FHWA Full Flow Equations

For culverts flowing full, the total head loss, or energy loss, through the culvert is measured in feet (or meters). The head loss, HL, is computed using the following formula:

1)	$\begin{array}{l}\displaystyle H_L= h_{en} +h_f +h_{ex}\end{array}$

Symbol	Description	Units
$\begin{array}{l}h_{en}\end{array}$	entrance loss	feet or meters
$\begin{array}{l}h_f\end{array}$	friction loss	feet or meters
$\begin{array}{l}h_{ex}\end{array}$	exit loss	feet or more

The friction loss in the culvert is computed using Manning's formula, which is expressed as follows:

2)	$\begin{array}{l}\displaystyle \displaystyle h_f = L \left( \frac{Qn}{1.486AR^{2/3}} \right) ^2\end{array}$

Symbol	Description	Units
$\begin{array}{l}h_f\end{array}$	friction loss	feet
$\begin{array}{l}L\end{array}$	culvert length	feet
$\begin{array}{l}Q\end{array}$	flow rate in the culvert	cfs
$\begin{array}{l}n\end{array}$	Manning's roughness coefficient
$\begin{array}{l}A\end{array}$	area of flow	square feet
$\begin{array}{l}R\end{array}$	hydraulic radius	feet

The exit energy loss is computed as a coefficient times the change in velocity head from just inside the culvert, at the downstream end, to outside of the culvert at the downstream end. The entrance loss is computed as a coefficient times the absolute velocity head of the flow inside the culvert at the upstream end. The exit and entrance loss coefficients are described in the next section of this chapter.