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Broad-Crested Rectangular Weir Discharge Calculator (ISO 3846)

Broad-crested weirs are robust hydraulic overflow structures used in irrigation canals, river diversion headworks, and reservoir spillways to meter volumetric flow.

Transverse clear width of the rectangular overflow opening.

Water surface elevation measured upstream above the weir crest horizontal sill.

Vertical height of weir sill above upstream canal bed.

Length of horizontal weir crest in the direction of flow.

Calculated Result
2.47 m³/s

Broad-Crested Weir Discharge

Discharge Flow Rate (Q)

2.47 m³/s (87.2 cfs)

Discharge Coefficient (C_d)

0.922

Critical Depth on Crest (y_c)

0.433 m

Crest Critical Velocity (V_c)

1.9 m/s

Broad-Crest Ratio (H / L)

0.43 (True Broad-Crest)

Calculation Breakdown

  1. Critical Depth Across Broad Cresty_c = (2/3) × H = (2/3) × 0.65 m = 0.433 m
  2. Theoretical Maximum Discharge FormulationQ = C_d × (2/3) × √[(2/3)g] × b × H^(1.5) = 0.922 × 1.705 × 3 × (0.65)^1.5 = 2.47 m³/s

Weir Hydraulic Discharge Profile

Interactive visualization based on your current inputs

Value
0.00.81.52.33.0Crest Width (m)Head (m)Discharge (m³/s)Critical Depth (m)Velocity (m/s)ParameterValue

What Is the Broad-Crested Rectangular Weir Discharge Calculator (ISO 3846)?

The Broad-Crested Rectangular Weir Discharge Calculator evaluates hydraulic flow rates across horizontal sill overflow structures.

How Does the Broad-Crested Rectangular Weir Discharge Calculator (ISO 3846) Work?

It computes critical depth along the crest and evaluates the ISO 3846 discharge coefficient as a function of head-to-length ratio.

Broad-Crested Rectangular Weir Discharge Calculator (ISO 3846) Formula & Variables

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

Q = C_d \left(\frac{2}{3}\right) \sqrt{\frac{2}{3} g} \cdot b \cdot H^{1.5}, \quad y_c = \frac{2}{3} H

ISO 3846 formulation where critical flow develops along the horizontal crest sill, maximizing specific energy conveyance.

How to Use the Broad-Crested Rectangular Weir Discharge Calculator (ISO 3846)

  1. Input weir crest width and longitudinal length.
  2. Specify upstream water head above crest level.
  3. Enter sill height above channel bed.

Step-by-Step Example Calculation

3.0-Meter Canal Diversion Weir

Input Values:

weirCrestWidthM:3
upstreamHeadAboveCrestM:0.65
weirCrestHeightAboveBedM:1.2
weirCrestLengthM:1.5
Worked Steps: Conveys 2.44 m³/s discharge at 0.433 m critical depth and 1.88 m/s crest velocity.

Understanding Your Result

Discharge Flow Rate: Volume rate conveyed in m³/s and cfs.

Critical Depth: Flow depth establishing atop the broad crest.

Discharge Coefficient (C_d): Dimensional correction accounting for streamline curvature.

Factors That Affect the Result

  • Flow scales with head to the power of 1.5 (H^1.5).
  • Wider crest widths proportionally scale total volumetric conveyance.

When Should You Use This Calculator?

  • Agricultural irrigation diversions, reservoir emergency spillways, river hydrometry gauging stations, and flume calibration.

Assumptions & Limitations

  • Assumes free modular discharge without downstream backwater drowning.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Conforms to ISO 3846:2008 and Bos Discharge Measurement Structures.

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