Head On Downstream Weir For Discharge Through Free Weir Portion Calculator

Formula Used:

\[ Head\ on\ Downstream\ of\ Weir = -\left(\frac{3 \times Discharge\ through\ Free\ Portion}{2 \times Coefficient\ of\ Discharge \times Length\ of\ Weir\ Crest \times \sqrt{2 \times Acceleration\ due\ to\ Gravity}}\right)^{\frac{2}{3}} + Head\ on\ Upstream\ of\ Weir \]

Discharge through Free Portion (Q1):

m³/s

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):

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1. What is the Head on Downstream Weir Formula?

The Head on Downstream Weir formula calculates the energy head downstream of a weir structure based on discharge, weir characteristics, and upstream head conditions. This calculation is essential for hydraulic engineering and water flow management.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h2 \) — Head on Downstream of Weir (m)
\( Q1 \) — 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)

Explanation: The formula accounts for the hydraulic characteristics of weir flow, including discharge coefficient and gravitational effects.

3. Importance of Head on Downstream Weir Calculation

Details: Accurate calculation of downstream head is crucial for designing weir structures, managing water flow, preventing flooding, and ensuring proper hydraulic system operation.

4. Using the Calculator

Tips: Enter discharge in m³/s, coefficient of discharge, length of weir crest in meters, acceleration due to gravity in m/s², and upstream head in meters. All values must be positive.

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 weir shape and flow conditions.

Q2: Why is acceleration due to gravity important in this calculation?
A: Gravity drives the flow over the weir, so it's a fundamental parameter in hydraulic calculations involving free surface flow.

Q3: What are common applications of this calculation?
A: This calculation is used in dam design, irrigation systems, flood control structures, and hydraulic research.

Q4: How accurate is this formula?
A: The formula provides good accuracy for standard weir configurations under normal flow conditions, but may require adjustments for complex geometries.

Q5: Can this formula be used for submerged weirs?
A: This specific formula is designed for free flow conditions. Different formulas apply for submerged or partially submerged weirs.