CHAPTER 9  SUBMERGED ORIFICES
13. Radial Gate Checks Used for Measuring Device
Radial gates are widely used in canal check structures to control canal flows and water levels. By measuring upstream water level, downstream water level, and gate position, radial gate checks can also be used to compute flow. Computing flow at check structures prevents the additional cost and head loss from flow measurement devices such as flumes, weirs, or flow meters.
Radial gate flow is a type of variablearea orifice flow, which may be either free or submerged. However, accurate computation of radial gate flow requires complex analysis. Discharge under a radial gate is influenced by numerous parameters and structure dimensions. Figure 98 shows a typical radial gate with some of the variables that affect gate flow. The angle of the gate's bottom edge (gate lip) varies with the gate opening, G_{o}, the pinion height, PH, and the gate's radius, r. Flow contraction is sensitive to the angle , the type of gate lip seal, and water levels.

The general equation for flow through an undershot gate can be derived from the Bernoulli equation and expressed as:
where:
Q = discharge (gate flow)
C_{d} = coefficient of discharge
G_{o} = vertical gate opening
B = gate width
g = gravitational constant
H = a head term
The head term, H, in the above equation can be either the upstream depth, Y_{u}, or the differential head across the gate, Y_{u}  Y_{d} (see figure 98). When differential head is used, equation 93 becomes the wellknown "orifice" equation. The development of the coefficient of discharge, C_{d}, depends on the definition of the head term as well as the various other parameters that affect gate flow. C_{d} has been predicted using a number of different methods, but most of these methods have limited application and accuracy.
In 1983, a research program at Reclamation's Hydraulics Laboratory developed gate flow algorithms that represent the complete discharge characteristics for canal radial gate check structures.
These algorithms are a complex set of equations that cover the range of water levels and gate geometry normally encountered at canal check structures. When applied correctly, they can be as accurate as any canal flow measurement device or procedure. The main disadvantages to using these algorithms are their complexity and the requirement to accurately measure two water levels, Y_{u} and Y_{d}, and the gate position, G_{o}. Additionally, sedimentation or check structure subsidence can change gate flow characteristics at existing structures and require recalibration over time.
A computer program has been developed to solve the radial gate flow algorithms. Program RADGAT executes on a personal computer to calculate either flow or gate position at a canal radial gate check structure. The user enters structure dimensions such as gate width, pinon height, gate radius, pier width (between gates), invert elevations, canal bottom widths and side slopes, and head loss coefficients for open transitions and siphons. These physical properties are saved in a data file so they need not be reentered for successive program execution. Then, the user enters upstream and downstream water depths and has the option either to compute discharge for a given gate opening or compute gate opening for a given discharge. RADGAT can also produce rating tables of flow versus gate opening for a range of upstream and downstream depths.
Buyalski (1983) contains detailed results from the research program and explanation of the discharge algorithms. It also contains the original version of program RADGAT developed for mainframe computer application. The personal computer version of RADGAT may be obtained through Reclamation's Hydraulic Investigations and Laboratory Services Group in Denver, Colorado.