When the upstream water surface is equal to or less than the top of the gate opening, the program calculates the flow through the gates as weir flow. An example of low flow through a gated structure is shown in the figure below.

The standard weir equation used for this calculation is shown below:

The user can specify either a broad crested, ogee, or sharp crested weir shape for the spillway crest of the gate. If the crest of the spillway is ogee shaped, the weir coefficient will be automatically adjusted when the upstream energy head is higher or lower than a user specified design head. The adjustment is based on the curve shown in the figure below (Bureau of Reclamation, 1977). The curve provides ratios for the discharge coefficient, based on the ratio of the actual head to the design head of the spillway. In the figure below, H_e is the upstream energy head; H_o is the design head; C_o is the coefficient of discharge at the design head; and C is the coefficient of discharge for an energy head other than the design head.

Submerged Weir Flow through the Gates

The program automatically accounts for submergence on the weir when the tailwater is high enough to slow down the flow. Submergence is defined as the depth of water above the weir on the downstream side divided by the headwater energy depth of water above the weir on the upstream side. As the degree of submergence increases, the program reduces the weir flow coefficient. Submergence corrections are based on the shape of the spillway crest (broad crested, ogee shaped weir, or sharp crested). If the spillway is a broad crested shape, then the same submergence curve that is used for flow over a roadway at a bridge (see figure below) is used. If the spillway crest is ogee shaped, a submergence curve from the USACE EM 1110-2-1603 (Plate 3-5, A-A) is used. If the spillway is sharp crested, then the Villemonte equation (Villemonte, 1947) is used to compute the flow reduction coefficient.