Broad Crested Weir Calculator

Calculate discharge, critical depth, and flow regime for broad crested weirs.

Determine the discharge capacity and hydraulic characteristics of broad crested weirs using standard hydraulic engineering formulas and coefficients.

Examples

Click on any example to load it into the calculator.

Concrete Weir

concrete

Standard concrete broad crested weir for irrigation channel flow measurement.

Width: 3.0 m

Head: 0.75 m

Height: 1.5 m

Manning n: 0.013

Cd: 0.85

Natural Channel Weir

natural

Broad crested weir in a natural river channel with higher roughness.

Width: 5.0 m

Head: 1.2 m

Height: 2.0 m

Manning n: 0.025

Cd: 0.82

Small Laboratory Weir

small

Small-scale broad crested weir for laboratory or research applications.

Width: 0.5 m

Head: 0.3 m

Height: 0.8 m

Manning n: 0.010

Cd: 0.88

Large Dam Spillway

large

Large broad crested weir used as a dam spillway for flood control.

Width: 20.0 m

Head: 2.5 m

Height: 5.0 m

Manning n: 0.015

Cd: 0.87

Other Titles
Understanding Broad Crested Weir Calculator: A Comprehensive Guide
Master the principles of broad crested weir hydraulics and learn how to accurately calculate discharge, critical depth, and flow characteristics for various applications in water management and hydraulic engineering.

What is a Broad Crested Weir?

  • Definition and Structure
  • Flow Characteristics
  • Advantages and Applications
A broad crested weir is a hydraulic structure used to measure and control water flow in open channels. It consists of a horizontal crest that is sufficiently wide to allow the flow to develop a parallel stream surface over the crest length. Unlike sharp-crested weirs, broad crested weirs have a substantial crest width that creates a more stable flow condition and reduces the sensitivity to approach velocity effects.
Physical Characteristics and Design
The key characteristic of a broad crested weir is its crest width, which must be wide enough to allow the flow to establish a parallel surface. Typically, the crest width should be at least 2-3 times the upstream head to ensure proper flow development. The weir height, measured from the channel bed to the crest, affects the approach velocity and overall flow conditions. The structure is usually constructed from concrete, masonry, or other durable materials that can withstand water flow and environmental conditions.
Flow Behavior and Hydraulic Principles
When water approaches a broad crested weir, it accelerates as it passes over the crest. The flow depth decreases and the velocity increases, creating a critical flow condition at the crest. This critical flow condition is characterized by a Froude number of approximately 1.0. The relationship between the upstream head and the discharge follows a power law, typically Q = Cd × L × H^(3/2), where Cd is the discharge coefficient, L is the weir width, and H is the upstream head.
Advantages Over Other Weir Types
Broad crested weirs offer several advantages compared to sharp-crested weirs. They are less sensitive to approach velocity effects, making them more suitable for channels with varying flow conditions. They also have better structural stability and are less prone to damage from debris or high flows. Additionally, they provide more accurate discharge measurements over a wider range of flow rates and are easier to maintain in field conditions.

Common Applications:

  • Irrigation channel flow measurement and control
  • River and stream discharge monitoring
  • Dam spillway design and operation
  • Laboratory hydraulic research and testing
  • Wastewater treatment plant flow measurement

Step-by-Step Guide to Using the Calculator

  • Data Collection
  • Input Parameters
  • Result Interpretation
Using the Broad Crested Weir Calculator requires accurate measurement of physical parameters and understanding of the underlying hydraulic principles. Follow these steps to obtain reliable results for your specific application.
1. Measure Physical Dimensions Accurately
Begin by measuring the weir width (L) perpendicular to the flow direction. This should be the effective width over which water flows. Next, measure the weir height (P) from the downstream channel bed to the crest level. The upstream head (H) should be measured at a distance of at least 3-4 times the upstream head upstream from the weir to avoid drawdown effects. Use precise measuring equipment and ensure all measurements are in consistent units (meters).
2. Determine Appropriate Coefficients
The Manning coefficient (n) depends on the channel material and surface roughness. For concrete channels, use values between 0.010-0.015. Natural channels with vegetation may require values of 0.020-0.030. The discharge coefficient (Cd) typically ranges from 0.80 to 0.90 for broad crested weirs, with higher values for well-designed structures with smooth surfaces. Consider the specific conditions of your weir when selecting these values.
3. Input Data and Calculate Results
Enter all measured values into the calculator, ensuring positive numbers for all parameters. The calculator will compute the discharge using the standard broad crested weir equation. It will also determine the critical depth, which is the depth at which the Froude number equals 1.0, and classify the flow regime based on the Froude number. Review the results to ensure they are physically reasonable for your application.
4. Validate and Apply Results
Compare the calculated discharge with expected values or historical data if available. Check that the flow regime classification makes sense for your conditions. Use the results to design flow control structures, calibrate measurement systems, or analyze hydraulic performance. Consider the limitations of the calculation method and the assumptions made in the analysis.

