Analytical Solution for Circular Gates as Flow Metering Structures

Water measurement in irrigation canals is frequently hindered by low head availability and high capital investment costs associated with construction of compatible hydraulic structures. Often irrigation systems have circular sliding gates in place used as diversion and flow control structures. The Fresno Irrigation District investigated the feasibility of using such circular gates (Armco Model 101) as flow metering stations in the 1920s. This early work demonstrated that circular gates could be used simultaneously for both flow control and as flow measurement structures. The original work is compiled by USBR as 10,500 data points and is presented in tabular fashion for gate diameters varying from $20.3\text{to}121.9\mathrm{cm}$ $(8–48\mathrm{in.})$ . An analytical equation of the form $Q=C_D(y,D)yD\sqrt{2gH}$ , [where $C_D(y,D)$ is a discharge function which depends on the gate displacement $y$ and the nominal gate diameter $D$ , $g$ represents the gravitational acceleration, and $H$ is the hydraulic headloss through the crescent-shaped orifice] accurately predicts most tabulated values. Equations are provided to compute the discharge function for nominal gate diameters varying from $20.3\text{to}121.9\mathrm{cm}$ $(8–48\mathrm{in.})$ for gate displacements between $5.1\mathrm{cm}$ $\left(2\mathrm{in.}\right)$ and fully open conditions. The precision of the proposed algorithms are excellent (predicted values are within $\pm 5\%$ of the corresponding reported values 95% of the time) for gates greater than $30.5\mathrm{cm}$ $\left(12\mathrm{in.}\right)$ .