Compute the discharge over a sharp-crested thin-plate weir. Rectangular (suppressed, no side contraction): Q = (2/3)·C_d·√(2g)·b·H^1.5. V-notch (triangular): Q = (8/15)·C_d·√(2g)·tan(θ/2)·H^2.5. b is the crest width, H the head over the crest (or over the vertex for a V-notch), θ the notch angle. If C_d is left blank it defaults to 0.611 for rectangular weirs (Rehbock/Francis typical value) and 0.58 for V-notch weirs. Crest width in m/cm, head in m/cm/mm; output in m³/s, L/s, L/min and m³/h.
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Key facts
Category
Math & Numbers
Input types
select, number
Output type
json
Sample coverage
4
API ready
Yes
Overview
The Weir Flow Calculator estimates discharge over a sharp-crested thin-plate weir using rectangular or V-notch formulas. Enter the crest width or notch angle, head, gravity, and optional discharge coefficient to get flow in m³/s, L/s, L/min, and m³/h.
When to use
Estimate flow over a suppressed rectangular weir without side contraction.
Calculate discharge through a triangular V-notch weir from the notch angle and measured head.
Convert a weir flow result into m³/s, L/s, L/min, and m³/h for hydraulic calculations.
How it works
1Select Rectangular Weir or V-Notch (Triangular) Weir.
2Enter the crest width for a rectangular weir, or the notch angle for a V-notch, along with the head and units.
3Optionally enter a discharge coefficient and gravitational acceleration; blank discharge coefficients use the type-specific defaults.
4The calculator applies the selected weir formula and reports the discharge in four flow-rate units.
Use cases
Open-channel flow estimation for hydraulic engineering calculations.
Sizing and checking measurements from laboratory or field weir setups.
Comparing rectangular and V-notch discharge under different head conditions.
Examples
1. Estimate flow over a rectangular weir
Hydraulic engineer
Background
An engineer is checking the discharge from a suppressed rectangular weir with a 1 m crest width and a measured head of 0.2 m.
Problem
Calculate the flow rate using the typical rectangular discharge coefficient.
How to use
Select Rectangular Weir, enter a crest width of 1 m and a head of 0.2 m, and leave the discharge coefficient blank.
Weir type: Rectangular; crest width: 1 m; head: 0.2 m; C_d: default 0.611; gravity: 9.81 m/s².
Outcome
The estimated discharge is approximately 0.1614 m³/s, or 161.378 L/s.
2. Measure low flow with a 90° V-notch
Water-resources technician
Background
A technician uses a 90° triangular notch and records a head of 0.15 m above the vertex.
Problem
Determine the discharge through the V-notch using the typical V-notch coefficient.
How to use
Select V-Notch (Triangular) Weir, enter a 90° notch angle and a 0.15 m head, and leave the discharge coefficient blank.
FAQ
What inputs are required for a rectangular weir?
Enter the crest width, head, and their units. The discharge coefficient and gravity can be left at their defaults.
What inputs are required for a V-notch weir?
Enter the notch angle and head with their units. The default notch angle is 90°.
What discharge coefficient is used by default?
The default is 0.611 for rectangular weirs and 0.58 for V-notch weirs.
Which units can I use for the head?
Head can be entered in meters, centimeters, or millimeters.
What flow units are included in the result?
Results are provided in m³/s, L/s, L/min, and m³/h.