Bernoulli Equation Calculator
Solve for pressure, velocity, or elevation at either of two points in a flowing fluid. Use mixed engineering units, fluid-density presets, optional head loss, and a clear energy-head breakdown.
Enter Flow Conditions
P + ½ρv² + ρgz1 Point 1
2 Point 2
How to Use the Bernoulli Equation Calculator
This calculator compares two locations along the same flow path. Select the unknown, enter the fluid properties and the other five pressure, velocity, and elevation values, then calculate the missing quantity.
Choose the unknown
Select P₁, v₁, z₁, P₂, v₂, or z₂. The calculator disables that field automatically.
Enter flow conditions
Add density, gravity, and the known values. You can mix supported units because all values are converted internally.
Review the energy balance
Read the solved value, pressure change, dynamic pressures, head breakdown, and substitution steps.
Bernoulli Equation Formula
The pressure term represents static-pressure energy per unit volume, the velocity term represents kinetic energy per unit volume, and the elevation term represents gravitational potential energy per unit volume. With head loss set to zero, the equation becomes the ideal Bernoulli equation.
| Symbol | Meaning | SI unit | Notes |
|---|---|---|---|
| P | Static pressure | Pa | Use the same pressure reference at both points. |
| ρ | Fluid density | kg/m³ | Assumed constant for incompressible flow. |
| v | Flow velocity | m/s | Average local speed along the streamline. |
| g | Gravity | m/s² | 9.80665 m/s² is standard gravity. |
| z | Elevation | m | Both elevations must use the same datum. |
| hL | Head loss | m | Optional user-entered loss between Point 1 and Point 2. |
Worked Example
Suppose water flows through a horizontal contraction. At Point 1, pressure is 200 kPa and velocity is 2 m/s. At Point 2, velocity rises to 5 m/s. Both points are at 5 m elevation, density is 1000 kg/m³, and head loss is zero.
Because the flow speeds up while elevation stays unchanged, kinetic energy increases and static pressure falls. The ideal Bernoulli result is approximately 189.5 kPa at Point 2.
Frequently Asked Questions
What can this Bernoulli Equation Calculator solve?
It can solve for pressure, velocity, or elevation at either of two points when the other required values, fluid density, and gravity are known.
Can I use different units in the same calculation?
Yes. Supported pressure, velocity, elevation, density, gravity, and head-loss units are converted to coherent SI units before the equation is solved.
What does head loss mean?
Head loss represents mechanical energy lost between the two points, commonly due to friction and fittings. This calculator lets you enter a known head loss but does not calculate it from pipe geometry or roughness.
Why can pressure drop when velocity increases?
In an ideal flow at the same elevation, an increase in kinetic-energy term can be balanced by a decrease in static pressure. That is one of the classic consequences of Bernoulli's equation.
Can Bernoulli's equation be used for air?
It can be a useful approximation when density changes are small. For strongly compressible gas flow, high Mach number, or large pressure changes, a compressible-flow model is more appropriate.
Does this calculator include pumps or turbines?
No. The calculator uses standard Bernoulli with an optional user-supplied head-loss term. Pump head and turbine head are outside this tool's current scope.