Radial Gates

An example radial gate with an ogee spillway crest is shown in the figure below.

The flow through the gate is considered to be "Free Flow" when the downstream tailwater elevation (Z_D) is not high enough to cause an increase in the upstream headwater elevation for a given flow rate. The equation used for a Radial gate under free flow conditions is as follows:

1)	$\begin{array}{l}\displaystyle \displaystyle Q=C_u \sqrt{2g} WT^{TE} B^{BE} H^{HE}\end{array}$

Symbol	Description	Units
$\begin{array}{l}Q\end{array}$	Flow rate	cfs
$\begin{array}{l}C_u\end{array}$	Unsubmerged discharge coefficient (typically ranges from 0.6 - 0.8)
$\begin{array}{l}W\end{array}$	Width of the gated spillway	ft
$\begin{array}{l}T\end{array}$	Trunnion height (from spillway crest to trunnion pivot point)
$\begin{array}{l}TE\end{array}$	Trunnion height exponent, typically about 0.16 (default 0.0)
$\begin{array}{l}B\end{array}$	Height of gate opening	ft
$\begin{array}{l}BE\end{array}$	Gate opening exponent, typically about 0.72 (default 1.0)
$\begin{array}{l}H\end{array}$	Upstream Energy Head above the spillway crest Z_U - Z_sp	ft
$\begin{array}{l}HE\end{array}$	Head exponent, typically about 0.62 (default 0.5)
$\begin{array}{l}Z_U\end{array}$	Elevation of the upstream energy grade line	ft
$\begin{array}{l}Z_D\end{array}$	Elevation of the downstream water surface	ft
$\begin{array}{l}Z_{sp}\end{array}$	Elevation of the spillway crest through the gate	ft

Note

The default values for the equation, reduce the form of the equation down to the sluice equation (T⁰ → 1). The trunnion exponent allows users to calibrate the exponents to match observed data through a specific radial gate.

When the downstream tailwater increases to the point at which the gate is no longer flowing freely (downstream submergence is causing a greater upstream headwater for a given flow), the program switches to the following form of the equation:

2)	$\begin{array}{l}\displaystyle \displaystyle Q=C_u \sqrt{2g} WT^{TE} B^{BE} (3H)^{HE}\end{array}$

where: $\begin{array}{l}H=Z_U -Z_D\end{array}$

Submergence begins to occur when the tailwater depth divided by the headwater energy depth above the spillway, is greater than 0.67. Equation (2) is used with (3) to compute a weighted flow for the transition between free flow and fully submerged flow. This transition is set up so the program will gradually change to the fully submerged Orifice equation when the gates reach a submergence of 0.80. The fully submerged Orifice equation is shown below:

3)	$\begin{array}{l}\displaystyle \displaystyle Q=C_sA \sqrt{2gH}\end{array}$

Symbol	Description	Units
$\begin{array}{l}A\end{array}$	Area of the gate opening
$\begin{array}{l}H\end{array}$	$\begin{array}{l}Z_U -Z_D\end{array}$
$\begin{array}{l}C_s\end{array}$	Submerged discharge coefficient (typically 0.8)