Length Of Crest Without Considering Velocity Calculator

Formula Used:

\[ L_w = \left( \frac{Q_{Fr} \times 2}{3 \times C_d \times \sqrt{2 \times g}} \right)^{2/3} + (0.1 \times n \times S_w) \]

Francis Discharge (QFr):

m³/s

Coefficient of Discharge (Cd):

Acceleration due to Gravity (g):

m/s²

Number of End Contraction (n):

Height of Water above Crest of Weir (Sw):

Length of Weir Crest (Lw):

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1. What is the Length of Crest Without Considering Velocity?

The Length of Crest Without Considering Velocity refers to the measurement of the weir crest length calculated using the Francis formula, which accounts for discharge, coefficient of discharge, gravity, end contractions, and water height above the crest, without considering velocity effects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_w = \left( \frac{Q_{Fr} \times 2}{3 \times C_d \times \sqrt{2 \times g}} \right)^{2/3} + (0.1 \times n \times S_w) \]

Where:

\( L_w \) — Length of Weir Crest (m)
\( Q_{Fr} \) — Francis Discharge (m³/s)
\( C_d \) — Coefficient of Discharge (-)
\( g \) — Acceleration due to Gravity (m/s²)
\( n \) — Number of End Contraction (-)
\( S_w \) — Height of Water above Crest of Weir (m)

Explanation: The formula calculates the effective length of a weir crest by considering the discharge characteristics and accounting for end contractions.

3. Importance of Weir Crest Length Calculation

Details: Accurate calculation of weir crest length is essential for proper hydraulic design of weirs, ensuring accurate flow measurement and control in open channel systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Francis discharge in m³/s, coefficient of discharge as a dimensionless value, gravity in m/s², number of end contractions as an integer, and water height in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for coefficient of discharge?
A: The coefficient of discharge typically ranges from 0.6 to 0.8 for sharp-crested weirs, depending on the weir geometry and flow conditions.

Q2: How do end contractions affect weir performance?
A: End contractions reduce the effective length of the weir crest, which decreases the discharge capacity for a given head of water.

Q3: When should this formula be used?
A: This formula is particularly useful for preliminary design of rectangular weirs and for educational purposes to understand weir hydraulics.

Q4: Are there limitations to this equation?
A: This formula doesn't account for velocity of approach, which can be significant in channels with high flow velocities approaching the weir.

Q5: What is the standard value for acceleration due to gravity?
A: The standard value is 9.8 m/s², but local variations exist. For precise calculations, use the local gravitational acceleration value.