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.
Quick start
Call this tool from your code in three languages.
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
POST https://api.elysiatools.com/en/api/tools/pump-affinity-lawsParameters
| 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:
{
"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:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Call this tool
Invoke the tool by its id, passing arguments built from its parameters:
{
"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
}
}
}