Weir flow

Flow over a broad-crested weir is an application that can be analyzed with momentum principles. The momentum principle has certain advantages in application to problems involving high internal energy changes (Chow 1959). The pressure force due to the weight of water and the obstruction of the weir is important. The gravitational force vector in the direction of flow may be neglected for a mild channel slope and small distance between the uncontracted upstream section and the cross section at the weir. The friction forces on the wetted boundary in the short distance between the two sections may be neglected, as well.

Weir flow is calculated using:

where:
L = weir length (ft)
C = weir discharge coefficient (usually from 3.05 to 2.67)
H = approach head (ft)

The actual value of C depends on factors such as the roundedness of the upstream corner of the weir and the width and slope of the weir crest. Brater and King (1976) give C = 3.087 as a maximum value for broadcrested weirs with a vertical upstream face under any conditions, given that the upstream corner is so rounded as to prevent flow contraction and the slope of the crest is at least as great as the head loss on the weir due to friction. Under these conditions, flow over the weir occurs at critical depth. Inclining one or both faces of the broad-crested weir can also increase the C value, and Brater and King document experiments that obtain values of C as high as 3.8.

The flow velocity vectors for this equation are considered to be perpendicular to the crest; that is, the flow momentum is straight into the weir. If the weir is a lateral one or the main channel flow is parallel to the crest and the weir draws flow off to the side, the weir capacity would be less.

The major use of sharp-crested weirs is for flow measurement. Many different crest cross-sectional shapes exist, such as a V-notch, but the weir width is always thin and is perpendicular to the flow. The same discharge
equation used for broad-crested weirs may be applied to horizontal, sharp-crested weirs, but the discharge coefficient, C, is highly dependent on the nappe conditions. The nappe is the sheet of water flowing or jetting over the weir. A fully aerated nappe has an air pocket at atmospheric pressure just downstream of the weir and below the sheet of flowing water. A weir with a fully aerated nappe has a higher discharge coefficient than one in which the nappe is partially (air pressure less than atmospheric) or fully submerged (no air pocket).