Length of Crest given Discharge Passing over Weir Calculator

Formula Used:

\[ Length\ of\ Weir\ Crest = \frac{Francis\ Discharge\ with\ Suppressed\ End \times 3}{2 \times Coefficient\ of\ Discharge \times \sqrt{2 \times Acceleration\ due\ to\ Gravity} \times ((Height\ of\ Water\ above\ Crest\ of\ Weir + Velocity\ Head)^{\frac{3}{2}} - Velocity\ Head^{\frac{3}{2}})} \]

Francis Discharge with Suppressed End:

m³/s

Coefficient of Discharge:

Acceleration due to Gravity:

m/s²

Height of Water above Crest of Weir:

Velocity Head:

Length of Weir Crest:

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1. What is the Length of Crest Formula?

The Length of Crest formula calculates the required length of a weir crest based on Francis discharge with suppressed end, coefficient of discharge, acceleration due to gravity, height of water above the crest, and velocity head. This is essential for proper weir design in hydraulic engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_w = \frac{Q_{Fr'} \times 3}{2 \times C_d \times \sqrt{2 \times g} \times ((S_w + H_v)^{\frac{3}{2}} - H_v^{\frac{3}{2}})} \]

Where:

\( L_w \) — Length of Weir Crest (m)
\( Q_{Fr'} \) — Francis Discharge with Suppressed End (m³/s)
\( C_d \) — Coefficient of Discharge
\( g \) — Acceleration due to Gravity (m/s²)
\( S_w \) — Height of Water above Crest of Weir (m)
\( H_v \) — Velocity Head (m)

Explanation: The formula accounts for the hydraulic characteristics of flow over a weir, considering both static and dynamic components of the water head.

3. Importance of Weir Crest Length Calculation

Details: Accurate calculation of weir crest length is crucial for proper hydraulic structure design, ensuring adequate water flow capacity, preventing overflow issues, and maintaining structural integrity in irrigation systems, dams, and water treatment facilities.

4. Using the Calculator

Tips: Enter all values in appropriate units. Francis discharge and coefficient of discharge must be positive values. Height of water and velocity head should be non-negative values. Use standard gravity value of 9.8 m/s² unless specific conditions require otherwise.

5. Frequently Asked Questions (FAQ)

Q1: What is Francis Discharge with Suppressed End?
A: Francis discharge with suppressed end refers to the flow rate over a weir without end contractions, where the weir spans the full width of the channel.

Q2: How is Coefficient of Discharge determined?
A: The coefficient of discharge is typically determined experimentally and varies based on weir shape, approach conditions, and flow characteristics. Common values range from 0.6 to 0.8 for sharp-crested weirs.

Q3: What is Velocity Head in this context?
A: Velocity head represents the kinetic energy of the approaching flow, calculated as \( \frac{v^2}{2g} \), where v is the velocity of approach.

Q4: When should this formula be used?
A: This formula is specifically designed for calculating weir crest length in hydraulic engineering applications where Francis formula with suppressed ends is applicable.

Q5: Are there limitations to this equation?
A: The formula assumes certain ideal conditions and may need adjustments for very high or low flow rates, unusual weir shapes, or non-standard approach conditions.