Critical Depth of Flow in the Culvert

Critical depth occurs when the flow in a channel has a minimum specific energy. Specific energy refers to the sum of the depth of flow and the velocity head. Critical depth depends on the channel shape and flow rate.

The depth of flow at the culvert outlet is assumed to be equal to critical depth for culverts operating under outlet control with low tailwater. Critical depth may also influence the inlet control headwater for unsubmerged conditions.

The culvert routines compute critical depth in the culvert by an iterative procedure, which arrives at a value satisfying the following equation:

1)	$\begin{array}{l}\displaystyle \displaystyle \frac{Q^2}{g} = \frac{A^3}{T}\end{array}$

Symbol	Description	Units
$\begin{array}{l}Q\end{array}$	flow rate in the channel	cfs
$\begin{array}{l}g\end{array}$	acceleration due to gravity, 32.2	ft/sec²
$\begin{array}{l}A\end{array}$	cross-sectional area of flow	square feet
$\begin{array}{l}T\end{array}$	Top width of flow	feet

Critical depth for box culverts can be solved directly with the following equation [AISI, 1980]:

2)	$\begin{array}{l}\displaystyle \displaystyle y_c = \sqrt[3]{\frac{q^2}{g}}\end{array}$

Symbol	Description	Units
$\begin{array}{l}y_c\end{array}$	critical depth	feet
$\begin{array}{l}q\end{array}$	unit discharge per linear foot of width	cfs/ft
$\begin{array}{l}g\end{array}$	acceleration due to gravity, 32.2	ft/sec²