Math & Numbers
Orifice Flow Calculator (Bernoulli, Q=Cd·A·√(2ΔP/ρ))
Compute the flow rate through a thin-plate orifice for an incompressible fluid (ISO 5167 Bernoulli form with discharge coefficient C_d). Orifice area A=π·d²/4; volumetric flow Q=C_d·A·√(2·ΔP/ρ); mass flow ṁ=C_d·A·√(2·ρ·ΔP); throat velocity v_orifice=C_d·√(2·ΔP/ρ). If the upstream pipe diameter D is supplied the diameter ratio β=d/D is also returned. ΔP≥0, ρ>0, C_d in 0..1 (default 0.61 for a sharp-edged plate). Diameter in m/cm/mm, pressure in Pa/kPa/bar/atm/psi, density in kg/m³/g/cm³; volumetric flow reported in m³/s, L/s, L/min and m³/h.
Quick start
Call this tool from your code in three languages.
curl -X POST 'https://api.elysiatools.com/en/api/tools/orifice-flow-calculator' \
-H 'Content-Type: application/json' \
-d '{"dischargeCoefficient":0.61,"orificeDiameter":0.05,"orificeDiameterUnit":"m","pipeDiameter":0.1,"pipeDiameterUnit":"m","pressureDiff":10000,"pressureUnit":"Pa","density":1000,"densityUnit":"kg/m3","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/orifice-flow-calculatorParameters
| Name | Type | Required | Description |
|---|---|---|---|
| dischargeCoefficient | number | Yes | Discharge coefficient C_d of the orifice (0 to 1). Typical sharp-edged thin-plate value ≈ 0.61. |
| orificeDiameter | number | Yes | Orifice (throat) diameter d. Enter in the selected Orifice Diameter Unit. |
| orificeDiameterUnit | select | No | — |
| pipeDiameter | number | No | Upstream pipe inner diameter D. Optional — used only to compute the diameter ratio β=d/D. Enter in the selected Pipe Diameter Unit. |
| pipeDiameterUnit |
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-orifice-flow-calculator": {
"name": "orifice-flow-calculator",
"description": "Compute the flow rate through a thin-plate orifice for an incompressible fluid (ISO 5167 Bernoulli form with discharge coefficient C_d). Orifice area A=π·d²/4; volumetric flow Q=C_d·A·√(2·ΔP/ρ); mass flow ṁ=C_d·A·√(2·ρ·ΔP); throat velocity v_orifice=C_d·√(2·ΔP/ρ). If the upstream pipe diameter D is supplied the diameter ratio β=d/D is also returned. ΔP≥0, ρ>0, C_d in 0..1 (default 0.61 for a sharp-edged plate). Diameter in m/cm/mm, pressure in Pa/kPa/bar/atm/psi, density in kg/m³/g/cm³; volumetric flow reported in m³/s, L/s, L/min and m³/h.",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=orifice-flow-calculator",
"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": "orifice-flow-calculator",
"arguments": {
"dischargeCoefficient": 0.61,
"orificeDiameter": 0.05,
"orificeDiameterUnit": "m",
"pipeDiameter": 0.1,
"pipeDiameterUnit": "m",
"pressureDiff": 10000,
"pressureUnit": "Pa",
"density": 1000,
"densityUnit": "kg/m3",
"decimalPlaces": 4
}
}
}