Francis Formula for Discharge for Rectangular Notch if Velocity is considered Calculator

Francis Formula:

\[ Q_{Fr} = 1.84 \times (L_w - 0.1 \times n \times H_{Stillwater}) \times (H_{Stillwater}^{3/2} - H_V^{3/2}) \]

Length of Weir Crest (L_w):

Number of End Contraction (n):

Still Water Head (H_Stillwater):

Velocity Head (H_V):

Francis Discharge (Q_Fr):

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1. What is the Francis Formula for Discharge?

The Francis formula calculates discharge over a rectangular notch when velocity is considered. It accounts for end contractions and provides an empirical relationship between discharge and various hydraulic parameters.

2. How Does the Calculator Work?

The calculator uses the Francis formula:

\[ Q_{Fr} = 1.84 \times (L_w - 0.1 \times n \times H_{Stillwater}) \times (H_{Stillwater}^{3/2} - H_V^{3/2}) \]

Where:

\( Q_{Fr} \) — Francis Discharge (m³/s)
\( L_w \) — Length of Weir Crest (m)
\( n \) — Number of End Contraction
\( H_{Stillwater} \) — Still Water Head (m)
\( H_V \) — Velocity Head (m)

Explanation: The formula accounts for the effective weir length reduction due to end contractions and the energy difference between still water head and velocity head.

3. Importance of Francis Discharge Calculation

Details: Accurate discharge calculation is crucial for hydraulic engineering, water resource management, and designing efficient weir systems for flow measurement and control.

4. Using the Calculator

Tips: Enter all parameters in appropriate units (meters for length measurements). Ensure positive values for all inputs, with weir length and still water head greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: When should the Francis formula be used?
A: The Francis formula is used for rectangular notches when velocity head is significant and needs to be considered in discharge calculations.

Q2: What are typical values for end contractions?
A: End contractions typically range from 0 to 2, depending on the weir configuration and channel geometry.

Q3: How accurate is the Francis formula?
A: The Francis formula provides good accuracy for most practical applications, though actual conditions may require calibration.

Q4: What are the limitations of this formula?
A: The formula assumes specific flow conditions and may not be accurate for very small or very large weirs, or for unusual flow patterns.

Q5: Can this formula be used for other weir shapes?
A: No, this specific formula is designed for rectangular notches. Other weir shapes require different discharge formulas.