Coefficient Of Discharge If Velocity Is Approached Given Discharge Through Free Weir Calculator

Coefficient of Discharge Formula:

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

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):

Velocity over Submerged Weir (v_su):

m/s

Coefficient of Discharge (C_d):

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1. What is the Coefficient of Discharge?

The Coefficient of Discharge (C_d) is a dimensionless parameter that represents the ratio of actual discharge to theoretical discharge in fluid flow systems. It accounts for energy losses and flow characteristics in weirs and other hydraulic structures.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

\( C_d \) — Coefficient of Discharge (dimensionless)
\( Q_1 \) — 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)
\( v_{su} \) — Velocity over submerged weir (m/s)

Explanation: This formula calculates the discharge coefficient by considering the geometric and hydraulic parameters of the weir system, including the velocity approach effect.

3. Importance of Coefficient of Discharge Calculation

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

4. Using the Calculator

Tips: Enter all required parameters in appropriate units. Ensure that upstream head is greater than downstream head for meaningful results. All values must be positive and within reasonable physical limits.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the velocity approach term important?
A: The velocity approach term accounts for the kinetic energy of the approaching flow, which significantly affects the discharge characteristics of the weir.

Q3: When is this formula applicable?
A: This formula is specifically designed for submerged weirs with free discharge conditions where velocity approach effects need to be considered.

Q4: What are the limitations of this equation?
A: The formula assumes ideal flow conditions and may need calibration for specific weir geometries, surface roughness, and extreme flow conditions.

Q5: How does weir crest length affect the coefficient?
A: Longer weir crests generally result in more efficient flow distribution and higher discharge coefficients, up to certain optimal lengths.