Discharge Through Free Weir Portion Calculator

Formula Used:

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

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):

Discharge through Free Portion (Q1):

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1. What is Discharge through Free Weir Portion?

Discharge through Free Weir Portion is a measure of the quantity of fluid flow over unit time through the free portion of a weir, representing the flow quantity between the upstream and downstream portions of the weir structure.

2. How Does the Calculator Work?

The calculator uses the discharge formula:

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

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)

Explanation: The formula calculates the discharge rate through the free portion of a weir based on the head difference between upstream and downstream water levels.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for hydraulic engineering, water resource management, irrigation system design, and flood control measures.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure the upstream head is greater than the downstream head for valid calculation results.

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 0.8 for most weir configurations, depending on the weir shape and flow conditions.

Q2: Why is the head difference raised to the power of 3/2?
A: The 3/2 power relationship comes from the fundamental hydraulic principles of weir flow, representing the non-linear relationship between head and discharge.

Q3: When is this formula applicable?
A: This formula applies to free-flow conditions where the downstream water level doesn't affect the weir discharge (free outflow conditions).

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

Q5: How accurate is this calculation for practical applications?
A: For well-designed weirs under controlled conditions, the formula provides good accuracy, though field measurements may require calibration for specific installations.