Math & Numbers

Weir Flow Calculator (Rectangular & V-Notch Weirs)

Compute the discharge over a sharp-crested thin-plate weir. Rectangular (suppressed, no side contraction): Q = (2/3)·C_d·√(2g)·b·H^1.5. V-notch (triangular): Q = (8/15)·C_d·√(2g)·tan(θ/2)·H^2.5. b is the crest width, H the head over the crest (or over the vertex for a V-notch), θ the notch angle. If C_d is left blank it defaults to 0.611 for rectangular weirs (Rehbock/Francis typical value) and 0.58 for V-notch weirs. Crest width in m/cm, head in m/cm/mm; output in m³/s, L/s, L/min and m³/h.

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/weir-flow-calculator' \
  -H 'Content-Type: application/json' \
  -d '{"weirType":"rectangular","crestWidth":1,"crestWidthUnit":"m","notchAngle":90,"head":0.2,"headUnit":"m","dischargeCoefficient":0.611,"gravity":9.81,"decimalPlaces":4}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/weir-flow-calculator

Parameters

Name	Type	Required	Description
weirType	select	No	Rectangular (suppressed, no side contraction) takes crest width b and head H. V-Notch (triangular) takes notch angle θ and head H.
crestWidth	number	Yes	Crest width b of the rectangular weir. Enter in the selected Crest Width Unit. Required when Weir Type = Rectangular.
crestWidthUnit	select	No	—
notchAngle	number	No	V-notch angle θ in degrees (0 < θ ≤ 180). Required when Weir Type = V-Notch.
head	number

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-weir-flow-calculator": {
      "name": "weir-flow-calculator",
      "description": "Compute the discharge over a sharp-crested thin-plate weir. Rectangular (suppressed, no side contraction): Q = (2/3)·C_d·√(2g)·b·H^1.5. V-notch (triangular): Q = (8/15)·C_d·√(2g)·tan(θ/2)·H^2.5. b is the crest width, H the head over the crest (or over the vertex for a V-notch), θ the notch angle. If C_d is left blank it defaults to 0.611 for rectangular weirs (Rehbock/Francis typical value) and 0.58 for V-notch weirs. Crest width in m/cm, head in m/cm/mm; output in m³/s, L/s, L/min and m³/h.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=weir-flow-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "weir-flow-calculator",
    "arguments": {
  "weirType": "rectangular",
  "crestWidth": 1,
  "crestWidthUnit": "m",
  "notchAngle": 90,
  "head": 0.2,
  "headUnit": "m",
  "dischargeCoefficient": 0.611,
  "gravity": 9.81,
  "decimalPlaces": 4
}
  }
}

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