Math & Numbers
Pump Head & Shaft Power Calculator (H, P=ρgQH/η)
Compute the total dynamic head H = (p_d - p_s)/(ρ·g) + Δz + (v_d² - v_s²)/(2g) of a centrifugal pump (m), then the fluid power P_fluid = ρ·g·Q·H and shaft power P_shaft = P_fluid/η. p_d and p_s are gauge pressures (suction may be negative for suction lift). Nozzle velocities v = 4Q/(π·D²) come from the flow rate and the discharge/suction nozzle diameters; if a nozzle diameter is left blank its velocity head is omitted. Pressure in Pa/kPa/bar/atm/psi, flow in m³/s/L/s/L/min/m³/h, density in kg/m³/g/cm³; power output in W/kW/hp.
Quick start
Call this tool from your code in three languages.
curl -X POST 'https://api.elysiatools.com/en/api/tools/pump-head-power' \
-H 'Content-Type: application/json' \
-d '{"dischargePressure":2,"pressureUnit":"bar","suctionPressure":0,"staticHeadDelta":0,"flowRate":10,"flowUnit":"L/s","density":1000,"densityUnit":"kg/m3","dischargeDiameter":0,"suctionDiameter":0,"nozzleDiameterUnit":"m","efficiency":75,"gravity":9.81,"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-head-powerParameters
| Name | Type | Required | Description |
|---|---|---|---|
| dischargePressure | number | Yes | Discharge gauge pressure p_d. Enter in the selected Pressure Unit. |
| pressureUnit | select | No | — |
| suctionPressure | number | No | Suction gauge pressure p_s (may be negative for suction lift). Enter in the selected Pressure Unit. |
| staticHeadDelta | number | No | Elevation difference Δz between the discharge and suction gauges (m). Positive if the discharge gauge is higher. |
| flowRate | 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-head-power": {
"name": "pump-head-power",
"description": "Compute the total dynamic head H = (p_d - p_s)/(ρ·g) + Δz + (v_d² - v_s²)/(2g) of a centrifugal pump (m), then the fluid power P_fluid = ρ·g·Q·H and shaft power P_shaft = P_fluid/η. p_d and p_s are gauge pressures (suction may be negative for suction lift). Nozzle velocities v = 4Q/(π·D²) come from the flow rate and the discharge/suction nozzle diameters; if a nozzle diameter is left blank its velocity head is omitted. Pressure in Pa/kPa/bar/atm/psi, flow in m³/s/L/s/L/min/m³/h, density in kg/m³/g/cm³; power output in W/kW/hp.",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=pump-head-power",
"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-head-power",
"arguments": {
"dischargePressure": 2,
"pressureUnit": "bar",
"suctionPressure": 0,
"staticHeadDelta": 0,
"flowRate": 10,
"flowUnit": "L/s",
"density": 1000,
"densityUnit": "kg/m3",
"dischargeDiameter": 0,
"suctionDiameter": 0,
"nozzleDiameterUnit": "m",
"efficiency": 75,
"gravity": 9.81,
"decimalPlaces": 4
}
}
}