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Broad-Crested Weir Tailwater Submergence & Discharge Calculator

Calculate drowned flow reduction factor C_s and actual submerged discharge for broad-crested weirs using the Villemonte empirical submergence equation.

Total water head measured upstream of weir crest.

Tailwater elevation above weir crest (0 for free uninhibited discharge).

Transverse width of the rectangular weir crest perpendicular to flow.

Standard free-flow broad crested weir coefficient (typically 0.36 - 0.40).

Calculated Result
2.12 m³/s

Submerged Discharge (Q)

Submergence Ratio (H₂/H₁)

0.688

Villemonte Factor (C_s)

0.723

Free-Flow Capacity

2.93 m³/s

Flow Regime

Drowned / Submerged Weir Flow (Tailwater retards discharge)

Calculation Breakdown

  1. Weir Submergence Ratio (H₂ / H₁)Submergence Ratio S = 0.55 / 0.8 = 0.688 (Modular Limit S_mod ≈ 0.67)
  2. Free-Discharge Capacity (Q_free)Q_free = C_d · (2/3) · √(2g/3) · b · H₁^1.5 = 2.93 m³/s
  3. Villemonte Submergence Reduction Factor (C_s)C_s = [1 - (0.55/0.8)^1.5]^0.385 = 0.723; Q_sub = Q_free · C_s = 2.12 m³/s

Weir Discharge Under Submergence

Interactive visualization based on your current inputs

Value
0.05.4111622Free Flow Q_freeDrowned Flow Q_subFlow Reduction %ParameterValue (m³/s)

What Is the Broad-Crested Weir Tailwater Submergence & Discharge Calculator?

Calculate drowned flow reduction factor C_s and actual submerged discharge for broad-crested weirs using the Villemonte empirical submergence equation.

The Broad-Crested Weir Tailwater Submergence & Discharge Calculator is an analytical tool in the construction domain designed to evaluate Upstream Total Head Above Crest (h₁), Downstream Tailwater Head Above Crest (h₂), Weir Crest Transverse Breadth (b), Free Discharge Coefficient (C_d) using verified mathematical equations. It provides reproducible, deterministic calculations for academic, professional, and practical applications.

How Does the Broad-Crested Weir Tailwater Submergence & Discharge Calculator Work?

This calculator computes results by taking input values for Upstream Total Head Above Crest (h₁), Downstream Tailwater Head Above Crest (h₂), Weir Crest Transverse Breadth (b), Free Discharge Coefficient (C_d) and applying the governing equation: Villemonte empirical submergence correction formula for drowned broad-crested open-channel weirs.. Values are checked for dimensional consistency and processed through standard arithmetic routines.

Broad-Crested Weir Tailwater Submergence & Discharge Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Qfree=Cd,bsqrt2g,h11.5,Cs=[1−(h2h1)1.5]0.385,Qsub=Cs,QfreeQ_{free} = C_d , b sqrt{2g} , h_1^{1.5}, \quad C_s = \left[ 1 - \left(\frac{h_2}{h_1}\right)^{1.5} \right]^{0.385}, \quad Q_{sub} = C_s , Q_{free}

Villemonte empirical submergence correction formula for drowned broad-crested open-channel weirs.

How to Use the Broad-Crested Weir Tailwater Submergence & Discharge Calculator

  1. Enter your value for Upstream Total Head Above Crest (h₁) in m.
  2. Enter your value for Downstream Tailwater Head Above Crest (h₂) in m.
  3. Enter your value for Weir Crest Transverse Breadth (b) in m.
  4. Enter your value for Free Discharge Coefficient (C_d).
  5. Verify your input parameters to ensure they match your design or problem specifications.
  6. Review the calculated results, intermediate mathematical steps, and graphical visualization below.

Step-by-Step Example Calculation

4m Wide Canal Weir Submerged by Tailwater (h1 = 0.8m, h2 = 0.55m)

Input Values:

upstreamHeadAboveCrestH1M:0.8
downstreamHeadAboveCrestH2M:0.55
crestLengthBreadthBM:4.0
dischargeCoeffFreeFlowCd:0.385
Worked Steps: Submergence ratio is 68.75%, reducing capacity by 21.6% (Cs = 0.784) from 4.87 m³/s to 3.82 m³/s.

Understanding Your Result

The calculated output gives the primary solution for Broad-Crested Weir Tailwater Submergence & Discharge under the specified conditions. Use this value to compare against standard design tolerances, benchmarks, or reference ranges in construction.

Factors That Affect the Result

  • Input precision and measurement accuracy of Upstream Total Head Above Crest (h₁), Downstream Tailwater Head Above Crest (h₂), Weir Crest Transverse Breadth (b), Free Discharge Coefficient (C_d).
  • Operating conditions, environmental parameters, and specific construction tolerances.
  • Boundary constraints and deviations from nominal theoretical model assumptions.

When Should You Use This Calculator?

  • When performing technical analysis or dimensioning related to Broad-Crested Weir Tailwater Submergence & Discharge.
  • To cross-verify manual calculations or theoretical models in construction.
  • For preliminary estimates before conducting detailed field measurements or laboratory testing.

Assumptions & Limitations

  • Free-Flow Discharge: Q_free = C_d · b · √(2·g) · h₁^(1.5).
  • Submergence Ratio: S = h₂ / h₁.
  • Villemonte Reduction Factor: C_s = [1 - (h₂ / h₁)^1.5]^0.385.
  • Actual Submerged Flow: Q_sub = C_s · Q_free.

Frequently Asked Questions

At what submergence ratio does drowning begin to affect weir flow?+
Broad-crested weirs can typically tolerate tailwater submergence ratios h2/h1 up to approximately 65-70% before discharge drops significantly. Above 70%, capacity drops sharply.
Can the Villemonte equation be applied to sharp-crested or V-notch weirs?+
Yes, Villemonte developed related exponents for sharp-crested and triangular weirs, but with different exponent values matching weir crest geometry.

Calculation Accuracy & Reference Note

This calculator implements verified mathematical formulas for Broad-Crested Weir Tailwater Submergence & Discharge Calculator. Always verify critical results against official domain standards and manufacturer documentation.

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