Coefficient Of Discharge Given Discharge Through Free Weir Portion Calculator

Formula Used:

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

Discharge through Free Portion (Q₁):

m³/s

Length of Weir Crest (L_w):

Acceleration due to Gravity (g):

m/s²

Head on Upstream of Weir (H_Upstream):

Head on Downstream of Weir (h₂):

Coefficient of Discharge (C_d):

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1. What is the Coefficient of Discharge?

The Coefficient of Discharge is the ratio of actual discharge to theoretical discharge in fluid flow systems. It accounts for energy losses and flow characteristics in hydraulic structures like weirs.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the discharge coefficient for flow over a weir, considering the geometric and hydraulic parameters of the system.

3. Importance of Coefficient of Discharge Calculation

Details: Accurate calculation of the discharge coefficient is crucial for designing hydraulic structures, predicting flow rates, and ensuring efficient water management in irrigation, drainage, and water supply systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure that upstream head is greater than downstream head to avoid negative values under the square root. All input values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Coefficient of Discharge?
A: The coefficient typically ranges between 0.6 and 0.9 for most weir configurations, depending on the geometry and flow conditions.

Q2: Why is the coefficient less than 1?
A: The coefficient is less than 1 due to energy losses, contraction effects, and other real-world factors that reduce the actual discharge compared to theoretical ideal conditions.

Q3: How does weir shape affect the discharge coefficient?
A: Different weir shapes (sharp-crested, broad-crested, etc.) have different coefficient values due to variations in flow patterns and energy dissipation.

Q4: What if the downstream head equals the upstream head?
A: If H_Upstream = h₂, the denominator becomes zero, making the coefficient undefined as there would be no flow.

Q5: Can this formula be used for all types of weirs?
A: This specific formula is designed for free weir flow conditions. Different formulas may be needed for submerged weirs or other specific configurations.