Length of Weir for Broad-Crested Weir and Head of Liquid at Middle Calculator

Formula Used:

\[ L_w = \frac{Q}{C_d \times \sqrt{2 \times g \times (h^2 \times l_a - h^3)}} \]

Discharge Weir (Q):

m³/s

Coefficient of Discharge (Cd):

Head of Liquid Middle (h):

Arc Length of Circle (la):

Length of Weir (Lw):

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1. What is Length of Weir for Broad-Crested Weir?

The Length of Weir for Broad-Crested Weir is the measurement of the base of the weir through which discharge is taking place. It is a critical parameter in hydraulic engineering for determining the flow characteristics over a broad-crested weir.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_w = \frac{Q}{C_d \times \sqrt{2 \times g \times (h^2 \times l_a - h^3)}} \]

Where:

\( L_w \) — Length of Weir (m)
\( Q \) — Discharge Weir (m³/s)
\( C_d \) — Coefficient of Discharge
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( h \) — Head of Liquid Middle (m)
\( l_a \) — Arc Length of Circle (m)

Explanation: This formula calculates the required length of a broad-crested weir based on discharge rate, discharge coefficient, gravitational acceleration, liquid head, and arc length.

3. Importance of Length of Weir Calculation

Details: Accurate calculation of weir length is essential for proper hydraulic design, ensuring efficient water flow management, flood control, and irrigation system design.

4. Using the Calculator

Tips: Enter discharge in m³/s, coefficient of discharge, head of liquid in meters, and arc length in meters. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a broad-crested weir?
A: A broad-crested weir is a hydraulic structure with a wide crest that allows water to flow over it, commonly used for flow measurement and control in open channels.

Q2: What is the typical range for coefficient of discharge?
A: The coefficient of discharge for broad-crested weirs typically ranges from 0.8 to 1.0, depending on the weir geometry and flow conditions.

Q3: Why is arc length of circle important in this calculation?
A: The arc length represents the curved surface over which the water flows, affecting the discharge characteristics and weir performance.

Q4: What factors affect the accuracy of this calculation?
A: Factors include weir geometry, water surface profile, approach velocity, and the accuracy of input parameters.

Q5: Can this formula be used for other types of weirs?
A: This specific formula is designed for broad-crested weirs. Other weir types (sharp-crested, V-notch, etc.) require different formulas.