Coefficient Of Discharge Given Actual Discharge Over Broad Crested Weir Calculator

Formula Used:

\[ C_d = \frac{Q_a}{L_w \cdot h_c \cdot \sqrt{(2 \cdot g) \cdot (H - h_c)}} \]

Actual Discharge over Broad Crested Weir (Qa):

m³/s

Length of Weir Crest (Lw):

Critical Depth of Weir (hc):

Acceleration due to Gravity (g):

m/s²

Total Head (H):

Coefficient of Discharge (Cd):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Coefficient of Discharge?

The Coefficient of Discharge (Cd) is a dimensionless parameter that represents the ratio of actual discharge to theoretical discharge in fluid flow systems. For broad crested weirs, it accounts for energy losses and flow characteristics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_d = \frac{Q_a}{L_w \cdot h_c \cdot \sqrt{(2 \cdot g) \cdot (H - h_c)}} \]

Where:

\( C_d \) — Coefficient of Discharge (dimensionless)
\( Q_a \) — Actual Discharge over Broad Crested Weir (m³/s)
\( L_w \) — Length of Weir Crest (m)
\( h_c \) — Critical Depth of Weir (m)
\( g \) — Acceleration due to Gravity (m/s²)
\( H \) — Total Head (m)

Explanation: The formula calculates the discharge coefficient by relating actual measured discharge to the theoretical discharge over a broad crested weir, considering the critical flow conditions and gravitational effects.

3. Importance of Coefficient of Discharge Calculation

Details: Accurate calculation of the discharge coefficient is essential for hydraulic engineering applications, including weir design, flow measurement, and water resource management. It helps in calibrating flow measurement devices and ensuring proper water management in irrigation systems, dams, and hydraulic structures.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length dimensions, m³/s for discharge, m/s² for gravity). Ensure that Total Head is greater than Critical Depth for valid calculation. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Coefficient of Discharge in broad crested weirs?
A: The Coefficient of Discharge for broad crested weirs typically ranges from 0.3 to 0.7, depending on the weir geometry and flow conditions.

Q2: Why is the Coefficient of Discharge less than 1?
A: The Coefficient of Discharge is less than 1 because it accounts for energy losses, contraction effects, and other real-world factors that reduce the actual discharge below the theoretical ideal.

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 calculator be used for other types of weirs?
A: This specific calculator is designed for broad crested weirs. Other weir types require different formulas and coefficients.

Q5: What factors can affect the accuracy of Coefficient of Discharge calculations?
A: Factors include approach velocity, weir geometry, surface roughness, water temperature, and measurement accuracy of input parameters.