Flow Measurement and Instrumentation 29 (2013) 19–24
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Flow Measurement and Instrumentation
journal homepage: www.elsevier.com/locate/ﬂowmeasinst
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
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 Ltd. All rights reserved.
1. Introduction In open channel ﬂows, the knowledge of the water discharge is a key parameter, and a range of measurement techniques were developed [4,8,10]. Many techniques rely upon some empirical coefﬁcients  and there is a need to obtain new accurate physical data to complement the existing evidence. Flow measuring structures in waterworks, canals and wastewater plants consist mainly of ﬂumes and thin plate weirs [5,9]. Thin-plate weirs enable an accurate discharge measurement with simple instruments . The V-notch weirs, also called triangular weirs, have an overﬂow edge in the form of an isosceles triangle. Fig. 1 presents a sketch of a 901 V-notch weir. Ref.  expresses the discharge calibration of a triangular V-notch thin-plate weir in the form: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 8 5 Q ¼ Cd Â Â tana Â 2 Â g Â h ð1Þ 15 where Q is the water discharge, Cd a dimensionless discharge coefﬁcient, a the notch opening angle, g the gravity acceleration and h the upstream water elevation above the notch (Fig. 1). Basic dimensional considerations show that the discharge coefﬁcient Cd is a function of the notch angle a, the relative weir height p/W and relative upstream depth h/p (Fig. 1). Ref.  presented some seminal experiments conducted with ﬁve different ﬂuids (Table 1), n
while Refs.  and  reviewed recent ﬁndings based upon steady ﬂow experiments. A very robust discharge measurement technique is the volume per time method: ‘‘the only rational method of calibrating weirs, i.e. in accordance with hydrometric principles, is the volumetric method, which depends on measuring the volume, with a measuring reservoir, and the time of ﬂow’’ (, p. 310). The technique may be adapted to unsteady ﬂow situations (e.g., [6,15]). The contribution herein presents a novel approach to determine the discharge calibration of a large 901 V-notch weir and associated accuracy based upon a comprehensive physical study. The calibration was...
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.
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