Bernoulli energy heads API

Decomposes the Bernoulli equation into pressure head P/(ρg), velocity head v²/(2g), and elevation head z at two points, returning total head, head difference, and the solved unknown pressure at point 2 for a given head loss. Answers 'What are the pressure/velocity/elevation heads?', 'What is the downstream pressure from Bernoulli?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/bernoulli-heads

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

engineeringthermofluidsfluidsbernoulliheadpressure-headvelocity-headhydraulics

API URLhttps://x402.hexl.dev/v1/engineering/bernoulli-heads

Integration docs

Example request

{
  "densityKgM3": 1000,
  "pressure1Pa": 200000,
  "velocity1Ms": 2,
  "elevation1M": 5,
  "velocity2Ms": 4,
  "elevation2M": 0,
  "headLossM": 1
}

Example response

{
  "densityKgM3": 1000,
  "gravityMs2": 9.80665,
  "point1": {
    "pressureHeadM": 20.394324,
    "velocityHeadM": 0.203943,
    "elevationHeadM": 5,
    "totalHeadM": 25.598268
  },
  "headLossM": 1,
  "formula": "P/(ρg) + v²/(2g) + z = const (− head loss)",
  "point2": {
    "pressureHeadM": 23.782495,
    "velocityHeadM": 0.815773,
    "elevationHeadM": 0,
    "totalHeadM": 24.598268
  },
  "solvedPressure2Pa": 233226.604882
}

Input schema

{
  "type": "object",
  "required": [
    "densityKgM3",
    "pressure1Pa",
    "velocity1Ms",
    "elevation1M"
  ],
  "properties": {
    "densityKgM3": {
      "type": "number",
      "description": "fluid density (kg/m^3)",
      "examples": [
        1000
      ]
    },
    "pressure1Pa": {
      "type": "number",
      "description": "pressure at point 1 (Pa)"
    },
    "velocity1Ms": {
      "type": "number",
      "description": "velocity at point 1 (m/s)"
    },
    "elevation1M": {
      "type": "number",
      "description": "elevation at point 1 (m)"
    },
    "velocity2Ms": {
      "type": "number",
      "description": "velocity at point 2 (m/s)"
    },
    "elevation2M": {
      "type": "number",
      "description": "elevation at point 2 (m)"
    },
    "pressure2Pa": {
      "type": "number",
      "description": "pressure at point 2 (Pa); omit to solve it"
    },
    "headLossM": {
      "type": "number",
      "description": "head loss between points (m)"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}