Discharge over Rectangle Weir with Two End Contractions Calculator

Formula Used:

\[ Q = \frac{2}{3} \times C_d \times (L_w - 0.2 \times H) \times \sqrt{2 \times g} \times H^{3/2} \]

Discharge Weir (Q):

m³/s

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1. What is the Discharge over Rectangle Weir with Two End Contractions Formula?

The formula calculates the discharge over a rectangular weir with two end contractions, which accounts for the reduction in effective weir length due to side contractions. This is important for accurate flow measurement in open channels.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{2}{3} \times C_d \times (L_w - 0.2 \times H) \times \sqrt{2 \times g} \times H^{3/2} \]

Where:

\( Q \) — Discharge Weir (m³/s)
\( C_d \) — Coefficient of Discharge
\( L_w \) — Length of Weir (m)
\( H \) — Head of Liquid (m)
\( g \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula accounts for the effective weir length reduction due to end contractions and uses the fundamental weir equation modified for rectangular weirs with two end contractions.

3. Importance of Weir Discharge Calculation

Details: Accurate discharge calculation is crucial for hydraulic engineering, water resource management, irrigation systems, and environmental flow monitoring in open channels.

4. Using the Calculator

Tips: Enter the coefficient of discharge, length of weir in meters, and head of liquid in meters. All values must be positive. Typical Cd values range from 0.6 to 0.8 for rectangular weirs.

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of discharge?
A: The coefficient of discharge is a dimensionless factor that accounts for energy losses and flow characteristics. It typically ranges from 0.6 to 0.8 for rectangular weirs.

Q2: Why subtract 0.2*H from the weir length?
A: This accounts for the end contractions - each end contraction reduces the effective weir length by approximately 0.1*H, so for two end contractions, we subtract 0.2*H.

Q3: What are typical applications of this formula?
A: This formula is used in water treatment plants, irrigation systems, hydraulic laboratories, and environmental monitoring for measuring flow rates in open channels.

Q4: Are there limitations to this equation?
A: The formula assumes a well-defined weir crest, adequate approach conditions, and that the weir is properly ventilated. It may not be accurate for very small or very large heads.

Q5: How does head measurement affect accuracy?
A: Head measurement should be taken at a distance upstream of the weir (typically 4-5 times the maximum head) to avoid surface curvature effects near the weir.