Scale Effects in Free-Flow Nonlinear Weir Head-Discharge Relationships
Publication: Journal of Hydraulic Engineering
Volume 146, Issue 2
Abstract
Using similitude relationships, laboratory-scale models have been used for decades to predict and confirm prototype hydraulic structure performance. For free-flow weir discharge conditions, gravity and inertia typically represent the dominant forces, and the Froude number scales the head-discharge performance between model and prototype. Under low-head flow conditions, other forces (e.g., viscous and surface-tension forces) can become relevant, resulting in differences between the model and prototype performance. In this study, the head-discharge relationships for 15 different nonlinear weirs (labyrinth and piano key) with prototype-to-model length ratios of 2, 3, 6, and 12 (based upon Froude modeling) were evaluated, with the largest weirs ( tall) serving as prototypes. This study found differences in the head-discharge performance between prototype and model that exceeded what could be explained solely by model and measurement effects, confirming the presence of scale effects. The range of small upstream heads influenced by scale effects, in general, increased with decreasing model size. The minimum dimensionless head above which scale effects were negligible increased with decreasing model size. As such, model size and geometric scale appear relevant because no single minimum upstream head limit was found that characterized a scale effects limit for all nonlinear weirs tested herein.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Funding for this study was provided by the State of Utah and the Utah Water Research Laboratory, Utah State University.
References
Alberle, J., C. Rennie, D. Admiraal, and M. Muste. 2017. Experimental hydraulics: Methods, instrumentation, data processing and management: Volume II: Instrumentation and measurement techniques. Boca Raton, FL: CRC Press.
ASME. 2006. Test uncertainty. ASME PTC 19.1-2005. New York: American Society of Mechanical Engineers.
Bazin, H. 1888. “Expériences Nouvelles sur l’Ecoulement en Déversoir” [Recent experiments on the flow of water over weirs]. [In French.] In Vol 16 of Memoires et Documents, Annales des Ponts et Chaussees, 393–448. Philadelphia: Engineers' Club of Philadelphia.
Bollrich, G., and D. Aigner. 2000. Hydraulisches Versuchswesen. Technische Hydromechanik 4. Berlin: Beuth.
Breitschneider, H. 1978. “Bauwerksmodelle: Abflussverhältnisse, Energieumwandlung, erosion” [Physical models: Discharge conditions, energy dissipation, erosion]. [In German.] In Mitteilungsheft 4, edited by H. Kobus, 195–216. Bonn, Germany: German Technical and Scientific Association for Gas and Water.
Castelli, B. 1628. Della misura dell’cque correnti (On the measurement of running water). [In Italian.] Rome: Stamperia Camerale.
Castro-Orgaz, O., and W. H. Hager. 2014. “Scale effects of round-crested weir flow.” J. Hydraul. Res. 52 (5): 653–665. https://doi.org/10.1080/00221686.2014.910277.
Cicero, G. M., J. M. Menon, and M. Luck. 2011. “Experimental study of side and scale effects on hydraulic performance of a piano key weirs.” In Proc., Labyrinth and Piano Key Weirs–PKW 2011. Boca Raton, FL: CRC Press.
Crookston, B. 2010. “Labyrinth weirs.” Ph.D. dissertation. Dept. of Civil and Environmental Engineering, Utah State Univ.
Curtis, K. 2016. “Size scale effect on linear weir hydraulics.” M.S. thesis, Dept. of Civil and Environmental Engineering, Utah State Univ.
Dillmann, O. 1933. “Investigation of weirs.” In Mitteilungen Heft 7. München, Germany: TU München.
Erpicum, S., F. Laugier, J.-L. Boillat, M. Pirotton, B. Reverchon, and A. J. Schleiss, eds. 2011. Labyrinth and piano key weirs. Boca Raton, FL: CRC Press.
Erpicum, S., F. Laugier, M. Ho Ta Khanh, and M. Pfister. 2017. Labyrinth and Piano Key Weirs III–PKW 2017. London: CRC Press.
Erpicum, S., F. Laugier, M. Pfister, M. Pirotton, G. Cicero, and A. Schleiss. 2013. Labyrinth and Piano Key Weirs II–PKW 2013. London: CRC Press.
Erpicum, S., B. P. Tullis, M. P. LodomezArchambeau, P. Archambeau, B. Dwals, and M. Pirotton. 2016. “Scale effects in physical piano key weir models.” J. Hydraul. Res. 54 (6): 692–698. https://doi.org/10.1080/00221686.2016.1211562.
Ettema, R. 2000. Hydraulic modeling, concepts and practice. Reston, VA: ASCE.
Falvey, H. T. 2002. Hydraulic design of labyrinth weirs. Reston, VA: ASCE.
Freeman, J. R. 1929. Hydraulic laboratory practice. Reston, VA: ASCE.
Hager, W. H., and M. Schwalt. 1994. “Broad-crested weir.” J. Irrig. Drain. Eng. 120 (1): 13–26. https://doi.org/10.1061/(ASCE)0733-9437(1994)120:1(13).
