Free Broad Crested Weir Calculator

Broad-Crested Weirs in Open Channel Flow

Weirs are fundamental hydraulic structures used across rivers, reservoir outlets, and canals to regulate water levels and gauge flow rates. Among the many types — sharp‑crested, broad‑crested, narrow‑crested, and Ogee‑shaped — the broad‑crested weir is especially valued for its reliability under high‑discharge conditions. Hydraulic engineers and hydrologists rely on a weir flow calculator to quickly estimate discharge without manual iteration.

Classification and Definition

A weir is considered broad‑crested when the upstream head (the vertical distance from the crest to the water surface) falls between 5 % and 50 % of the crest length. If the head exceeds that range, the same structure may behave as a sharp‑crested weir because the flow no longer adheres to the crest surface over a sufficient distance. Broad‑crested weirs are typically rectangular in cross‑section and are designed to handle large volumes of water. They are common in irrigation canals, stormwater systems, and low‑head dam applications.

How It Works

As water approaches the weir, it rises and flows over the flat crest. The weir’s width creates friction that decelerates the flow, causing a gradual transition to supercritical conditions just downstream. The water then falls in a smooth, waterfall‑like profile — a distinct visual signature of broad‑crested flow. This behavior contrasts with sharp‑crested weirs, where the flow springs free from the crest.

The Broad‑Crested Weir Equation

The fundamental broad crested weir equation expresses discharge as:

$$Q = C \cdot L \cdot H^{3/2}$$

where:

• $Q$ = volumetric flow rate (m³/s),
• $L$ = length of the weir crest (m),
• $H$ = upstream head above the crest (m),
• $C$ = discharge coefficient (m$^{0.5}$ s$^{-1}$).

The coefficient $C$ is derived from energy and momentum principles for a critical‑flow control section:

$$C = \sqrt{g} \left(\frac{2}{3}\right)^{3/2}$$

With standard gravitational acceleration $g = 9.8067\ \text{m/s}^2$, the coefficient computes to approximately $1.705\ \text{m}^{0.5}\,\text{s}^{-1}$. This value holds for ideal conditions; in practice, minor adjustments may be applied for approach velocity and crest shape.

Using the Broad Crested Weir Calculator

The hydraulic weir calculator automates the open channel flow calculation, requiring only three inputs:

1. Upstream head ($H$) – measured from the crest to the water surface.
2. Crest length ($L$) – the width of the weir perpendicular to flow.
3. Acceleration due to gravity ($g$) – usually 9.8067 m/s², but adjustable for location‑specific values.

Worked Example

Consider a channel with a $2\ \text{m}$‑long weir and a measured head of $0.5\ \text{m}$.

Step 1 – Compute the coefficient:

$$C = \sqrt{9.8067} \times \left(\frac{2}{3}\right)^{3/2} \approx 3.132 \times 0.5443 \approx 1.705\ \text{m}^{0.5}\,\text{s}^{-1}$$

Step 2 – Calculate discharge:

$$Q = 1.705 \times 2 \times (0.5)^{1.5} = 1.705 \times 2 \times 0.3536 \approx 1.206\ \text{m}^3/\text{s}$$

The result, about 1.21 m³/s, is immediately obtained from the weir flow calculator, eliminating the need for repeated manual multiplication.

Practical Considerations and Applications

The equation is valid only when the upstream head is between 5 % and 50 % of the crest length. Outside this window, the flow may not be fully controlled by the crest width, and a different weir type should be considered. Broad‑crested weirs are preferred for permanent installations because of their robust construction and predictable performance over a wide range of discharges.

Whether you are designing an irrigation off‑take, a stormwater detention basin, or an experimental flume, this free online weir discharge calculator provides a quick and accurate estimate of discharge. It serves as a valuable cross‑check for field measurements and a teaching aid for hydraulics students.