Free Flow Discharge Under Head Using Submerged Flow Over Weir Calculator

Formula Used:

\[ Q1 = \frac{Qs}{(1 - (H2/H1)^{nhead})^{0.385}} \]

Submerged Discharge (Qs):

m³/s

Downstream Water Surface Elevation (H2):

Upstream Water Surface Elevation (H1):

Exponent of Head (nhead):

Free Flow Discharge under Head H1 (Q1):

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1. What is Free Flow Discharge under Head?

Free Flow Discharge under Head H1 is the volumetric flow rate of water that is transported in a weir when there is insufficient backwater to reduce the discharge through the flume. It represents the maximum flow capacity of the weir under ideal conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q1 = \frac{Qs}{(1 - (H2/H1)^{nhead})^{0.385}} \]

Where:

\( Q1 \) — Free Flow Discharge under Head H1 (m³/s)
\( Qs \) — Submerged Discharge (m³/s)
\( H2 \) — Downstream Water Surface Elevation (m)
\( H1 \) — Upstream Water Surface Elevation (m)
\( nhead \) — Exponent of Head (m)

Explanation: This formula calculates the free flow discharge by accounting for the submerged flow conditions and the head exponent relationship in weir flow calculations.

3. Importance of Free Flow Discharge Calculation

Details: Accurate calculation of free flow discharge is essential for hydraulic engineering design, flood control systems, irrigation planning, and water resource management. It helps determine the capacity of weirs and other flow control structures.

4. Using the Calculator

Tips: Enter submerged discharge in m³/s, water surface elevations in meters, and head exponent value. Ensure H2 is less than H1 for valid calculations. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between free flow and submerged flow?
A: Free flow occurs when the downstream water level doesn't affect the discharge over the weir, while submerged flow occurs when the downstream water level rises high enough to reduce the discharge capacity.

Q2: What is the typical range for head exponent (nhead)?
A: The head exponent typically ranges from 1.5 to 3.0, depending on the weir shape and flow conditions. Common values are around 1.5 for sharp-crested weirs and 2.5-3.0 for broad-crested weirs.

Q3: When is this calculation most applicable?
A: This calculation is particularly useful for hydraulic engineers designing weirs, spillways, and other flow measurement structures where both free and submerged flow conditions need to be considered.

Q4: What are the limitations of this formula?
A: The formula assumes specific flow conditions and may not be accurate for extremely high or low flow rates, or for weirs with unusual geometries. Field calibration is recommended for critical applications.

Q5: How does the head exponent affect the calculation?
A: The head exponent (nhead) accounts for the non-linear relationship between head and discharge. Higher values indicate a more rapid increase in discharge with increasing head.