The flow of water over a dam, also known as the discharge, can be calculated using a specific formula that considers the dam's length and the water's depth above the dam's crest (head).
Weir Equation for Calculating Dam Flow
The most common method involves using the weir equation, specifically tailored for dams. A simplified version, derived from the reference, is:
Q = 3.09 B H3/2
Where:
- Q = Flow rate (discharge) in cubic feet per second (ft³/s)
- B = Length of the dam (or weir) in feet (ft)
- H = Depth of the water above the top of the dam (head) in feet (ft)
Explanation of Variables:
- Flow Rate (Q): This represents the volume of water passing over the dam in a given time, typically measured in ft³/s. A higher flow rate indicates a greater volume of water discharge.
- Dam Length (B): This is the horizontal distance across the dam's crest where water flows. A longer dam allows for a greater flow rate, assuming other factors remain constant.
- Head (H): This is the vertical distance between the water surface upstream of the dam and the top of the dam's crest. A larger head results in a significantly greater flow rate due to increased water pressure and velocity.
Example Calculation:
Let's assume a dam has a length (B) of 50 feet and the water depth above the dam (H) is 2 feet.
Q = 3.09 50 23/2
Q = 3.09 50 2.828
Q ≈ 437.17 ft³/s
Therefore, the flow rate over the dam is approximately 437.17 cubic feet per second.
Important Considerations:
- Units: Ensure all measurements are in feet for B and H to obtain Q in ft³/s.
- Weir Type: This formula is a simplified version. More complex formulas exist for different weir shapes (e.g., sharp-crested, ogee-crested) and account for factors like approach velocity and discharge coefficients. Consult specialized hydraulics resources for more precise calculations.
- Submergence: If the downstream water level is high enough to submerge the weir crest, the flow calculation becomes more complex and requires adjustments to the basic weir equation.
- Accuracy: This simplified equation provides an estimate. Real-world conditions can affect the actual flow rate.
