Coefficient of Discharge if Velocity is Approached for Submerged Weir Calculator

Formula Used:

\[ C_d = \frac{Q_2}{L_w \cdot h_2 \cdot \left( \sqrt{2 \cdot g \cdot (H_{\text{Upstream}} - h_2) + v_{su}^2} \right)} \]

Discharge through Drowned Portion (Q₂):

m³/s

Length of Weir Crest (L_w):

Head on Downstream of Weir (h₂):

Acceleration due to Gravity (g):

m/s²

Head on Upstream of Weir (H_Upstream):

Velocity over Submerged Weir (v_su):

m/s

Coefficient of Discharge (C_d):

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1. What is the Coefficient of Discharge for Submerged Weir?

The Coefficient of Discharge (C_d) for a submerged weir is a dimensionless parameter that represents the ratio of actual discharge to theoretical discharge through the drowned portion of the weir. It accounts for various energy losses and flow characteristics in submerged weir conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_d = \frac{Q_2}{L_w \cdot h_2 \cdot \left( \sqrt{2 \cdot g \cdot (H_{\text{Upstream}} - h_2) + v_{su}^2} \right)} \]

Where:

\( C_d \) — Coefficient of Discharge (dimensionless)
\( Q_2 \) — Discharge through drowned portion (m³/s)
\( L_w \) — Length of weir crest (m)
\( h_2 \) — Head on downstream of weir (m)
\( g \) — Acceleration due to gravity (9.8 m/s²)
\( H_{\text{Upstream}} \) — Head on upstream of weir (m)
\( v_{su} \) — Velocity over submerged weir (m/s)

Explanation: This formula calculates the discharge coefficient by considering the geometric parameters of the weir, the hydraulic heads, and the flow velocity over the submerged section.

3. Importance of Coefficient of Discharge Calculation

Details: Accurate calculation of the coefficient of discharge is crucial for designing hydraulic structures, predicting flow rates through weirs, and ensuring proper water management in irrigation systems, dams, and other hydraulic engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m³/s for discharge, m/s for velocity). Ensure that upstream head is greater than downstream head 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 submerged weirs?
A: The coefficient typically ranges between 0.6-0.8 for most submerged weir configurations, depending on the specific geometry and flow conditions.

Q2: How does submergence affect the discharge coefficient?
A: Increased submergence (higher downstream head relative to upstream head) generally decreases the discharge coefficient due to reduced effective head difference.

Q3: What factors influence the coefficient of discharge?
A: The coefficient is influenced by weir shape, approach velocity, viscosity, surface tension, and the degree of submergence.

Q4: When is this formula most accurate?
A: This formula provides good accuracy for fully submerged weirs with well-defined crest geometry and steady flow conditions.

Q5: Can this calculator be used for partially submerged weirs?
A: This specific formula is designed for fully submerged conditions. For partially submerged weirs, different approaches may be needed.