Calculation
p1 + ½ρv1² + ρgz1 = p2 + ½ρv2² + ρgz2
Pressure can convert to velocity or elevation; friction and pump heads must be added separately.
Bernoulli-Gleichung
Bernoulli Equation Calculator
Pressure can convert to velocity or elevation; friction and pump heads must be added separately.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Pressure at point 2 p2 — The unknown static pressure at the second point of the flow. Computed as a result from the Bernoulli equation: pressure there may have partly converted into velocity or elevation.
- Pressure at point 1 p1 — The known static pressure at the first (reference) point of the flow. Source: a pressure measurement (manometer) at that location.
- Density ρ — The density of the fluid, assumed incompressible. Source: a material table (water ≈ 1000 kg/m³) or a datasheet.
- Velocity v1 — The mean flow velocity at the first point. Source: computed from Q/A, or measured.
- Velocity v2 — The mean flow velocity at the second point.
- Elevation z1 — The elevation of the first point above a freely chosen datum (e.g. ground level or pipe axis).
- Elevation z2 — The elevation of the second point above the same datum as z1.
Example
A higher outlet or faster outlet lowers ideal static pressure.
Assumptions and limits
Steady, incompressible, frictionless; no pump between points.
Understand Bernoulli Equation Calculator
This calculator finds the ideal static pressure at a second point in a flow from pressure, velocity and elevation at a first point plus velocity and elevation at the second. Using perfume atomizers and carburetors, it explains how accelerating a flow deliberately creates a pressure drop.
What does this quantity describe?
Bernoulli's equation describes, for steady, frictionless, incompressible flow, conservation of the sum of static pressure, dynamic pressure and elevation pressure along a streamline: p1 + ½ρv1² + ρgz1 = p2 + ½ρv2² + ρgz2.
A perfume atomizer uses exactly this effect: squeezing the rubber bulb sends air at high speed through a narrow tube. Per Bernoulli, static pressure in this fast airstream drops below atmospheric pressure, so outside air pressure pushes liquid up through a second, perpendicular tube into the airstream — where it's atomised into a fine mist. Classic automotive carburettors used the exact same principle to introduce fuel into an engine's intake airflow.
Formula and variables
p1 + ½ρv1² + ρgz1 = p2 + ½ρv2² + ρgz2
p1 + ½ρv1² + ρgz1 = p2 + ½ρv2² + ρgz2p2 = p1 + ½ρ(v1²−v2²) + ρg(z1−z2)
| Symbol / input | Meaning |
|---|---|
| Pressure at point 2 p2 | The unknown static pressure at the second point of the flow. Computed as a result from the Bernoulli equation: pressure there may have partly converted into velocity or elevation. |
| Pressure at point 1 p1 | The known static pressure at the first (reference) point of the flow. Source: a pressure measurement (manometer) at that location. |
| Density ρ | The density of the fluid, assumed incompressible. Source: a material table (water ≈ 1000 kg/m³) or a datasheet. |
| Velocity v1 | The mean flow velocity at the first point. Source: computed from Q/A, or measured. |
| Velocity v2 | The mean flow velocity at the second point. |
| Elevation z1 | The elevation of the first point above a freely chosen datum (e.g. ground level or pipe axis). |
| Elevation z2 | The elevation of the second point above the same datum as z1. |
Choose the inputs correctly
Enter pressure, velocity and elevation at the first point plus velocity and elevation at the second point; the calculator finds the ideal pressure at the second point. Both points must lie on the same streamline, with no pump or turbine between them.
How to use the calculator
Choose a common reference level for z1 and z2 and enter the known values with units. Check that no energy is actually added or removed between the points (no pump, no significant friction loss), since these cases break the simple Bernoulli balance.
Worked example
Given p1 = 2 bar, v1 = 1 m/s, z1 = 0 m, plus v2 = 2 m/s and z2 = 1 m, substitution gives an ideal p2 lower than p1, since both the higher speed and greater elevation at the second point 'consume' pressure.
Understand the result and units
A lower pressure at the second point shows that part of the pressure energy there converted into velocity or elevation energy. This conversion is reversible: if speed or elevation later fall again, pressure rises back by the same amount, as long as no friction losses occur.
Pressure in bar or Pa, velocity in m/s, elevation in metres, density in kg/m³. Every term in Bernoulli's equation has units of pressure (Pa = N/m²) and must be converted consistently.
How does an atomiser deliberately create a pressure drop?
When air is forced at high speed through a narrow nozzle, Bernoulli's equation says its static pressure drops below the surrounding atmospheric pressure. A side tube dipping into a liquid then experiences a pressure difference: the higher atmospheric pressure at the liquid surface pushes liquid up through the tube into the airstream, where the fast-moving air sweeps it up and atomises it into fine droplets. Carburettors in combustion engines used this exact operating principle before being replaced by electronic fuel injection.
Typical applications
Bernoulli's equation is used to design Venturi flow meters, atomisers, carburettors, airfoil profiles, and to roughly estimate pressure changes in pipework with varying cross-section or elevation.
Assumptions, limits and common mistakes
The equation applies to steady, frictionless, incompressible flow along the same streamline with no energy added by pumps or removed by turbines. Real pipe flow with friction needs an additional loss term; compressible gases at high speed require an extended form of the equation.
Common mistake: Do not apply the simple Bernoulli equation across sections with pumps, turbines or significant friction without adding a corresponding extra term. Also, z1 and z2 must reference the same datum, or the elevation terms won't combine correctly.
Frequently asked questions
Why does pressure fall as a flow's velocity rises?
Because per Bernoulli, the sum of static pressure, dynamic pressure and elevation term stays constant along a streamline. Higher velocity raises the dynamic-pressure term (½ρv²), which must be offset by a correspondingly lower static pressure.
How does a perfume atomiser work on this principle?
A fast airstream through a narrow tube creates a pressure drop there, which draws liquid up through a second tube and atomises it into fine droplets.
Does Bernoulli's equation still hold with friction in the line?
Only approximately. With significant friction, an additional pressure-loss term must be added, correcting the Bernoulli balance for dissipated energy.