Length Of Crest For Discharge Through Free Weir Portion Calculator

Formula Used:

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

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):

Length of Weir Crest (L_w):

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

The Length of Crest for Discharge through Free Weir Portion is a hydraulic engineering calculation that determines the required length of a weir crest to allow a specific discharge of water under free flow conditions, considering various hydraulic parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

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

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)

Explanation: The formula calculates the required weir crest length based on the discharge rate, discharge coefficient, gravitational acceleration, and the difference between upstream and downstream heads.

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 control, flood management, and efficient water resource utilization in irrigation systems, dams, and other water management structures.

4. Using the Calculator

Tips: Enter discharge in m³/s, coefficient of discharge, gravitational acceleration in m/s² (default 9.8), and both head measurements in meters. Ensure upstream head is greater than downstream head for valid calculation.

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 shape and flow conditions.

Q2: When is this formula applicable?
A: This formula is applicable for free flow conditions where the downstream water level doesn't affect the flow over the weir (modular flow).

Q3: What are common weir types this calculation applies to?
A: This calculation applies to various weir types including rectangular, triangular, and trapezoidal weirs under free flow conditions.

Q4: How does head difference affect the weir length?
A: Greater head difference requires shorter weir length for the same discharge, as the flow velocity increases with higher head difference.

Q5: What are practical applications of this calculation?
A: This calculation is used in designing irrigation systems, spillways, flow measurement structures, and water control systems in hydraulic engineering projects.