Length Of Crest Given Time Required To Lower Liquid Surface Using Francis Formula Calculator

Francis Formula:

\[ L_w = \left( \frac{2 \cdot A_R}{1.84 \cdot t_F} \cdot \left( \frac{1}{\sqrt{h_2}} - \frac{1}{\sqrt{H_{Upstream}}} \right) \right) + (0.1 \cdot n \cdot H_{Avg}) \]

Cross-Sectional Area of Reservoir (A_R):

m²

Time Interval for Francis (t_F):

Head on Downstream of Weir (h₂):

Head on Upstream of Weir (H_Upstream):

Number of End Contraction (n):

Average Height of Downstream and Upstream (H_Avg):

Length of Weir Crest (L_w):

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1. What is the Francis Formula?

The Francis formula is used to calculate the length of weir crest required to lower the liquid surface in a reservoir over a specific time interval. It accounts for various hydraulic parameters including cross-sectional area, head measurements, and end contractions.

2. How Does the Calculator Work?

The calculator uses the Francis formula:

\[ L_w = \left( \frac{2 \cdot A_R}{1.84 \cdot t_F} \cdot \left( \frac{1}{\sqrt{h_2}} - \frac{1}{\sqrt{H_{Upstream}}} \right) \right) + (0.1 \cdot n \cdot H_{Avg}) \]

Where:

\( L_w \) — Length of Weir Crest (m)
\( A_R \) — Cross-Sectional Area of Reservoir (m²)
\( t_F \) — Time Interval for Francis (s)
\( h_2 \) — Head on Downstream of Weir (m)
\( H_{Upstream} \) — Head on Upstream of Weir (m)
\( n \) — Number of End Contraction
\( H_{Avg} \) — Average Height of Downstream and Upstream (m)

Explanation: The formula calculates the required weir crest length by considering the reservoir geometry, time factor, hydraulic heads, and end contraction effects.

3. Importance of Length of Weir Crest Calculation

Details: Accurate calculation of weir crest length is crucial for proper hydraulic structure design, ensuring efficient water flow control, and preventing overflow or underflow conditions in reservoirs and channels.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure cross-sectional area, time interval, and head values are positive numbers. Number of end contractions and average height should be non-negative values.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 1.84 constant in the formula?
A: The constant 1.84 is derived from empirical studies and represents the discharge coefficient for a sharp-crested weir under standard conditions.

Q2: How does the number of end contractions affect the result?
A: More end contractions generally require a longer weir crest to achieve the same flow characteristics, as each contraction reduces the effective length.

Q3: What are typical values for the time interval in practical applications?
A: Time intervals can vary from seconds to hours depending on the reservoir size and required drawdown rate, typically ranging from 30 seconds to several hours.

Q4: Are there limitations to this formula?
A: The formula assumes ideal flow conditions and may need adjustments for very large reservoirs, complex geometries, or non-standard weir configurations.

Q5: How accurate is this calculation for real-world applications?
A: The formula provides a good estimate for preliminary design, but final designs should incorporate safety factors and consider site-specific conditions through physical or numerical modeling.