Broad Crested Weir Calculator – Discharge & Flow
Calculate discharge, critical depth, and flow regime for broad crested weirs using standard hydraulic engineering formulas.
Enter the weir geometry and flow parameters to determine discharge capacity and hydraulic characteristics of a broad crested weir.
Broad Crested Weir Calculator – Discharge & Flow
Calculate discharge, critical depth, and flow regime for broad crested weirs using standard hydraulic engineering formulas.
About the Broad Crested Weir Calculator
A broad crested weir is a hydraulic structure built across an open channel to measure or control the flow of water. Unlike a sharp-crested weir, which has a thin crest so that the overflowing nappe springs clear of the structure, a broad crested weir has a flat, wide crest over which the flow passes in a subcritical state upstream and transitions to critical flow at or near the downstream edge of the crest. This behavior makes the broad crested weir one of the most reliable and self-regulating discharge measurement structures in hydraulic engineering.
The fundamental discharge formula for a broad crested weir is derived from the critical flow condition. At critical flow, the Froude number equals 1 and the specific energy of the flow is at its minimum for a given discharge. The relationship between upstream head H (measured above the weir crest), weir width B, gravitational acceleration g, and discharge coefficient Cd gives: Q = Cd × (2/3) × B × √(2g/3) × H^(3/2). Substituting g = 9.81 m/s² and simplifying, the coefficient √(2g/3) ≈ 2.553 m^(1/2)/s. The discharge coefficient Cd accounts for approach velocity effects, friction over the crest, and departure from ideal critical flow conditions; it typically ranges from 0.82 to 0.92 for well-maintained concrete weirs.
Critical depth on the weir crest is the flow depth at which critical flow occurs. For a rectangular channel section, critical depth yc = (2/3) × H, which follows directly from the critical flow condition. At critical depth, the critical velocity Vc = √(g × yc). The Froude number at the crest section equals 1 by definition of critical flow, confirming that the weir is operating in the standard regime. If the downstream tailwater rises above a certain submergence limit, critical flow may not develop and the weir begins to operate in a submerged condition, causing the actual discharge to be lower than the free-flow formula predicts.
The Manning roughness coefficient n appears in the full analysis of flow over the weir crest when the crest length is significant and friction losses must be estimated. Smooth concrete surfaces have n ≈ 0.011–0.013, while rougher concrete or stone masonry may reach 0.015–0.025, and natural earth channels can exceed 0.030. For the simplified broad crested weir formula used in discharge measurement, the Manning coefficient primarily influences the effective discharge coefficient.
Broad crested weirs are used in irrigation canals, drainage channels, river engineering, and environmental flow studies. They are preferred over sharp-crested weirs in situations where debris, floating material, or high sediment loads could damage a thin crest. They are also more structurally robust and easier to maintain. Engineers use the discharge–head relationship to prepare rating curves: tables or graphs relating upstream head to discharge, which allow field staff to determine flow by simply measuring the upstream water level.
The weir height P (the vertical distance from the channel bed to the weir crest) influences the approach velocity. A higher weir relative to the head produces slower approach flow and makes the velocity head correction negligible. When P is small relative to H, the approach velocity is significant and the effective head includes a velocity head correction term V²/(2g), where V is the mean approach velocity.
Broad Crested Weir Examples
Discharge calculations for typical weir configurations in irrigation, drainage, and water management applications.