Typical Manning Coefficients (n):

  • Smooth concrete: 0.010-0.012
  • Rough concrete: 0.013-0.015
  • Natural channels (clean): 0.020-0.025
  • Natural channels (weeds): 0.025-0.035
  • Riprap channels: 0.030-0.040

Real-World Applications and Engineering Design

  • Irrigation Systems
  • Flood Control
  • Environmental Monitoring
Broad crested weirs find extensive applications in water resources engineering, from small-scale irrigation systems to large dam spillways. Understanding their design and operation is crucial for effective water management.
Irrigation and Agricultural Applications
In irrigation systems, broad crested weirs are used to measure and control water delivery to agricultural fields. They provide accurate flow measurement without significant head loss, making them ideal for gravity-fed irrigation systems. The calculator helps engineers design weirs that can handle the expected flow rates while maintaining measurement accuracy. Proper sizing ensures adequate water delivery during peak demand periods while preventing overtopping during high flows.
Flood Control and Dam Safety
Large broad crested weirs serve as spillways for dams and reservoirs, providing controlled release of water during flood events. The calculator assists in designing spillways that can safely pass design flood flows while maintaining structural integrity. Engineers must consider the relationship between reservoir level, spillway capacity, and downstream channel capacity to ensure effective flood control without causing downstream flooding.
Environmental and Water Quality Monitoring
Broad crested weirs are used in environmental monitoring programs to measure stream flows for water quality assessment and ecosystem studies. The stable flow conditions they create make them suitable for continuous monitoring applications. The calculator helps researchers and environmental engineers design measurement structures that provide reliable data for long-term monitoring programs.

Common Misconceptions and Design Considerations

  • Flow Regime Assumptions
  • Coefficient Selection
  • Measurement Errors
Several misconceptions exist regarding broad crested weir design and operation that can lead to significant errors in flow measurement and structural design.
Misconception: All Broad Crested Weirs Behave Similarly
The performance of broad crested weirs varies significantly based on their geometry, surface roughness, and approach conditions. The discharge coefficient is not constant but depends on the ratio of upstream head to weir height (H/P), the crest length, and surface roughness. Engineers must carefully consider these factors when selecting design parameters and interpreting measurement results.
Misconception: Approach Velocity Can Be Ignored
While broad crested weirs are less sensitive to approach velocity than sharp-crested weirs, the approach velocity can still affect the discharge coefficient, especially for low weirs or high approach velocities. The calculator assumes subcritical approach flow, but if the approach flow is supercritical, the weir may not function as intended. Proper channel design upstream of the weir is essential for accurate measurements.
Design Consideration: Submergence Effects
When the downstream water level rises above the weir crest, the weir becomes submerged and the discharge relationship changes significantly. The calculator assumes free-flow conditions. For submerged flow, different equations and coefficients must be used. Engineers must ensure that the downstream channel has sufficient capacity to prevent submergence under normal operating conditions.

Design Guidelines:

  • Crest width should be at least 2-3 times the upstream head
  • Weir height should be sufficient to prevent downstream submergence
  • Approach channel should be straight for at least 10 times the upstream head
  • Regular maintenance is required to prevent debris accumulation and surface deterioration

Mathematical Derivation and Theoretical Background

  • Energy Principles
  • Critical Flow Theory
  • Discharge Equation Development
The calculation of discharge through a broad crested weir is based on fundamental principles of fluid mechanics and open channel flow theory.
Energy Conservation and Bernoulli's Equation
The analysis begins with the application of Bernoulli's equation between the upstream approach section and the weir crest. The total energy head consists of the elevation head, pressure head, and velocity head. As water flows over the weir, the elevation head decreases while the velocity head increases. At the crest, the flow reaches critical conditions where the specific energy is minimized for the given discharge.
Critical Flow and Froude Number
Critical flow occurs when the Froude number equals 1.0, indicating that the flow velocity equals the wave celerity. At this condition, the specific energy is minimized and the flow depth is called the critical depth. For a rectangular channel, the critical depth is related to the discharge per unit width by the equation: yc = (q²/g)^(1/3), where q is the discharge per unit width and g is the gravitational acceleration.
Discharge Equation Development
The discharge equation for a broad crested weir is derived by combining the critical flow relationship with the energy equation. The resulting equation is: Q = Cd × L × H^(3/2) × √(2g/3), where Cd is the discharge coefficient that accounts for energy losses and flow contraction effects. The coefficient Cd typically ranges from 0.80 to 0.90 and depends on the weir geometry and flow conditions.

Key Equations:

  • Discharge: Q = Cd × L × H^(3/2) × √(2g/3)
  • Critical depth: yc = (q²/g)^(1/3)
  • Froude number: Fr = v/√(gy)
  • Specific energy: E = y + v²/(2g)