Civil Engineering

Flow Measurement and Instrumentation 29 (2013) 19–24

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Unsteady discharge calibration of a large V-notch weir
Hubert Chanson n, Hang Wang
The University of Queensland, School of Civil Engineering, Brisbane, QLD 4072, Australia

a r t i c l e i n f o
Article history: Received 13 July 2012 Received in revised form 16 October 2012 Accepted 16 October 2012 Available online 29 October 2012 Keywords: 901 V-notch weir Unsteady experiments Calibration Discharge measurement Seiche Sloshing Dam break wave Physical modelling Triangular V-notch thin-plate weir

abstract
Thin-plate weirs are commonly used as measuring devices in flumes and channels, enabling an accurate discharge measurement with simple instruments. The calibration formulae of such devices rely upon some empirical coefficients and there is a need to obtain new accurate physical data to complement the existing evidence. In the present study, the discharge calibration of a large 901 V-notch thin plate weir was performed using an unsteady volume per time technique. The V-notch weir was initially closed by a fast-opening gate. The sudden opening induced an initial phase of the water motion dominated by the free-falling motion of a volume of fluid in the vicinity of the weir, followed by a gradually-varied phase, during which some seiche was observed in the tank. The relationship between water discharge and upstream water elevation was derived from the integral form of the continuity equation. The results yielded a dimensionless discharge coefficient Cd ¼ 0.58 close to previous experiments for 901 V-notch weirs. The findings showed that the unsteady discharge calibration of the V-notch weir yielded similar results to a more traditional calibration approach based upon steady flow experiments, allowing a rapid testing over a broad range of flow rates. & 2012 Elsevier

References: 0 0 0.1 0.2 h (m) 0.3 0.4 Fig. 8. Relationship between instantaneous discharge Q and upstream water depth h for the 901 V-notch weir—comparison between experimental data and Eq. (7a). 5. Conclusion A discharge calibration of a large 901 V-notch thin plate weir was performed using an unsteady volume per time technique. The V-notch weir was initially closed by a fast-opening gate. The sudden opening induced an initial phase of the water motion followed by a gradually-varied flow phase. The initial phase was dominated by the free-falling motion of a volume of fluid in the vicinity of the weir and the generation of a negative wave propagating upstream into the reservoir. The water volume affected by the sudden opening was encompassed by a quasicircular arc during the initial phase. During this gradually-varied phase, some seiche was observed in the tank. A frequency analysis of the water elevation data yielded results which compared favourably with the first mode of natural sloshing in the longitudinal and transverse directions of the intake basin, although the wave motion was three-dimensional. The relationship between water discharge and upstream water elevation was derived from the integral form of the continuity equation based upon high-frequency water elevation recordings. The water elevation data were de-trended before processing. The results yielded a dimensionless discharge coefficient Cd ¼0.58 close to previous findings for 901 V-notch weirs, as well as a series of unsteady orifice flow experiments. The findings showed that the unsteady discharge calibration of the V-notch weir yielded similar results to a more traditional calibration approach based upon steady flow experiments, enabling a relatively rapid calibration of the weir for a broad range of flow rates and upstream water levels. Another advantage is the ability to test relatively large flow rates, when the water supply (e.g. of a laboratory) cannot sustain such large steady flow rates. [1] Ackers P, White WR, Perkins JA, Harrison AJM. Weirs and flumes for flow measurement. Chichester, UK: John Wiley; 1978 [327 pages]. [2] Apelt CJ. Hydraulics of Minimum energy culverts and bridge waterways. Australian Civil Engineering Transactions. Institution of Engineers: Australia; 1983. vol. CE25, 2, p. 89–95. [3] Australian Standards. Measurement of water flow in open channels. Part 4: Measurement using flow gauging structures. Method 4.1: Thin-Plate Weirs. Australian Standard AS 3778.4.1–1991 (ISO 1438/1-1980), Council of Standards Australia; 1991 34 pages. [4] Bos MG. Discharge measurement structures. Publication no. 161. Delft Hydraulic Laboratory, Delft: The Netherlands; 1976. (Also Publication no. 20, ILRI, Wageningen, The Netherlands). [5] Bos MG, Replogle JA, Clemmens AJ. Flow measuring flumes for open channel systems. St. Joseph MI, USA: ASAE Publications; 1991 [321 pages]. [6] Chanson H, Aoki S, Maruyama M. Unsteady two-dimensional orifice flow: a large-size experimental investigation. Journal of Hydraulic Research, IAHR 2002;40(1):63–71. [7] Chanson H, Wang H. Unsteady discharge calibration of a large V-notch weir. Hydraulic model report no. CH88/12. School of Civil Engineering, The University of Queensland. Brisbane: Australia; 2012. 50 pages & 4 movies (ISBN 9781742720579). [8] Darcy HPG, Bazin H. Recherches hydrauliques. (Hydraulic research). Imprimerie ´ Imperiales. Paris, France, Parties 1ere et 2eme (in French); 1865. [9] Herschy RW. General purpose flow measurement equations for flumes and thin plate weirs. Flow Measurement and Instrumentation 1995;6(4):283–293. [10] Herschy RW. Editorial to: open channel flow measurement. Flow Measurement and Instrumentation 2002;12:189–190. [11] International Organization for Standardization. Water flow measurement in open channels using weirs and venturi flumes—Part 1: Thin-plate weirs. ISO 1438/1–1980. International Organization for Standardization; 1980. [12] Lauber G. Experimente zur Talsperrenbruchwelle im glatten geneigten Rechteckkanal. (Dam break wave experiments in rectangular channels.) ¨ PhD thesis. VAW-ETH, Zurich: Switzerland; 1997 (in German). (also Mitteilungen der Versuchsanstalt fur Wasserbau. Hydrologie und Glaziologie. ETH-Zurich. Switzerland, no. 152). [13] Lenz AT. Viscosity and surface tension effects on V-notch weir coefficients. Transactions of the American Society of Civil Engineers 1943;108(2195): 759–782 [Discussion: vol. 108, p. 783–802]. [14] Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes: the art of scientific computing. 3rd ed. Oxford, UK: Cambridge University Press; 2007 [1235 pages]. [15] Soulis KX, Dercas N. Field calibration of weirs using partial volumetric flow measurements. Journal of Irrigation and Drainage Engineering, ASCE 2012;138(5):481–484, http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0000424. [16] Troskolanski AT. Hydrometry: theory and practice of hydraulic measurements. Oxford, UK: Pergamon Press; 1960 [684 pages].