| Weir Parameters | Discharge (Q) | Application |
|---|---|---|
| B = 3.0 m, H = 0.75 m, P = 1.5 m, n = 0.013, Cd = 0.85 | Q ≈ 2.82 m³/s | Concrete irrigation weir. Critical depth yc = 0.50 m, critical velocity ≈ 2.21 m/s. Friction head loss is tiny for smooth concrete; effective head ≈ upstream head. |
| B = 5.0 m, H = 1.2 m, P = 2.0 m, n = 0.025, Cd = 0.82 | Q ≈ 9.16 m³/s | Natural river channel weir with higher roughness. Wider crest and higher head produce significantly larger discharge. Used for river flow monitoring. |
| B = 0.5 m, H = 0.3 m, P = 0.8 m, n = 0.010, Cd = 0.88 | Q ≈ 0.123 m³/s | Small laboratory or research weir. Smooth surface, low head. Used for precision flow measurement in experimental hydraulics. |
| B = 20.0 m, H = 2.5 m, P = 5.0 m, n = 0.015, Cd = 0.87 | Q ≈ 117 m³/s | Dam spillway design. Very large discharge at high head. The broad crest provides structural stability and predictable flow control during flood events. |
How to Use the Broad Crested Weir Calculator
- Enter the weir width B in meters, which is the horizontal dimension of the crest perpendicular to the flow direction.
- Enter the upstream head H in meters, measured as the depth of water above the weir crest at a point upstream where the flow is undisturbed (typically 3–5 times the head upstream of the weir).
- Enter the weir height P in meters (from channel bed to crest), Manning's roughness coefficient n for the crest material, and the discharge coefficient Cd.
- Click Calculate to obtain the discharge Q, critical depth, critical velocity, and Froude number.
- Use the discharge value to construct a rating curve by repeating the calculation for a range of head values, or compare with field measurements to calibrate the coefficient Cd.
Frequently Asked Questions
What is the difference between a broad crested weir and a sharp crested weir?
A sharp crested weir has a thin edge (≤ 2 mm) so that the flowing nappe springs clear of the crest as a free-falling jet, and the flow pattern is governed by the contracted nappe geometry. A broad crested weir has a flat crest wide enough (typically crest length L ≥ 3× head H) that the flow passes over it in a quasi-uniform critical state. The broad crested weir is more robust, handles debris better, and gives more stable discharge measurements when the head is high relative to crest length.
What does the discharge coefficient Cd represent?
The discharge coefficient Cd accounts for real-fluid effects that cause the actual discharge to differ from the ideal theoretical value. These include approach velocity, viscous friction over the crest, turbulence, and the slight departure from perfect critical flow conditions. For smooth concrete weirs in good condition, Cd typically falls between 0.82 and 0.92. Lower values apply when the weir is rough, the head is very small, or the crest length is very long. Cd is usually determined by physical model tests or field calibration.
What is critical flow and why does it occur on a broad crested weir?
Critical flow is the condition at which the Froude number equals 1 and specific energy is at its minimum for a given discharge. On a broad crested weir, the flow accelerates as it passes over the raised crest section. Because the crest acts as a hydraulic control, the flow naturally adjusts to critical conditions somewhere on the crest. This self-regulating behavior is what makes the broad crested weir a reliable discharge measurement structure — the discharge depends only on upstream head and is independent of downstream tailwater levels as long as free-flow conditions persist.
How is the upstream head H measured correctly?
The upstream head H must be measured as the depth of water above the weir crest elevation, not above the channel bed. The measurement point should be located 3–5 times the maximum head upstream of the weir face, where approach velocity effects are negligible and the water surface is relatively flat. A staff gauge, float gauge, or pressure transducer at this location provides the head reading. Measuring too close to the weir introduces velocity head errors.
When does a broad crested weir become submerged?
Submergence occurs when the downstream tailwater rises high enough to drown out the critical flow condition on the crest. The submergence ratio (tailwater depth / upstream head above crest) beyond which discharge is affected is typically 0.66–0.80 for broad crested weirs, depending on geometry and Cd. Under submerged conditions the actual discharge is less than the free-flow formula predicts, and corrections must be applied using submergence correction curves.
What Manning's n value should I use for my weir?
For smooth formed concrete or precast concrete weirs, use n = 0.011–0.013. For rough concrete or stone masonry, use n = 0.015–0.020. For earth or grass-lined crests, use n = 0.025–0.035. When in doubt, use a slightly higher n value to obtain a conservative (lower) discharge estimate. The Manning coefficient primarily affects the effective Cd, so if you have a measured Cd from calibration data, that already incorporates the roughness effects.