Discharge Through Free Weir If Velocity Is Approached Calculator

Formula Used:

\[ Q1 = \frac{2}{3} \times Cd \times Lw \times \sqrt{2 \times g} \times \left( \left( (HUpstream - h2) + \frac{vsu^2}{2 \times g} \right)^{\frac{3}{2}} - \left( \frac{vsu^2}{2 \times g} \right)^{\frac{3}{2}} \right) \]

Coefficient of Discharge (Cd):

Length of Weir Crest (Lw):

Acceleration due to Gravity (g):

m/s²

Head on Upstream of Weir (HUpstream):

Head on Downstream of Weir (h2):

Velocity over Submerged Weir (vsu):

m/s

Discharge through Free Portion (Q1):

m³/s

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1. What is Discharge through Free Weir if Velocity is Approached?

Discharge through Free Weir if Velocity is Approached refers to the volumetric flow rate of water over a weir when the approach velocity is considered in the calculation. This provides a more accurate measurement of flow compared to simplified weir equations that neglect approach velocity.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( Q1 \) — Discharge through Free Portion (m³/s)
\( Cd \) — Coefficient of Discharge
\( Lw \) — Length of Weir Crest (m)
\( g \) — Acceleration due to Gravity (m/s²)
\( HUpstream \) — Head on Upstream of Weir (m)
\( h2 \) — Head on Downstream of Weir (m)
\( vsu \) — Velocity over Submerged Weir (m/s)

Explanation: The formula accounts for the energy approach velocity in weir flow calculations, providing a more precise discharge measurement by considering both static head and velocity head components.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation through weirs is essential for hydraulic engineering, water resource management, irrigation system design, and environmental flow monitoring. Considering approach velocity provides more realistic flow measurements in practical applications.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure values are positive and physically meaningful (Cd typically ranges 0.6-0.8, g is approximately 9.8 m/s²). All measurements should be in consistent SI units.

5. Frequently Asked Questions (FAQ)

Q1: Why include velocity in weir discharge calculations?
A: Including approach velocity provides more accurate flow measurements, especially when the approach channel has significant velocity that contributes to the total energy head.

Q2: What is the typical range for Coefficient of Discharge?
A: The Coefficient of Discharge typically ranges from 0.6 to 0.8 for sharp-crested weirs, depending on weir geometry and flow conditions.

Q3: When should this formula be used instead of simpler weir equations?
A: This formula should be used when approach velocity is significant (typically when vsu > 0.3 m/s) or when high precision is required in flow measurement.

Q4: What are the limitations of this calculation?
A: The formula assumes ideal flow conditions, uniform velocity distribution, and may not account for turbulence, viscosity effects, or non-standard weir geometries.

Q5: How does downstream head affect the discharge calculation?
A: The difference between upstream and downstream head (HUpstream - h2) represents the effective head driving the flow over the weir, with larger differences resulting in higher discharge rates.