Discharge Through Submerged Weir If Velocity Is Approached Calculator

Formula Used:

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

Coefficient of Discharge (Cd):

Length of Weir Crest (Lw):

Head on Downstream of Weir (h2):

Acceleration due to Gravity (g):

m/s²

Head on Upstream of Weir (HUpstream):

Velocity over Submerged Weir (vsu):

m/s

Discharge through Drowned Portion (Q2):

m³/s

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1. What is Discharge through Submerged Weir?

Discharge through submerged weir refers to the flow rate of water passing through a weir that is partially or fully submerged. It is a crucial parameter in hydraulic engineering for designing and analyzing water flow systems.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( Q_2 \) — Discharge through drowned portion (m³/s)
\( C_d \) — Coefficient of discharge
\( L_w \) — Length of weir crest (m)
\( h_2 \) — Head on downstream of weir (m)
\( g \) — Acceleration due to gravity (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 through the submerged portion of a weir, accounting for the energy difference between upstream and downstream heads and the velocity approach.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is essential for designing hydraulic structures, flood control systems, irrigation networks, and water resource management.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure that upstream head is greater than downstream head for valid calculations. Use standard values for gravity (9.8 m/s²) unless specific conditions apply.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for coefficient of discharge?
A: The coefficient of discharge typically ranges from 0.6 to 0.9, depending on the weir shape and flow conditions.

Q2: When is a weir considered submerged?
A: A weir is considered submerged when the downstream water level rises above the weir crest, affecting the flow characteristics.

Q3: How does velocity approach affect discharge calculation?
A: Velocity approach accounts for the kinetic energy of water approaching the weir, which can significantly impact the discharge rate.

Q4: What are common applications of submerged weir calculations?
A: These calculations are used in dam design, spillway analysis, irrigation systems, and environmental flow management.

Q5: Are there limitations to this formula?
A: This formula assumes steady flow conditions and may need adjustments for highly turbulent flows, complex weir geometries, or significant energy losses.