Length of Crest When Francis Formula Discharge and Velocity Is Considered Calculator

Formula Used:

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

Francis Discharge (QFr):

m³/s

Still Water Head (HStillwater):

Velocity Head (HV):

Number of End Contraction (n):

Length of Weir Crest (Lw):

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1. What is the Length of Weir Crest Formula?

The Length of Weir Crest formula calculates the required length of a weir crest based on Francis discharge, still water head, velocity head, and number of end contractions. It is derived from Francis formula for discharge over a weir.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula accounts for the discharge over the weir and the effect of end contractions on the effective length of the weir.

3. Importance of Length of Weir Crest Calculation

Details: Accurate calculation of weir crest length is essential for proper design of weirs in hydraulic engineering, ensuring efficient water flow measurement and control in channels.

4. Using the Calculator

Tips: Enter Francis discharge in m³/s, still water head in m, velocity head in m, and number of end contractions. All values must be valid (discharge > 0, still water head > 0, velocity head ≥ 0, number of end contractions ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is Francis discharge?
A: Francis discharge is the flow rate over a weir calculated using the empirical formula developed by James B. Francis.

Q2: What is still water head?
A: Still water head is the height of water above the weir crest when the water is stationary.

Q3: What is velocity head?
A: Velocity head represents the kinetic energy of the fluid in terms of equivalent height.

Q4: What are end contractions?
A: End contractions refer to the reduction in effective length of the weir due to the sides of the channel.

Q5: When is this formula applicable?
A: This formula is applicable for suppressed weirs with end contractions and under conditions where Francis formula is valid.