Heller, V. 2011. “Scale effects in physical hydraulic engineering models.” J. Hydraul. Res. 49 (3): 293–306. https://doi.org/10.1080/00221686.2011.578914.
Heller, V. 2017. “Self-similarity and Reynolds number invariance in Froude modelling.” J. Hydraul. Res. 55 (3): 293–309. https://doi.org/10.1080/00221686.2016.1250832.
Johnson, M. C. 1996. “Discharge coefficients scale effects analysis for weirs.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Utah State Univ.
Kirschmer, O. 1928. “Untersuchung der Überfallkoeffizienten für einige Where mit gerundeter Krone” [Investigation of discharge coefficients of cylindrical weirs] In Mitteilungen Heft 2, edited by D. Thoma, 5–28. München, Germany: TU München.
Machiels, O. 2012. “Experimental study of the hydraulic behavior of piano key weirs.” Ph.D. dissertation, Dept. of Architecture, Geology, Environment, and Constructions, Univ. of Liège.
Montes, J. S. 1963. “An investigation of some characteristics of suppressed weir flow.”. Wallingford, UK: Hydraulics Research Station.
Montes, J. S. 1998. Hydraulics of open channel flow. Reston, VA: ASCE.
Muste, M., D. A. Lyn, D. Admiraal, R. Ettema, V. Nikora, and M. H. Garcia. 2017. Experimental hydraulics: Methods, instrumentation, data processing and management: Volume 1: Fundamentals and methods. Boca Raton, FL: CRC Press.
Novak, P. 1984. “Scaling factors and scale effects in modelling hydraulic structures.” In Proc., Symp. Scale Effects in Modelling Hydraulic Structures, 1–5, H. Rouse, ed. Esslingen, Germany: Technische Akademie, Esslingen.
Novak, P., and J. Cabelka. 1981. Models in hydraulic engineering, physical principles and design applications. London: Pitman.
Novak, P., V. Guinot, A. Jeffrey, and D. E. Reeve. 2010. Hydraulic modeling—An introduction. Boca Raton, FL: CRC Press.
Pfister, M., E. Battisacco, G. De Cesare, and A. J. Schleiss. 2013. “Scale effects related to the rate curve of cylindrically crested piano key weirs.” In Proc., Labyrinth and Piano Key Weirs II–PKW 2013. Boca Raton, FL: CRC Press.
Pfister, M., S. Erpicum, O. Machiels, A. Schliess, and M. Pirotton. 2012. “Discharge coefficients for free and submerged flow over piano key weirs—Discussion.” J. Hydraul. Res. 50 (6): 642–643. https://doi.org/10.1080/00221686.2012.728025.
Poleni, J. 1717. De motu aquae mixto libri duo. [In Italian.] Padova, Italy: Typis Iosephi Comini.
Rehbock, T. 1909. Die Ausbildung der Überfalle beim Abfluss von Wasser über Wehre. [In German.]. Karlsruhe, Germany: Technische Hochschule Fridericiana.
Rehbock, T. 1929. “Discussion of precise weir measurements by E. W. Schoder and K.B. Turner.” Trans. ASCE 93 (1): 999–1110.
Rouse, H., and S. Ince. 1957. History of hydraulics. New York: Dover.
Sarginson, E. J. 1972. “The influence of surface tension on weir flow.” J. Hydraul. Res. 10 (4): 431–446. https://doi.org/10.1080/00221687209500034.
Swiss Society of Engineers and Architects. 1926. Contribution à l’étude des méthodes de jaugeage. [In French.] Bern, Switzerland: Amt für Wasserwirtschaft.
Torricelli, E. 1644. Opera Geometrica. Florenz, Italy: Amatoris Masse & Laurentij de Landis.
Tullis, B., and N. Young. 2018. “Size-scale effects of piano key weir hydraulics.” In Proc., 38th Annual USSD Conf. Miami.
Tullis, B. P., N. Young, and B. M. Crookston. 2017. “Physical modeling size-scale effects for labyrinth weirs with half-round crests.” In Proc., Labyrinth and Piano Key Weirs III–PKW 2017. Boca Raton, FL: CRC Press.
Tullis, B. P., N. Young, and B. M. Crookston. 2018. “Size-scale effects of labyrinth weir hydraulics.” In Proc., 7th IAHR Int. Symp. on Hydraulic Structures, 15–18. Logan, UT: Utah State Univ.
Weisbach, J. 1845. “Lehrbuch der Ingenieur- und Maschinen-Mechanik.” In Vol. 1 of Theoretische Mechanik. [In German.] Braunschweig, Germany: Vieweg.
Yalin, M. S. 1971. Theory of hydraulic models. London: MacMillan.
Young, N. 2018. “Size-scale effects of nonlinear weir hydraulics.” M.Sc. thesis, Dept. of Civil and Environmental Engineering, Utah State Univ.
Information & Authors
Information
Published In
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jan 23, 2019
Accepted: May 28, 2019
Published online: Dec 3, 2019
Published in print: Feb 1, 2020
Discussion open until: May 3, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.