Coefficient Of Discharge For Max Discharge Over Crested Weir Calculator

Formula Used:

\[ C_d = \frac{Q_{W(max)}}{1.70 \times L_w \times H^{3/2}} \]

Max Discharge Over Broad Crested Weir (Q_W(max)):

m³/s

Length of Weir Crest (L_w):

Total Head (H):

Coefficient of Discharge (C_d):

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1. What is the Coefficient of Discharge?

The Coefficient of Discharge (C_d) is the ratio of actual discharge to theoretical discharge. It is a dimensionless parameter used to account for energy losses and flow characteristics in fluid mechanics calculations, particularly for flow over weirs.

2. How Does the Calculator Work?

The calculator uses the formula for broad crested weirs:

\[ C_d = \frac{Q_{W(max)}}{1.70 \times L_w \times H^{3/2}} \]

Where:

\( C_d \) — Coefficient of Discharge (dimensionless)
\( Q_{W(max)} \) — Maximum discharge over broad crested weir (m³/s)
\( L_w \) — Length of weir crest (m)
\( H \) — Total head (combination of weir crested and additional head) (m)

Explanation: This formula calculates the discharge coefficient for flow over broad crested weirs, accounting for the relationship between maximum discharge, weir geometry, and head conditions.

3. Importance of Coefficient of Discharge

Details: The coefficient of discharge is crucial for accurate flow measurement in hydraulic engineering. It helps in designing efficient weirs, spillways, and other flow control structures by accounting for real-world flow conditions that differ from theoretical predictions.

4. Using the Calculator

Tips: Enter maximum discharge in m³/s, length of weir crest in meters, and total head in meters. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for coefficient of discharge values?
A: For broad crested weirs, the coefficient of discharge typically ranges from 0.6 to 0.9, depending on weir geometry and flow conditions.

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

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

Q4: Can this formula be used for all types of weirs?
A: No, this specific formula is designed for broad crested weirs. Other weir types require different formulas and coefficients.

Q5: What factors influence the coefficient of discharge?
A: Factors include weir geometry, approach velocity, viscosity, surface roughness, and the ratio of head to weir height.