Flow Rate Equation for Suppressed and Submerged Sluice Gates www.itrc.org/reports/sluicegate.htm ITRC Report No. R 20-001 Flow Rate Equation for Suppressed and Submerged Sluice Gates Prepared by Charles M. Burt Albert J. Clemmens Kyle Feist May 2020 IRRIGATION TRAINING & RESEARCH CENTER California Polytechnic State University San Luis Obispo, CA 93407-0730 Office Phone: (805) 756-2434 FAX: (805) 756-2433 www.itrc.org Reference to any specific process, product or service by manufacturer, trade name, trademark or otherwise does not necessarily imply endorsement or recommendation of use by either California Polytechnic State University, the Irrigation Training & Research Center, or any other party mentioned in this document. No party makes any warranty, express or implied and assumes no legal liability or responsibility for the accuracy or completeness of any apparatus, product, process or data described. This report was prepared by ITRC as an account of work done to date. All designs and cost estimates are subject to final confirmation. Flow Rate Equation for Suppressed and Submerged Sluice Gates www.itrc.org/reports/sluicegate.htm ITRC Report No. R 20-001 Acknowledgements This work was funded by the California Dept. of Water Resources (Agreement No. 4600011908) and the USBR Mid-Pacific Region. Notation The following symbols are used in this report: a = relative gate opening; B = horizontal dimension of the rectangular sluice gate opening; Cc = a dimensionless contraction coefficient equaling the ratio of the area of the vena contracta to the area of the gate opening; Cd = discharge coefficient; CdBos = Bos (1989) adjusted Cd; Cdcomb = Cd combining concepts in Bos (1989) and Belaud et al (2009); Cdadj = adjusted Cd; CP = contracted portion; Cv = a dimensionless coefficient, accounting for the velocity head of approach; Cva = a dimensionless coefficient, accounting for the water head only but does not fully account for the velocity head of approach; Cvf = a dimensionless correction factor for the velocity distribution and friction losses; g = gravitation acceleration constant; H = head, or water depth above the horizontal floor; Q = flow rate; R = a dimensionless ratio related to the suppressed versus contracted perimeter; W = vertical dimension of the rectangular sluice gate opening; Y = water depth; Y1 = water depth measured approximately 2.2 m upstream of the gate; Y1A = water depth immediately upstream of the sluice gate; Y2freeflow = shallowest water depth downstream of the gate in a free-flow condition; Y2submerged = shallowest depth for a submerged condition; Y3 = Water depth downstream of the gate, beyond any turbulence Z = a “best fit” factor in a discharge equation by Bos (1989). Irrigation Training & Research Center i Flow Rate Equation for Suppressed and Submerged Sluice Gates www.itrc.org/reports/sluicegate.htm ITRC Report No. R 20-001 Table of Contents Introduction ............................................................................................................................ 1 Theory ...................................................................................................................................................... 2 Experiment .............................................................................................................................. 5 Test Conditions ........................................................................................................................................ 5 Data Analysis ............................................................................................................................................ 7 Submerged Discharge Coefficient Determination ................................................................................. 10 Conclusions ........................................................................................................................... 14 References............................................................................................................................. 15 List of Figures Figure 1. Profile view of a sluice gate – horizontal floor .............................................................................. 2 Figure 2. Contraction coefficient as a function of relative gate opening. Submerged sluice gate ............. 4 Figure 3. Plan view of 374 mm wide sluice gate dimensions. All dimensions are mm. Flow is from left to right. ................................................................................................................................. 5 Figure 4. Side view of 374 mm wide sluice gate dimensions. All dimensions are mm. .............................. 5 0.5 Figure 5. Cd for submerged conditions where Q = Cd A (2gΔH) .............................................................. 10 Figure 6. Predicted flow rates versus measured (actual), using CdBos ........................................................ 11 Figure 7. Cdadj versus a for submerged sluice gates, where Cdadj = Cd /(1 + .9 B/(B+W)) ............................ 12 Figure 8. Predicted flow rates versus actual, using the new Cdcomb ........................................................... 13 Figure 9. Comparison of predicted versus measured submerged sluice gate flows using three techniques for estimating a discharge coefficient ................................................................... 13 List of Tables Table 1. Data from submerged sluice gates .................................................................................................. 8 Irrigation Training & Research Center ii Flow Rate Equation for Suppressed and Submerged Sluice Gates www.itrc.org/reports/sluicegate.htm ITRC Report No. R 20-001 Flow Rate Equation for Suppressed and Submerged Sluice Gates Introduction In irrigation projects, the control and measurement of flow rates at key bifurcation points is essential. Flumes in canals can be excellent measurement devices, but in some cases, they can be expensive and can have maintenance issues. A key limitation is that they require enough head (difference in water level across the flume) for accuracy. Acoustic Doppler flow meters and other similar devices can have problems including high cost, the need for excellent calibration, the need to average data for at least 30 minutes, and early failures. Sluice gates are often used at the heads of canals and at turnouts (offtakes) in irrigation districts to control flows, and sometimes to estimate flow rates. They are also increasingly used as combination flow control and flow measurement structures, for which programmable logic controllers (PLCs) measure upstream and downstream water levels and gate openings, and automatically adjust gate openings to maintain a constant target flow rate. Using sluice gates for accurate flow measurement has proven to be problematic because of the uncertainty regarding what discharge coefficient to use in the flow rate equation. There are numerous entrance and exit conditions of sluice gates in the field, including how far side gate frames extend into the flow path, floor steps (either up or down), length of upstream walls, orientation of the gates to the main canal flow, and exit conditions. Upstream and downstream water levels are measured in a wide variety of locations; some automated gate manufacturers attach upstream and downstream water level sensors to the gate frame itself, while other engineers specify water level sensors completely upstream and/or downstream of gate entrance sections. The differences result in theoretical and practical differences between the constants that must be used in any flow rate equation. Furthermore, there are submerged, free flow, and “uncertain” or “transition” hydraulic conditions as related to downstream water levels. Belaud et al (2009) noted that there can be large deviations between models and discharge measurements. Although a wide range of entrance and exit conditions can exist in the field, the specific condition of rectangular sluice gates with suppressed sides and bottom is of interest because ITRC frequently designs gates with those configurations and has felt that existing formulas were inadequate based on occasional comparisons with current meters and various acoustic doppler flow meters. Furthermore, there are many large-scale installations, such as in Sindh Province of Pakistan that have suppressed sluice gates already installed. An empirical understanding of what conditions gave predictable results was pursued. This empirical approach, obtained without a complete organization of the theory behind the answers, has provided long-standing hydraulics solutions using dimensionless variables such as the Moody diagram, which describes (but does not explain) pipe friction. Irrigation Training & Research Center 1 Flow Rate Equation for Suppressed and Submerged Sluice Gates www.itrc.org/reports/sluicegate.htm ITRC Report No. R 20-001 Theory Pertinent hydraulic variables for submerged and free flow conditions are frequently illustrated as in Figure 1. Figure 1. Profile view of a sluice gate – horizontal floor Y2freeflow is defined as the shallowest water depth downstream of the gate for a free-flow condition. Y2submerged is defined as the shallowest depth downstream of the gate for a submerged condition. The head (H) in a flat channel for any section is defined as the water depth above the floor. The difference in head, used in various discharge equations, is defined as: ΔH = Y1 – Y3 (Eq. 1) The general equation to compute the flow rate through a sluice gate