Developing a Simple Unique Head-Discharge Equation for Pivot Weirs with Different Side Contractions

Introduction: Pivot weirs (sharp crested inclined weirs, Fig. 1-a) is frequently used for discharge measurement, controlling water surface and flow diversion. Some typical features of pivot weirs are: (a) overshot design for better water level control, (b) Their application as head gates, turnout or check structure which requiring low head loss and high accuracy, (c) ease of removing sediment deposit behind the weir, and (d) ability to manage and monitor on-site or operating remotely when connected to a supervisory control and data acquisition (SCADA) network. Kindsvater and Carter (8) derived a weir discharge equation based on energy and continuity equations. Hulsing (4) determined head-discharge relationship of inclined suppressed sharp crested weir with the slope of 3:3, 2:3 and 1:3 toward downstream and compared them with the equivalent normal sharp crested weir. In the USBR report on pivot weirs (regarding The Boulder Canyon Project,1948) the head discharge data of the suppressed pivot weir were presented in a channel with 5.5m length, 2.9m depth and 0.61m width. Some field experiments were also carried out in the IID (Imperial Irrigation District) on a trapezoidal cross-section (0.61 m bottom width) channel with pivot weir of 1.7m length, and two different widths of 1.63m. The flow rate (350-880 lit/s) was held constant and different angles (15-50°) calibrated instead of holding the angle constant and varying the flow rate. Some other laboratory tests were performed with Wahlin and Replogle (1994) on two pivot weirs with 1.2 m and 1.14 m width for the 0.61 m and 0.46 m length of blade and contraction factor of 0.925. RUBICON Company established an extensive operation on the application and automation of pivot weirs in irrigation channels in Australia (Www.rubicon.com). All previous studies concentrated on modifying the normal rectangular weir head-discharge equation so that it can be used for the pivot weirs. In this study, it is trying to derive a unique head-discharge equation for pivot weirs based on dimension analysis and critical discharge equation (implementing Ferro rule). This equation can be used for different inclined angles and side contractions. The obtained unique and simple discharge equation can be used in automation of this structure. Material and Method: In this research, experimental data consist of experiments carried out in hydraulic research institute of Tehran, Iran and experiments of USBR on Pivot weir with side contraction in 0.925 in the canal with 1.14 m width and 0.46 m blade length (Wahlin and Replogle, 1994). Experiments of the water institute of Tehran were carried out in the concrete rectangular weir with 10.30m long, 1m wide and 1m depth (Fig.2). Experimental model was consisted of canals, water supply system, dampers (avoided of turbulent flow upstream of pivot weir), pivot weirs, sluice gate at the end of the channel (make different tail waters). With respect to laboratory equipment’s, three pivot weirs with of 80×65, 60×55 and 40×40 (cm×cm) respectively length of the blade and the width was built and set 5.5 m far from the first of the canal. Discharge was determined from the calibrated weir located at the upstream of pivot weir. A manual point gauge with ±0.01 mm sensitivity was used to measure water surface levels. Extraction of discharge equation: Dimensional Analysis based on Ferro rule (2000 and 2001) is used to determine the discharge formula of pivot weirs. Since the h-Q function is usually exponential, the relation between dimensionless parameters could be defined as Ferro rule. Results and Discussion: The rating curve of the pivot weirs with different side contractions is compared with the normal suppressed rectangular weir (equal weir height) in Fig. 3. The discharge of normal suppressed rectangular weir was calculated from the discharge equation of Kindsvater-Carter and discharge coefficient of Rehbock (1) for the equal weir height and head of pivot weirs. For a constant water head, the discharge of pivot weir with a side contraction of 0.925 is more than the normal suppressed weir. When the weir plate is inclined to the bottom of the canal, because of the stagnation area behind the weir plate, the streamlines approach the weir blade smoothly and the energy dissipation is lower than for the normal weirs. The vortex behind the weir plate increases as the inclined angle increases and subsequently the discharge coefficient decreases. Reduction of discharge for a constant water head in contract weirs is simply justified by decreasing of the weir width. The α and β coefficients were obtained based on all experimental data. Discharge equation obtained based on critical depth-discharge equation. Conclusion: In this study, based on dimension analysis a unique head-discharge relation was obtained which could be used for different inclined angels and side contractions. This equation is more appropriate than previous formulas which are modifications to the normal weir head-discharge equation. The accuracy of this equation was evaluated by different data sets including different inclined angle, side contractions, weir heights and also a wide discharge range. This equation could be used in the automated irrigation network easily.