Math & Numbers

Pump Affinity Laws Calculator (Q∝n, H∝n², P∝n³)

Apply the pump affinity laws to the same pump at different speeds or with a different impeller diameter. Speed mode: ratio = n2/n1; diameter mode: ratio = D2/D1. Then Q2 = Q1·ratio, H2 = H1·ratio², P2 = P1·ratio³. Q1, H1 and P1 are optional baseline-condition inputs; if all three are omitted, only the ratio is returned. Flow in m³/s/L/s/L/min/m³/h, head in m/ft, power in W/kW/hp, impeller diameter in m/cm/mm; SI equivalents (m³/s, m, W) are also reported.

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/pump-affinity-laws' \
  -H 'Content-Type: application/json' \
  -d '{"mode":"speed","speedN1":1750,"speedN2":3500,"diameterD1":0,"diameterD2":0,"diameterUnit":"m","flowQ1":10,"flowUnit":"L/s","headH1":20,"headUnit":"m","powerP1":1000,"powerUnit":"W","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/pump-affinity-laws

Parameters

Name	Type	Required	Description
mode	select	No	Speed mode uses the speed ratio n2/n1. Diameter mode uses the impeller diameter ratio D2/D1.
speedN1	number	Yes	Initial pump speed n1 (rpm). Required when Mode = Speed.
speedN2	number	No	New pump speed n2 (rpm). Required when Mode = Speed.
diameterD1	number	No	Initial impeller diameter D1. Enter in the selected Diameter Unit. Required when Mode = Diameter.
diameterD2	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-pump-affinity-laws": {
      "name": "pump-affinity-laws",
      "description": "Apply the pump affinity laws to the same pump at different speeds or with a different impeller diameter. Speed mode: ratio = n2/n1; diameter mode: ratio = D2/D1. Then Q2 = Q1·ratio, H2 = H1·ratio², P2 = P1·ratio³. Q1, H1 and P1 are optional baseline-condition inputs; if all three are omitted, only the ratio is returned. Flow in m³/s/L/s/L/min/m³/h, head in m/ft, power in W/kW/hp, impeller diameter in m/cm/mm; SI equivalents (m³/s, m, W) are also reported.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=pump-affinity-laws",
      "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": "pump-affinity-laws",
    "arguments": {
  "mode": "speed",
  "speedN1": 1750,
  "speedN2": 3500,
  "diameterD1": 0,
  "diameterD2": 0,
  "diameterUnit": "m",
  "flowQ1": 10,
  "flowUnit": "L/s",
  "headH1": 20,
  "headUnit": "m",
  "powerP1": 1000,
  "powerUnit": "W",
  "decimalPlaces": 4
}
  }
}

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