,15
0,20
0,25
0 45 90 135 180 225 270 315 360
graus
Vel
ocid
ade
Méd
ia N
orm
aliz
ada
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-14: Swirl na seção transversal a 0D (2C2P).
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251
W Normalizada (1C; 0D)
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 45 90 135 180 225 270 315 360
graus
W
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-15: Velocidade w na seção transversal a 0D (1C).
W Normalizada (2C2P; 0D)
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 45 90 135 180 225 270 315 360
graus
W
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura C-16: Velocidade w na seção transversal a 0D (2C2P).
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252
Apêndice D Curvas: Fator na Seção Transversal.
Fator do Medidor (1C; 0D)
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
1,10
1,20
1,30
1,40
1,50
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-1: Fator do medidor a 0D (1C).
Fator do Medidor (1C; 5D)
0,60
0,70
0,80
0,90
1,00
1,10
1,20
1,30
1,40
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-2: Fator do medidor a 5D (1C).
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253
Fator do Medidor (1C; 20D)
0,80
0,85
0,90
0,95
1,00
1,05
1,10
1,15
1,20
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-3: Fator do medidor a 20D (1C).
Fator do Medidor (1C; 80D)
0,995
0,996
0,997
0,998
0,999
1,000
1,001
1,002
1,003
1,004
1,005
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-4: Fator do medidor a 80D (1C).
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254
Fator do Medidor (2C1P; 0D)
0,60
0,70
0,80
0,90
1,00
1,10
1,20
1,30
1,40
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-5: Fator do medidor a 0D (2C1P).
Fator do Medidor (2C1P; 5D)
0,70
0,80
0,90
1,00
1,10
1,20
1,30
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-6: Fator do medidor a 5D (2C1P).
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255
Fator do Medidor (2C1P; 20D)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-7: Fator do medidor a 20D (2C1P).
Fator do Medidor (2C1P; 80D)
0,995
0,996
0,997
0,998
0,999
1,000
1,001
1,002
1,003
1,004
1,005
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal
2canais
3canais
4canais
5canais
C8
K5
X
K3
Figura D-8: Fator do medidor a 80D (2C1P).
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256
Fator do Medidor (2C2P; 0D)
0,70
0,80
0,90
1,00
1,10
1,20
1,30
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-9: Fator do medidor a 0D (2C2P).
Fator do Medidor (2C2P; 5D)
0,85
0,90
0,95
1,00
1,05
1,10
1,15
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-10: Fator do medidor a 5D (2C2P).
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257
Fator do Medidor (2C2P; 20D)
0,90
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-11: Fator do medidor a 20D (2C2P).
Fator do Medidor (2C2P; 80D)
0,995
0,996
0,997
0,998
0,999
1,000
1,001
1,002
1,003
1,004
1,005
0 45 90 135 180 225 270 315 360
graus
Fat
or
1canal2canais3canais4canais5canaisC8K5XK3
Figura D-12: Fator do medidor a 80D (2C2P).
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258
Apêndice E Curvas: Parâmetros de Diagnóstico
Parâmetros de Turbulência ( beta = 0o)(4canais; 5canais; 5cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-1: Parâmetros de diagnóstico para β = 0º (1C).
Parâmetros de Turbulência ( beta = 90o)(4canais; 5canais; 5cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-2: Parâmetros de diagnóstico para β = 90º (1C).
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Parâmetros de Turbulência ( beta = 180o)(4 canais paralelos; 5 canais paralelos; 5 canais cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.70
0.80
0.90
1.00
1.10
1.20
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-3: Parâmetros de diagnóstico para β = 180º (1C).
Parâmetros de Turbulência ( beta = 270o)(4 canais paralelos; 5 canais paralelos; 5 canais cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.90
1.10
1.30
1.50
1.70
1.90
2.10
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-4: Parâmetros de diagnóstico para β = 270º (1C).
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Parâmetros de Turbulência ( beta = 0o)(4canais; 5canais; 5cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-5: Parâmetros de diagnóstico para β = 0º (2C1P).
Parâmetros de Turbulência ( beta = 90o)(4canais; 5canais; 5cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-6: Parâmetros de diagnóstico para β = 90º (2C1P).
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Parâmetros de Turbulência ( beta = 180o)(4 canais paralelos; 5 canais paralelos; 5 canais cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.70
0.80
0.90
1.00
1.10
1.20
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-7: Parâmetros de diagnóstico para β = 180º (2C1P).
Parâmetros de Turbulência ( beta = 270o)(4 canais paralelos; 5 canais paralelos; 5 canais cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.90
1.10
1.30
1.50
1.70
1.90
2.10
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-8: Parâmetros de diagnóstico para β = 270º (2C1P).
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Parâmetros de Turbulência ( beta = 0o)(4canais; 5canais; 5cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-9: Parâmetros de diagnóstico para β = 0º (2C2P).
Parâmetros de Turbulência ( beta = 90o)(4canais; 5canais; 5cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.70
0.80
0.90
1.00
1.10
1.20
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-10: Parâmetros de diagnóstico para β = 90º (2C2P).
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Parâmetros de Turbulência ( beta = 180o)(4 canais paralelos; 5 canais paralelos; 5 canais cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-11: Parâmetros de diagnóstico para β = 180º (2C2P).
