Flow Over a Weir Type Spillway

This example model demonstrates how to simulate spillway flow at a dam using the weir equation. The model has a default 1-day time step, which may be relatively large compared to the volume that would drain from the reservoir over a 24-hour period. To achieve a more accurate representation of the spillway flow, we explore the difference between a constant 1-day time step and a dynamic time step approach.

Dynamic Time Step Approach

In the container "Spillway_Dynamic," the time step is reduced to 1 hour when the reservoir water level rises above the spillway crest. This approach allows for a more precise calculation of the spillway flow during periods of high water levels.

Constant 1-Day Time Step Method

In the container "Spillway_1Day_TS," the weir flow calculation is performed using a constant 1-day time step. This method can result in a discharge that is higher than the actual volume that would flow over the spillway in a 24-hour period. To address this, a different equation is used to calculate the spillway flow:

Q=DTmax(Pool1 − Volume_at_Weir_Crest + inflow × DT, 0)​

This equation represents the maximum amount of volume that can discharge over the time step. In the constant 1-day time step option, this is the controlling factor. However, if the time step is reduced to 1 hour, the weir flow calculation will control the discharge.

Weir Flow Calculation

The spillway flow is represented using a weir flow calculation assuming free flow conditions. The spillway flow rate Q depends on the length of the weir crest L and the head above the crest h. The equation used is:

Q=Cw​Lh3/2

The weir flow coefficient Cw accounts for various flow factors, including approach velocity. Typically, Cw is obtained from tables and depends on the height of the weir Hd and h. The weir equation is calculated in standard units (cfs and feet). For conversion to SI units, an adjustment to Cw is required, typically multiplying by 0.552.

Limiting Discharge Check

To prevent overestimation of spillway outflow when using long time steps, a simple volumetric flow check is added. The available water volume above the spillway invert is calculated and divided by the model characteristic time step to provide a limiting boundary on the calculated spillway flow rate. This limiting flow rate calculation is provided in the Function element "Flood_Volume_Flow," with the model characteristic time step duration specified by the Data element "DT."

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