Length of Crest for Discharge through Free Weir Calculator

Formula Used:

\[ L_w = \frac{3 \times Q_1}{2 \times C_d \times \sqrt{2 \times g} \times \left( \left( (H_{Upstream} - h_2) + \frac{v_{su}^2}{2 \times g} \right)^{3/2} - \left( \frac{v_{su}^2}{2 \times g} \right)^{3/2} \right)} \]

Discharge through Free Portion (Q₁):

m³/s

Coefficient of Discharge (C_d):

Acceleration due to Gravity (g):

m/s²

Head on Upstream of Weir (H_Upstream):

Head on Downstream of Weir (h₂):

Velocity over Submerged Weir (v_su):

m/s

Length of Weir Crest (L_w):

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1. What is the Length of Crest for Discharge through Free Weir?

The Length of Crest for Discharge through Free Weir calculation determines the required length of a weir crest to handle a specific discharge flow rate. This is essential in hydraulic engineering for designing efficient water control structures.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( L_w \) — Length of Weir Crest (m)
\( Q_1 \) — Discharge through Free Portion (m³/s)
\( C_d \) — Coefficient of Discharge
\( g \) — Acceleration due to Gravity (m/s²)
\( H_{Upstream} \) — Head on Upstream of Weir (m)
\( h_2 \) — Head on Downstream of Weir (m)
\( v_{su} \) — Velocity over Submerged Weir (m/s)

Explanation: The formula accounts for the hydraulic characteristics of flow over a weir, considering both static head differences and velocity head contributions.

3. Importance of Weir Crest Length Calculation

Details: Accurate calculation of weir crest length is crucial for proper hydraulic structure design, ensuring adequate flow capacity while maintaining structural stability and efficiency.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure upstream head is greater than downstream head for meaningful results. Use standard values for coefficient of discharge (typically 0.6-0.7 for sharp-crested weirs).

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for coefficient of discharge?
A: For sharp-crested weirs, C_d typically ranges from 0.60 to 0.75, depending on the weir geometry and flow conditions.

Q2: How does velocity affect the weir crest length calculation?
A: Higher approach velocities increase the velocity head term, which affects the effective head difference and thus the required crest length.

Q3: What is the significance of the 3/2 exponent in the formula?
A: The 3/2 exponent comes from the theoretical derivation of flow over weirs, representing the relationship between head and discharge.

Q4: When is this formula most applicable?
A: This formula is particularly useful for submerged weir flow conditions where both upstream and downstream heads influence the discharge.

Q5: What are the limitations of this calculation?
A: The formula assumes ideal flow conditions and may need adjustment for very high velocities, unusual weir shapes, or significant turbulence effects.