Computing Outlet Control Headwater

For outlet control flow, the required upstream energy to pass the given flow must be computed considering several conditions within the culvert and downstream of the culvert. The figure below illustrates the logic of the outlet control computations. HEC-RAS use's Bernoulli's equation in order to compute the change in energy through the culvert under outlet control conditions. The outlet control computations are energy based. The equation used by the program is the following:

1)	$\begin{array}{l}\displaystyle \displaystyle Z_3 +Y_3 + \frac{a_3V^2_3}{2g} = Z_2 +Y_2 + \frac{a_2 V^2_2}{2g} +H_L\end{array}$

Symbols	Description	Units
$\begin{array}{l}Z_3\end{array}$	Upstream invert elevation of the culvert
$\begin{array}{l}Y_3\end{array}$	The depth of water above the upstream culvert inlet
$\begin{array}{l}V_3\end{array}$	The average velocity upstream of the culvert
$\begin{array}{l}a_3\end{array}$	The velocity weighting coefficient upstream of the culvert
$\begin{array}{l}g\end{array}$	The acceleration of gravity
$\begin{array}{l}Z_2\end{array}$	Downstream invert elevation of the culvert
$\begin{array}{l}Y_2\end{array}$	The depth of water above the downstream culvert inlet
$\begin{array}{l}V_2\end{array}$	The average velocity downstream of the culvert
$\begin{array}{l}a_2\end{array}$	The velocity weighting coefficient downstream of the culvert
$\begin{array}{l}H_L\end{array}$	Total energy loss through the culvert (from section 2 to 3)

Figure 6-9 Flow Chart for Outlet Control Computations