What Is the Weir Discharge & Open Channel Flow Calculator (Francis & V-Notch)?
A weir is an overflow hydraulic structure used to measure volumetric flow in open channels by establishing a fixed mathematical head-discharge relationship.
How Does the Weir Discharge & Open Channel Flow Calculator (Francis & V-Notch) Work?
Integrates Torricelli’s velocity v = √(2gh) across the cross-sectional area of the nappe overflow geometry.
Weir Discharge & Open Channel Flow Calculator (Francis & V-Notch) Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Rectangular flow scales with head to the 1.5 power. Triangular V-notch flow scales with head to the 2.5 power.
How to Use the Weir Discharge & Open Channel Flow Calculator (Francis & V-Notch)
- Select rectangular or 90° V-notch weir.
- Enter upstream head height above weir crest in meters.
- Specify crest length L for rectangular weirs.
Step-by-Step Example Calculation
2.0m Rectangular Weir with 35 cm Head
Input Values:
weirType:rectangular-suppressed
headAboveCrestMeters:0.35
crestLengthMeters:2.0
Worked Steps: Generates a discharge of 761.9 L/s (0.7619 m³/s or 26.9 CFS) across the 2-meter crest.
Understanding Your Result
Discharge (L/s / m³/s / CFS): Volumetric open-channel stream flow.
Head: Upstream hydraulic elevation.
Factors That Affect the Result
- Head H is the primary driver (exponential power 1.5 or 2.5); crest length scales rectangular flow linearly.
When Should You Use This Calculator?
- Irrigation canal flow metering, wastewater treatment discharge monitoring, and river storm stream gauging.
Assumptions & Limitations
- Assumes free-discharge conditions (aerated nappe without tailwater submergence).
Frequently Asked Questions
Where should water level head H be measured upstream of a weir?+
Head H must be measured at least 3 to 4 times the maximum head upstream of the weir face to avoid the surface drawdown curvature that naturally accelerates near the crest.
Calculation Accuracy & Reference Note
Standard Francis and Thomson open channel weir discharge calibrations.