Length of Weir Considering Francis's Formula Calculator

Francis's Formula:

\[ L_w = \frac{Q}{1.84 \times \left((H_i + h_a)^{3/2} - h_a^{3/2}\right)} \]

Discharge Weir (Q):

m³/s

Initial Height of Liquid (H_i):

Head Due to Velocity of Approach (h_a):

Length of Weir (L_w):

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1. What is Francis's Formula?

Francis's Formula is used to calculate the length of a weir required for a specific discharge, taking into account the initial height of liquid and the head due to velocity of approach. It provides an accurate estimation for weir design in hydraulic engineering.

2. How Does the Calculator Work?

The calculator uses Francis's Formula:

\[ L_w = \frac{Q}{1.84 \times \left((H_i + h_a)^{3/2} - h_a^{3/2}\right)} \]

Where:

\( L_w \) — Length of Weir (m)
\( Q \) — Discharge Weir (m³/s)
\( H_i \) — Initial Height of Liquid (m)
\( h_a \) — Head Due to Velocity of Approach (m)

Explanation: The formula accounts for the relationship between discharge, liquid height, and velocity head to determine the appropriate weir length.

3. Importance of Weir Length Calculation

Details: Accurate weir length calculation is crucial for proper hydraulic structure design, ensuring efficient water flow control and measurement in channels and reservoirs.

4. Using the Calculator

Tips: Enter discharge in m³/s, initial height of liquid in meters, and head due to velocity of approach in meters. All values must be valid (discharge > 0, heights ≥ 0).

5. Frequently Asked Questions (FAQ)

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

Q2: When is Francis's Formula most applicable?
A: Francis's Formula is most applicable for sharp-crested weirs with suppressed end contractions and under conditions where the velocity of approach is significant.

Q3: What are the limitations of this formula?
A: The formula assumes ideal flow conditions and may require adjustments for weirs with end contractions, submerged conditions, or non-standard geometries.

Q4: How does velocity of approach affect weir length?
A: Higher velocity of approach increases the effective head over the weir, which in turn affects the required weir length for a given discharge.

Q5: Can this formula be used for all types of weirs?
A: This formula is specifically designed for sharp-crested rectangular weirs. Different formulas apply for other weir types such as triangular, trapezoidal, or broad-crested weirs.