Broad Crested Weir Calculator
Flow Analysis Results
What Is a Broad Crested Weir Calculator?
A broad crested weir calculator estimates the flow rate of water passing over a wide, horizontal weir crest. It uses the measured upstream head and the weir’s dimensions to calculate the estimated discharge. This tool also adjusts the energy head for the velocity of water in the approach channel.
The calculator is useful for engineers, technicians, students, water managers, and property owners working with open-channel flow. It can support preliminary analysis of canals, drainage systems, irrigation channels, laboratory flumes, and water-control structures.
To calculate broad-crested weir discharge, enter the upstream head, weir height, crest length, weir width, and approach channel width. The calculator applies an iterative velocity-head correction, then displays the estimated flow rate, discharge coefficient, total energy head, and a note about whether the selected geometry fits the formula’s intended range.
How the Broad Crested Weir Formula Works
The calculator begins by setting the total energy head equal to the measured upstream head. It then calculates a discharge coefficient based on the ratio of total energy head to crest length.
The estimated discharge is then calculated with the following equation:
The variables are:
- Q is the estimated discharge in cubic meters per second or cubic feet per second.
- Cd is the calculated discharge coefficient.
- b is the weir width.
- g is gravitational acceleration: 9.81 for metric units or 32.174 for imperial units.
- H is the total energy head.
- L is the crest length in the direction of flow.
The calculator estimates the approach-flow area and velocity using these equations:
It then updates the total energy head by adding the velocity head:
This process repeats until the change in total energy head is less than 0.00001 or the calculator reaches 50 iterations.
Worked Metric Example
Assume a measured upstream head of 0.5 meters, a weir height of 1 meter, a crest length of 2 meters, a weir width of 3 meters, and an approach channel width of 3 meters.
- The calculation starts with H equal to 0.5 meters.
- The calculator determines Cd from the current H-to-L ratio.
- It calculates Q, the approach velocity, and the added velocity head.
- After the iterative correction converges, Q is approximately 1.268 cubic meters per second.
The displayed results are 1.268 m³/s for estimated discharge, 0.3772 for the discharge coefficient, and 0.5040 m for total energy head. The measured head-to-crest-length ratio is 0.25, which falls within the calculator’s stated standard range of 0.1 to 1.5.
How to Use the Broad Crested Weir Calculator: Step by Step
- Select Metric for meters and cubic meters per second, or select Imperial for feet and cubic feet per second.
- Enter the Measured Upstream Head (h). This is the measured water depth above the weir crest at the upstream measurement point.
- Enter the Weir Height (P). Use the vertical height of the weir above the approach-channel bottom.
- Enter the Crest Length (L). This is the horizontal crest dimension in the direction that water flows.
- Enter the Weir Width (b). This is the width of the flowing section across the channel.
- Enter the Approach Channel Width (B). It must be equal to or greater than the weir width.
- Select Calculate to display the flow analysis. Select Reset to clear the fields and return to metric units.
The main result is estimated discharge, shown as m³/s or ft³/s. The discharge coefficient is a dimensionless value used by the equation. Total energy head includes the measured upstream head and the calculated approach velocity head. The engineering analysis explains how the measured h-to-L ratio may affect the formula’s suitability.
What Can Affect Your Broad Crested Weir Result?
Head-to-Crest-Length Ratio
The calculator compares the measured upstream head with the crest length using h divided by L. This ratio is used only for the engineering note. The discharge coefficient itself uses total energy head divided by crest length.
| Measured h/L Ratio | Calculator Interpretation |
|---|---|
| Below 0.1 | Friction along the broad crest may dominate, so actual discharge may be lower than the theoretical estimate. |
| 0.1 to 1.5 | The calculator treats this as the standard operating range for established broad-crested flow. |
| Above 1.5 | Flow may behave more like flow over a sharp-crested weir, reducing the suitability of this formula. |
Channel and Weir Width
The weir width cannot exceed the approach channel width. If the weir is narrower than the channel, the calculator still produces a result but adds a lateral-contraction warning. The equation assumes minimal contraction, so the actual flow may be slightly lower than the estimate.
Geometry and Surface Conditions
The calculation assumes a standard rectangular weir with a smooth, horizontal, broad crest. Damage, sediment, debris, surface roughness, an uneven crest, downstream submergence, or unusual approach flow can change the real discharge. These conditions are not entered or corrected for by the calculator.
Measurement and Unit Consistency
All five measurements must be positive numbers and must use the selected unit system. Do not mix feet and meters. Small errors in the upstream head can noticeably change the result because total energy head is raised to the power of 1.5 in the discharge equation.
This calculator provides an engineering estimate, not a guaranteed field measurement. Actual discharge may vary because of installation geometry, measurement error, flow conditions, crest roughness, contraction, and other site-specific factors. Use field calibration or a qualified hydraulic professional when the result affects design, safety, permitting, or regulatory decisions.
Frequently Asked Questions
What is a broad crested weir?
A broad crested weir is an open-channel structure with a long, generally horizontal crest over which water flows. Its crest is long enough for the flow profile to develop across the top. Engineers use these structures for flow control, water-level management, and discharge measurement in channels and canals.
How do I calculate flow over a broad crested weir?
Enter the upstream head, weir height, crest length, weir width, and approach channel width. The calculator determines a discharge coefficient, estimates discharge, calculates the approach velocity, and updates the total energy head. It repeats this process until the energy-head value converges or reaches the iteration limit.
What is total energy head in this calculator?
Total energy head is the measured upstream head plus the calculated approach velocity head. The calculator estimates velocity from the discharge and the approach-flow area. It then adds v² divided by 2g to the measured head and repeats the discharge calculation using the updated energy head.
Why does the calculator need the weir height?
The weir height is used to estimate the approach-flow area. The calculator multiplies the approach channel width by the sum of weir height and measured upstream head. That area is used to calculate approach velocity, which affects the velocity-head correction and the final total energy head.
Can the weir width be smaller than the channel width?
Yes, the calculator allows the weir width to be smaller than the approach channel width. It then displays a note about lateral contraction. Because the formula assumes minimal contraction, the calculated discharge may be somewhat higher than the actual flow through a narrower weir opening.
What happens if the weir width exceeds the channel width?
The calculator will not perform the calculation if the weir width is greater than the approach channel width. It displays an alert asking you to correct the dimensions. The weir width must be less than or equal to the width of the approach channel.
How accurate is the broad crested weir calculator?
The result is a theoretical estimate based on the coded equation, an iterative velocity-head correction, and an assumed smooth rectangular weir with a horizontal crest. Accuracy may decrease with strong contraction, crest friction, sharp-crested flow behavior, poor measurements, debris, submergence, rough surfaces, or nonstandard geometry.