Weir Flow Rate Calculator
Find discharge Q over a rectangular or V-notch weir from head, discharge coefficient, and crest geometry.
🧱 What is the Weir Flow Rate Calculator?
A weir is a low wall or obstruction built across an open channel that forces water to flow over a fixed crest at a measurable depth. Because the discharge over a weir relates predictably to the head (depth) of water above the crest, weirs are one of the simplest and most accurate ways to measure flow rate in open channels, with no moving parts to calibrate or maintain. This calculator finds discharge Q for both a rectangular (suppressed, full-width sharp-crested) weir and a V-notch (triangular) weir.
Weirs are used constantly in irrigation control structures to measure water delivered to farmland, in laboratory flumes for teaching and research in open-channel hydraulics, in water and wastewater treatment plants to monitor flow between process stages, and in small dam spillways where the crest itself doubles as the flow-measurement device. Weirs remain popular because they require only a single head measurement and no power or moving parts.
Rectangular weirs have a flat, horizontal crest and handle larger, steadier flows well, since discharge grows with head to the power 1.5. V-notch weirs concentrate flow into a narrow triangular notch, so discharge grows with head to the power 2.5, which makes small flow changes produce a much larger, more measurable change in head. This is exactly why V-notch weirs are the standard choice for low-flow and highly variable-flow monitoring, while rectangular weirs are preferred for larger, steadier discharges where their simpler construction is an advantage.
This calculator is useful for civil and irrigation engineers sizing a weir for a target flow range, lab technicians converting a measured head into a discharge reading, and students verifying the Francis and V-notch weir formulas by hand.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Small dam spillway (rectangular weir)
Example 2 - Irrigation control structure (rectangular weir)
Example 3 - Lab flume 90° V-notch weir
❓ Frequently Asked Questions
🔗 Related Calculators
What is a weir and why is it used to measure flow?
A weir is a low wall or obstruction placed across an open channel that forces water to flow over its crest at a known depth. Because discharge relates predictably to the measured head above the crest, weirs are a simple, accurate way to measure flow rate in irrigation channels, labs, and water treatment plants without any moving parts.
What is the formula for a rectangular weir?
Q = Cd x (2/3) x sqrt(2g) x L x H^1.5, where Cd is the discharge coefficient, g is 9.81 m/s2, L is the crest length, and H is the head (depth of water) above the crest, measured upstream of the drawdown zone.
What is the formula for a V-notch weir?
Q = Cd x (8/15) x sqrt(2g) x tan(theta/2) x H^2.5, where theta is the full notch angle in degrees (commonly 90 degrees), and H is the head above the vertex of the notch. Converting theta to radians before taking the tangent is required.
What is the difference between a rectangular and a V-notch weir?
A rectangular weir has a flat, horizontal crest and is simpler to build, better suited to measuring larger, steadier flows. A V-notch (triangular) weir concentrates flow into a narrow notch, giving much better sensitivity and accuracy for small and rapidly changing flows, which is why V-notch weirs are the standard choice in laboratory flumes and low-flow monitoring stations.
What is a typical discharge coefficient for a weir?
For a fully suppressed rectangular weir, Cd is typically around 0.60 to 0.62. For a 90-degree V-notch weir, Cd is typically around 0.58 to 0.60. Both values assume a sharp crest, fully ventilated nappe, and negligible approach velocity, real installations should be calibrated when precision matters.
Why does a V-notch weir use H to the power 2.5 instead of 1.5?
A V-notch's flow area grows with both depth and width simultaneously, since the notch widens linearly with height, adding an extra factor of H to the rectangular weir's H^1.5 relationship and giving H^2.5 overall. This makes the V-notch far more sensitive to small head changes at low flow.
What is the nappe in weir flow measurement?
The nappe is the sheet of water that falls freely over the weir crest. For accurate measurement, the nappe must be fully ventilated, meaning air can freely enter the space beneath it, otherwise a partial vacuum forms that pulls the nappe down and increases the apparent discharge coefficient, causing measurement error.
Where should I measure the head H for a weir?
Head H should be measured upstream of the weir at a distance of at least 3 to 4 times the maximum expected head above the crest, so the reading is taken before the water surface begins to draw down as it accelerates toward the crest.
Can this calculator be used for a broad-crested weir?
No, this calculator covers only sharp-crested rectangular (Francis-type) and V-notch weirs. Broad-crested weirs use a different formula because the flow passes over a wide, flat crest where critical flow depth develops on top of the weir itself, rather than falling freely as a nappe.
How does crest length affect rectangular weir discharge?
Discharge is directly proportional to crest length L, so doubling the crest length doubles the discharge for the same head and discharge coefficient. This linear relationship makes rectangular weirs well suited to handling large flow ranges by sizing the crest length to the expected maximum flow.