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Cipolletti Trapezoidal Weir Discharge Calculator

Determine volumetric water discharge over a Cipolletti trapezoidal weir with 1:4 side slope end contraction compensation.

Horizontal bottom crest notch length b.

Measured water head above weir horizontal crest.

Standard Cipolletti coefficient in SI units (typically 1.86 to 1.88).

Calculated Result
1.404 m³/s

Discharge Flow Rate

Discharge in Liters/sec

1403.7 L/s

Trapezoidal Side Slope

1H : 4V (14.04°)

Crest Froude Number

0.57

Crest Length

2.5 m

Calculation Breakdown

  1. Cipolletti Trapezoidal Weir GeometrySide slope 1:4 (14.04°) expands flow area to exactly offset lateral end contraction head losses.
  2. Francis-Cipolletti Discharge FormulaQ = C_d · b · h^1.5 = 1.86 · 2.5 · (0.45)^1.5 = 1.404 m³/s (1403.7 L/s)

Cipolletti Weir Hydraulics

Interactive visualization based on your current inputs

Value
0.00.30.71.01.4Discharge (m³/s)Discharge (kL/s)Head (m)Area (m²)ParameterValue

What Is the Cipolletti Trapezoidal Weir Discharge Calculator?

Determine volumetric water discharge over a Cipolletti trapezoidal weir with 1:4 side slope end contraction compensation.

The Cipolletti Trapezoidal Weir Discharge Calculator is an analytical tool in the construction domain designed to evaluate Crest Length (b), Upstream Head (h), Discharge Coefficient (Cd) using verified mathematical equations. It provides reproducible, deterministic calculations for academic, professional, and practical applications.

How Does the Cipolletti Trapezoidal Weir Discharge Calculator Work?

This calculator computes results by taking input values for Crest Length (b), Upstream Head (h), Discharge Coefficient (Cd) and applying the governing equation: Cipolletti trapezoidal weir discharge formula where end flaring compensates exactly for crest side contractions.. Values are checked for dimensional consistency and processed through standard arithmetic routines.

Cipolletti Trapezoidal Weir Discharge Calculator Formula & Variables

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

Q=Cd⋅b⋅h1.5(with1H:4Vsideslopes)Q = Cd · b · h^{1.5} (with 1H:4V side slopes)

Cipolletti trapezoidal weir discharge formula where end flaring compensates exactly for crest side contractions.

How to Use the Cipolletti Trapezoidal Weir Discharge Calculator

  1. Enter your value for Crest Length (b) in m.
  2. Enter your value for Upstream Head (h) in m.
  3. Enter your value for Discharge Coefficient (Cd).
  4. Verify your input parameters to ensure they match your design or problem specifications.
  5. Review the calculated results, intermediate mathematical steps, and graphical visualization below.

Step-by-Step Example Calculation

Irrigation Canal Gauging (b = 2.5m, h = 0.45m)

Input Values:

crestLengthBM:2.5
headAboveCrestHM:0.45
dischargeCoefficientCd:1.86
Worked Steps: Computes discharge Q = 1.403 m³/s (1403.4 L/s) with crest velocity of 1.19 m/s.

Understanding Your Result

The calculated output gives the primary solution for Cipolletti Trapezoidal Weir 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 Crest Length (b), Upstream Head (h), Discharge Coefficient (Cd).
  • 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 Cipolletti Trapezoidal Weir Discharge.
  • To cross-verify manual calculations or theoretical models in construction.
  • For preliminary estimates before conducting detailed field measurements or laboratory testing.

Assumptions & Limitations

  • Head h should be measured upstream of the weir at a distance of at least 4·h to avoid draw-down curvature.
  • Head-to-crest length ratio h/b should ideally remain below 0.33 for standard accuracy.

Frequently Asked Questions

Why are the side slopes exactly 1:4?+
Cesare Cipolletti demonstrated mathematically and experimentally that a 1:4 (H:V) triangular flare adds triangular flow that perfectly cancels out the Francis end-contraction correction factor 0.2·h.
What is the minimum head for accurate measurement?+
Head should be at least 0.06 m (6 cm) to prevent the falling nappe from adhering to the downstream face of the weir plate.

Calculation Accuracy & Reference Note

This calculator implements verified mathematical formulas for Cipolletti Trapezoidal Weir Discharge Calculator. Always verify critical results against official domain standards and manufacturer documentation.

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