Culvert formula (Water Overlay)

Flow through culverts is based on an open channel flow calculation.

The actual height of the culvert is at least the height of the terrain on either end of the culvert:

CH_real = max( CH_attr , T_left , T_right )

The height of the water column at either end of the culvert, relative to the culvert, is calculated:

WH_left = max(0, WL_left-CH_real)

WH_right = max(0, WL_right-CH_real)

The loss coefficient for the culvert is calculated:

U = sqrt( 1.0 / ( 1.0 + 2.0 * G * CN * CN * length / (Rh ^ (4 / 3 ) ) )

The potential flow through the culvert is then calculated:

C = U * A * sqrt( 2 * G * abs(WH_left - WH_right) )

Finally the actual amount of water flow is calculated:

Δw = Δt * C / cell

Where:

• Δw = The water flow which takes place.
• Δt = Computational timestep.
• cell = Cell size.

• C = The potential rate of water flow through the culvert.
• U = Loss coefficient for culverts.
• WH_left = The height of the water column relative to the bottom of the culvert on the left side of the culvert.
• WH_right = The height of the water column relative to the bottom of the culvert on the right side of the culvert.
• CH_real = The CULVERT_THRESHOLD of the culvert, recalculated so the culvert is not below ground on either side.

• A = Flow area, based on the height of the water in the (circular) culvert.
• G = Acceleration factor of gravity
• CW = The CULVERT_DIAMETER attribute of the culvert.
• CH_attr = The CULVERT_THRESHOLD attribute of the culvert.
• CN = The CULVERT_N attribute of the culvert.
• WL_left = The water level on the left side of the culvert, relative to datum.
• WL_right = The water level on the right side of the culvert, relative to datum.
• L = The length of the culvert, calculated as the distance between the culvert's endpoints.
• Rh = The hydrological radius in the culvert.