Bernoulli Equation Calculator
Downstream pressure from upstream conditions, with the velocity and height contributions shown separately.
Results
Pressure
240.6989
kPa
Difference
-59.3011
kPa
Pressure
29.9400
kPa
Pressure
29.3611
kPa
What this tool does
Bernoulli says the total of pressure, speed and height energy stays constant along a streamline, so whatever speed gains, pressure must give up. That is why a narrowing pipe reads a lower pressure and why a roof lifts in a gale. It assumes no friction, so treat the answer as the ideal case: real pipes always lose a little more.
Formula
p₁ + ½ρv₁² + ρgh₁ = p₂ + ½ρv₂² + ρgh₂
Variables
| Symbol | Meaning | Unit |
|---|---|---|
p1 | Pressure | kPa |
v1 | Initial velocity | m/s |
v2 | Final velocity | m/s |
h1 | Height | m |
h2 | Height | m |
ro | Fluid density | kg/m³ |
P2 | Pressure | kPa |
DP | Difference | kPa |
DV | Pressure | kPa |
DH | Pressure | kPa |
Worked example
- Pressure300 kPa
- Initial velocity2 m/s
- Final velocity8 m/s
- Height0 m
- Height3 m
- Fluid density998 kg/m³
- Pressure240.6989 kPa
- Difference-59.3011 kPa
- Pressure29.9400 kPa
- Pressure29.3611 kPa
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.