Parâmetros de Turbulência ( beta = 270o)(4 canais paralelos; 5 canais paralelos; 5 canais cruzados)
Assimetria (Ass); Escoamento Cruzado (Cruz); Turbulência (Turb)
0.70
0.80
0.90
1.00
1.10
1.20
1.30
0 10 20 30 40 50 60 70 80 90 100
diametro
Ass_4c
Cruz_4c
Turb_4c
Ass_5c
Cruz_5c
Turb_5c
Ass_5K
Cruz_5K
Turb_5K
Figura E-12: Parâmetros de diagnóstico para β = 270º (2C2P).
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Apêndice F Degrau-Duplo: Velocidade e Fator
Velocidade no Degrau-Duplo de -7%
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 100000 200000 300000 400000 500000
Re
Vel
ocid
ade
Nor
mal
izad
a
1 canal2 canais3 canais4 canais5 canais
Figura F-1: Velocidade para o degrau-duplo convergente de −7%.
Fator para Degrau-Duplo de -7%
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 100000 200000 300000 400000 500000
Re
Fat
or
1 canal2 canais3 canais4 canais5 canais
Figura F-2: Fator para degrau-duplo convergente de −7%.
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Velocidade no Degrau-Duplo de -4%
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 100000 200000 300000 400000 500000
Re
Vel
ocid
ade
Nor
mal
izad
a
1 canal2 canais3 canais4 canais5 canais
Figura F-3: Velocidade para o degrau-duplo convergente de −4%.
Fator para Degrau-Duplo de -4%
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 100000 200000 300000 400000 500000
Re
Fat
or
1 canal2 canais3 canais4 canais5 canais
Figura F-4: Fator para o degrau-duplo convergente de −4%.
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Velocidade no Degrau-Duplo de -1%
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 100000 200000 300000 400000 500000
Re
Vel
ocid
ade
Nor
mal
izad
a
1 canal2 canais3 canais4 canais5 canais
Figura F-5: Velocidade para o degrau-duplo convergente de −1%.
Fator para Degrau-Duplo de -1%
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 100000 200000 300000 400000 500000
Re
Fat
or
1 canal2 canais3 canais4 canais5 canais
Figura F-6: Fator para o degrau-duplo convergente de −1%.
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267
Velocidade no Degrau-Duplo de 7%
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 100000 200000 300000 400000 500000
Re
Vel
ocid
ade
Nor
mal
izad
a
1 canal2 canais3 canais4 canais5 canais
Figura F-7: Velocidade para o degrau-duplo divergente de 7%.
Fator para Degrau-Duplo de 7%
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 100000 200000 300000 400000 500000
Re
Fat
or
1 canal2 canais3 canais4 canais5 canais
Figura F-8: Fator para o degrau-duplo divergente de 7%.
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Velocidade no Degrau-Duplo de 4%
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 100000 200000 300000 400000 500000
Re
Vel
ocid
ade
Nor
mal
izad
a
1 canal2 canais3 canais4 canais5 canais
Figura F-9: Velocidade para o degrau-duplo divergente de 4%.
Fator para Degrau-Duplo de 4%
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 100000 200000 300000 400000 500000
Re
Fat
or
1 canal2 canais3 canais4 canais5 canais
Figura F-10: Fator para o degrau-duplo divergente de 4%.
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Velocidade no Degrau-Duplo de 1%
0,94
0,96
0,98
1,00
1,02
1,04
1,06
1,08
1,10
0 100000 200000 300000 400000 500000
Re
Vel
ocid
ade
Nor
mal
izad
a
1 canal2 canais3 canais4 canais5 canais
Figura F-11: Velocidade para o degrau-duplo divergente de 1%.
Fator para Degrau-Duplo de 1%
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 100000 200000 300000 400000 500000
Re
Fat
or
1 canal2 canais3 canais4 canais5 canais
Figura F-12: Fator para o degrau-duplo divergente de 1%.
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Fator para Degrau-Duplo (Re = 50000)
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
-8-7-6-5-4-3-2-10
Degrau (%)
1 canal2 canais3 canais4 canais5 canais
Figura F-13: Fator para o degrau-duplo convergente com Re = 50.000.
Fator para Degrau-Duplo (Re = 50000)
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 1 2 3 4 5 6 7 8
Degrau (%)
1 canal2 canais3 canais4 canais5 canais
Figura F-14: Fator para o degrau-duplo divergente com Re = 50.000.
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Fator para Degrau-Duplo (Re = 150000)
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
-8-7-6-5-4-3-2-10
Degrau (%)
1 canal2 canais3 canais4 canais5 canais
Figura F-15: Fator para o degrau-duplo convergente com Re = 150.000.
Fator para Degrau-Duplo (Re = 150000)
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 1 2 3 4 5 6 7 8
Degrau (%)
1 canal2 canais3 canais4 canais5 canais
Figura F-16: Fator para o degrau-duplo divergente com Re = 150.000.
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Fator para Degrau-Duplo (Re = 400000)
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
-8-7-6-5-4-3-2-10
Degrau (%)
1 canal2 canais3 canais4 canais5 canais
Figura F-17: Fator para o degrau-duplo convergente com Re = 400.000.
Fator para Degrau-Duplo (Re = 400000)
0,975
0,980
0,985
0,990
0,995
1,000
1,005
1,010
1,015
1,020
1,025
0 1 2 3 4 5 6 7 8
Degrau (%)
1 canal2 canais3 canais4 canais5 canais
Figura F-18: Fator para o degrau-duplo divergente com Re = 400.000.