Math & Numbers

Pipe Friction Factor Calculator (Colebrook-White / Haaland)

Compute the Darcy friction factor: laminar closed-form f=64/Re for Re<2000, or iterative Colebrook-White solution for transitional/turbulent flow, with the explicit Haaland approximation always returned as a cross-check. Reports relative roughness ε/D, absolute roughness (m), diameter (m), flow regime (laminar/transitional/turbulent), effective method and iteration count. Roughness ε in m/mm/µm, diameter D in m/cm/mm.

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/pipe-friction-factor' \
  -H 'Content-Type: application/json' \
  -d '{"reynolds":100000,"roughness":0.0457,"roughnessUnit":"mm","diameter":0.05,"diameterUnit":"m","method":"Auto","decimalPlaces":6}'

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/pipe-friction-factor

Parameters

Name	Type	Required	Description
reynolds	number	Yes	Reynolds number Re = ρ·v·D/μ. Must be positive.
roughness	number	Yes	Absolute pipe roughness ε in the selected unit. 0 = perfectly smooth.
roughnessUnit	select	No	—
diameter	number	Yes	Internal (hydraulic) pipe diameter D in the selected unit.
diameterUnit	select	No

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-pipe-friction-factor": {
      "name": "pipe-friction-factor",
      "description": "Compute the Darcy friction factor: laminar closed-form f=64/Re for Re<2000, or iterative Colebrook-White solution for transitional/turbulent flow, with the explicit Haaland approximation always returned as a cross-check. Reports relative roughness ε/D, absolute roughness (m), diameter (m), flow regime (laminar/transitional/turbulent), effective method and iteration count. Roughness ε in m/mm/µm, diameter D in m/cm/mm.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=pipe-friction-factor",
      "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": "pipe-friction-factor",
    "arguments": {
  "reynolds": 100000,
  "roughness": 0.0457,
  "roughnessUnit": "mm",
  "diameter": 0.05,
  "diameterUnit": "m",
  "method": "Auto",
  "decimalPlaces": 6
}
  }
}

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