{
    "name": "Bernoulli Equation Calculator",
    "url": "https://calculators.geekmidst.com/calculators/bernoulli-equation-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/bernoulli-equation-calculator.md",
    "category": "Science & engineering",
    "description": "Apply Bernoulli’s equation between two points in a flow to find the downstream pressure and pressure difference, or the velocity at the second point.",
    "summary": "Along a streamline of steady, frictionless, incompressible flow, p + ½ρv² + ρgz stays constant. Faster flow or higher elevation means lower pressure.",
    "also_called": [
        "Bernoulli’s principle calculator",
        "Bernoulli pressure difference calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "solve",
            "label": "Solve for",
            "type": "segmented",
            "default": "p2",
            "options": {
                "p2": "Pressure at point 2",
                "v2": "Velocity at point 2"
            }
        },
        {
            "name": "density",
            "label": "Fluid density",
            "type": "number",
            "default": "1000"
        },
        {
            "name": "density_unit",
            "label": "Density unit",
            "type": "select",
            "default": "kgm3",
            "options": {
                "kgm3": "kg/m³",
                "gcm3": "g/cm³",
                "lbft3": "lb/ft³"
            }
        },
        {
            "name": "p1",
            "label": "Pressure at point 1",
            "type": "number",
            "default": "200"
        },
        {
            "name": "p2",
            "label": "Pressure at point 2",
            "type": "number",
            "default": "150",
            "shown_when": {
                "solve": "v2"
            }
        },
        {
            "name": "pressure_unit",
            "label": "Pressure unit",
            "type": "select",
            "default": "kpa",
            "options": {
                "pa": "pascals (Pa)",
                "kpa": "kilopascals (kPa)",
                "mpa": "megapascals (MPa)",
                "bar": "bar",
                "atm": "atmospheres (atm)",
                "psi": "psi",
                "mmhg": "mmHg"
            }
        },
        {
            "name": "v1",
            "label": "Velocity at point 1",
            "type": "number",
            "default": "2"
        },
        {
            "name": "v2",
            "label": "Velocity at point 2",
            "type": "number",
            "default": "6",
            "shown_when": {
                "solve": "p2"
            }
        },
        {
            "name": "velocity_unit",
            "label": "Velocity unit",
            "type": "select",
            "default": "ms",
            "options": {
                "ms": "m/s",
                "kmh": "km/h",
                "mph": "mph",
                "fts": "ft/s",
                "kn": "knots"
            }
        },
        {
            "name": "z1",
            "label": "Elevation of point 1",
            "type": "number",
            "default": "0",
            "optional": true
        },
        {
            "name": "z2",
            "label": "Elevation of point 2",
            "type": "number",
            "default": "3",
            "optional": true
        },
        {
            "name": "height_unit",
            "label": "Elevation unit",
            "type": "select",
            "default": "m",
            "options": {
                "m": "metres (m)",
                "cm": "centimetres (cm)",
                "mm": "millimetres (mm)",
                "km": "kilometres (km)",
                "ft": "feet (ft)",
                "in": "inches (in)",
                "mi": "miles (mi)"
            }
        },
        {
            "name": "gravity",
            "label": "Gravitational acceleration (g)",
            "type": "number",
            "default": "9.80665",
            "unit": "m/s²"
        }
    ],
    "outputs": [
        {
            "key": "answer",
            "label": "Result",
            "format": "text"
        },
        {
            "key": "p2_kpa",
            "label": "Pressure at point 2",
            "format": "number"
        },
        {
            "key": "delta_p_kpa",
            "label": "Pressure drop p₁ − p₂",
            "format": "number"
        },
        {
            "key": "v2_ms",
            "label": "Velocity at point 2",
            "format": "number"
        },
        {
            "key": "dynamic_1_kpa",
            "label": "Dynamic pressure at point 1 (½ρv₁²)",
            "format": "number"
        },
        {
            "key": "dynamic_2_kpa",
            "label": "Dynamic pressure at point 2 (½ρv₂²)",
            "format": "number"
        }
    ],
    "formula": {
        "text": "p₁ + ½ρv₁² + ρgz₁ = p₂ + ½ρv₂² + ρgz₂;  p₂ = p₁ + ½ρ(v₁² − v₂²) + ρg(z₁ − z₂)",
        "variables": {
            "p": "static pressure in Pa",
            "ρ": "fluid density in kg/m³",
            "v": "flow velocity in m/s",
            "z": "elevation in m",
            "g": "gravitational acceleration"
        }
    },
    "worked_example": {
        "inputs": {
            "solve": "v2",
            "density": "1000",
            "density_unit": "kgm3",
            "p1": "104.5",
            "p2": "100",
            "pressure_unit": "kpa",
            "v1": "0",
            "v2": "6",
            "velocity_unit": "ms",
            "z1": "0",
            "z2": "0",
            "height_unit": "m",
            "gravity": "9.80665"
        },
        "steps": [
            "Level flow starting from rest, so v₂² = 2 (p₁ − p₂) ÷ ρ.",
            "v₂² = 2 × 4,500 ÷ 1,000 = 9, so v₂ = 3 m/s."
        ],
        "result": "A 4.5 kPa pressure difference accelerates water from rest to 3 m/s."
    },
    "interpretation": "Bernoulli explains why pressure drops in a venturi throat, how a Pitot tube measures speed and how a siphon works. A negative absolute pressure at point 2 is impossible: in practice the liquid would cavitate first.",
    "assumptions": [
        "Steady, incompressible, frictionless flow along one streamline, with no pump or turbine between the points."
    ],
    "limitations": [
        "Real pipes lose pressure to friction; add a head-loss term for long runs, fittings and valves.",
        "For gases, use only when velocities are below about 30% of the speed of sound."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Should I use gauge or absolute pressure?",
            "answer": "Either, as long as both points use the same. Check absolute pressure stays above the liquid’s vapour pressure."
        },
        {
            "question": "Where does the pressure go when velocity increases?",
            "answer": "Pressure energy turns into kinetic energy. The total head (pressure + velocity + elevation) is unchanged."
        }
    ],
    "sources": [
        {
            "title": "BIPM: The International System of Units (SI)",
            "url": "https://www.bipm.org/"
        }
    ],
    "related": [
        {
            "name": "Flow Rate Calculator",
            "url": "https://calculators.geekmidst.com/calculators/fluid-flow-rate-calculator"
        },
        {
            "name": "Hydrostatic Pressure Calculator",
            "url": "https://calculators.geekmidst.com/calculators/hydrostatic-pressure-calculator"
        },
        {
            "name": "Reynolds Number Calculator",
            "url": "https://calculators.geekmidst.com/calculators/reynolds-number-calculator"
        },
        {
            "name": "Pressure Calculator",
            "url": "https://calculators.geekmidst.com/calculators/pressure-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}