Weir Discharge Calculator
Estimate open-channel flow rate over a rectangular or V-notch sharp-crested weir from the head, discharge coefficient, and weir geometry — with the result reported in m³/s, L/s, m³/h and US gpm at once.
Input
Water surface elevation above the weir crest, in meters, measured upstream clear of the drawdown curve.
Empirical coefficient accounting for real flow losses vs the ideal formula — around 0.60-0.63 for a sharp-crested weir under typical conditions unless you have a calibrated value.
Length of the weir crest, in meters, measured perpendicular to the flow.
Output
| Metric | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/weir-discharge-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"weirType": "rectangular",
"head": "0.3",
"dischargeCoefficient": "0.62",
"crestWidth": "1.5"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `weir-discharge-calculator` tool (Weir Discharge Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/weir-discharge-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Weir Discharge Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|
Also available with
Guides
The Weir Discharge Calculator estimates open-channel flow rate over a sharp-crested rectangular or V-notch weir — the standard method hydraulics engineers, surveyors and irrigation designers use to gauge flow from a simple upstream head measurement.
How to use it
- Pick the weir type: rectangular (a full-width, straight crest) or V-notch (a triangular notch).
- Enter the head over the crest (H) — the water surface elevation above the crest, measured upstream far enough that the drawdown curve near the weir doesn't affect the reading.
- Set the discharge coefficient (Cd) — 0.60-0.63 is a reasonable default for a sharp-crested weir under typical conditions; use a calibrated value from a field test or manufacturer spec if you have one.
- For a rectangular weir, enter the crest width (L). For a V-notch weir, enter the notch angle (θ) — 90° is the most common.
- Read the discharge in the summary table, reported in four units at once: m³/s, L/s, m³/h, and US gpm.
The formulas
Rectangular (full-width, suppressed): Q = Cd × (2/3) × √(2g) × L × H^1.5
V-notch (triangular): Q = Cd × (8/15) × √(2g) × tan(θ/2) × H^2.5where g = 9.80665 m/s², H and L are in meters, and θ is the full included notch angle in degrees. These are the standard sharp-crested weir equations used across civil and hydraulic engineering references.
Rather than stopping at one flow-rate number in whichever unit the tool happens to default to, this calculator converts the result into the four units most commonly needed downstream — cubic meters per second for design calculations, liters per second and cubic meters per hour for utility/process contexts, and US gallons per minute for pump sizing — so you don't need a separate unit converter for whichever one your next step actually needs.
Is my data private?
Yes. The entire calculation runs locally in your browser — nothing you enter is sent anywhere.
What are the limitations?
This tool assumes free (non-submerged), fully aerated flow with no approach-velocity correction — the same idealized conditions the standard weir equations assume. It does not handle:
- Submerged flow — where the downstream water level is high enough to interfere with the nappe (the falling sheet of water over the crest).
- Approach velocity — significant upstream channel velocity can require a correction term.
- Nappe ventilation — an unventilated nappe can pull in extra flow and throw off the coefficient.
Treat the result as a solid working estimate for planning and preliminary design, not a substitute for a field-calibrated flow measurement where precision matters (billing, regulatory compliance, or critical process control).
What discharge coefficient should I use?
Cd depends on the weir's exact geometry, the approach channel, and how well-defined the crest edge is. 0.60-0.63 is a common assumption for a sharp-crested weir in typical conditions; consult a hydraulics reference (or a field calibration) for anything precision-sensitive.
Common uses
Estimating stream or channel flow from a simple head reading, sizing a downstream pump or pipe from an upstream weir's discharge, and checking flow-monitoring station readings against the underlying weir equation. For pipe-flow or open-channel calculations instead of a weir, see the Pipe Flow Velocity Calculator and Manning Flow Calculator tools.