Submerged Flow over Weir using Villemonte Formula Calculator

Villemonte Formula:

\[ Q_s = Q_1 \times \left(1 - \left(\frac{H_2}{H_1}\right)^{n_{head}}\right)^{0.385} \]

Free Flow Discharge under Head H1:

m³/s

Downstream Water Surface Elevation:

Upstream Water Surface Elevation:

Exponent of Head:

Submerged Discharge (Qs):

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1. What is the Villemonte Formula?

The Villemonte Formula is used to calculate the submerged discharge over a weir. It accounts for the reduction in flow rate when the downstream water level rises above the weir crest, creating submerged flow conditions.

2. How Does the Calculator Work?

The calculator uses the Villemonte formula:

\[ Q_s = Q_1 \times \left(1 - \left(\frac{H_2}{H_1}\right)^{n_{head}}\right)^{0.385} \]

Where:

\( Q_s \) — Submerged discharge (m³/s)
\( Q_1 \) — Free flow discharge under head H1 (m³/s)
\( H_2 \) — Downstream water surface elevation (m)
\( H_1 \) — Upstream water surface elevation (m)
\( n_{head} \) — Exponent of head in free flow head discharge relation

Explanation: The formula calculates the reduced discharge when a weir becomes submerged, accounting for the ratio of downstream to upstream head and the head exponent.

3. Importance of Submerged Flow Calculation

Details: Accurate calculation of submerged flow is crucial for hydraulic engineering, flood control, irrigation systems, and water resource management when weirs operate under submerged conditions.

4. Using the Calculator

Tips: Enter free flow discharge in m³/s, water surface elevations in meters, and the head exponent. All values must be positive, with upstream elevation greater than downstream elevation for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: When is a weir considered submerged?
A: A weir is considered submerged when the downstream water level rises above the weir crest, affecting the discharge characteristics.

Q2: What is the typical range for the head exponent?
A: The head exponent typically ranges from 1.5 to 3.0, depending on the weir shape and flow conditions.

Q3: How accurate is the Villemonte formula?
A: The Villemonte formula provides good accuracy for most practical engineering applications involving submerged weir flow.

Q4: Can this formula be used for all weir types?
A: The formula is generally applicable to various weir types, though specific coefficients may vary slightly depending on weir geometry.

Q5: What happens when H2/H1 approaches 1?
A: As the downstream head approaches the upstream head, the submerged discharge approaches zero, indicating complete submergence.