Bernoulli Pressure Calculator
Bernoulli pressure change in Pa and psi from speed change.
What it does
Bernoulli ties speed to pressure with one elegant trade: where a fluid hurries, it pushes less. Pipes narrow, wings lift, and sprayers mist on this exact exchange.
The tool above takes two speeds with air or water in metric or imperial. It returns the pressure change in Pa and psi plus the direction word.
The default air case from 10 to 30 m/s drops 490 Pa, or 0.071 psi, with faster flow reading lower pressure. The imperial mirror at 32.81 to 98.43 ft/s lands on the same 490 Pa.
OpenStax University Physics builds Bernoulli from energy conservation on moving fluids. HyperPhysics frames the same velocity pressure seesaw with worked pipe cases.
Venturi meters invert the tool: they read the pressure dip to report the flow rate. Our Reynolds sibling sorts whether that flow runs smooth or wild.
How to use
- Pick metric or imperial units.
- Pick air or water.
- Type the first speed.
- Type the second speed.
- Read the Pa drop first.
- Read psi and direction beside it.
Formula
- rho
- Fluid density: air 1.225, water 1000 kg per m3.
- v1, v2
- Upstream and downstream speeds.
- delta P
- Pressure difference magnitude.
OpenStax University Physics derives Bernoulli from work energy on fluids with the same pressure plus kinetic plus potential sum. HyperPhysics walks the pressure velocity trade with the same equation. Display uses magnitude with a direction word; air 1.225 and water 1000 kg per m3 near room conditions.
Worked example
Example: air speeds from 10 to 30 m/s
Metric defaults: air, 10 to 30 m/s.
- Flow: air speeds 10 m/s to 30 m/s.
- Air density: 1.225 kg per m3.
- Drop: 0.5 x 1.225 x (100 minus 900) = 490 Pa magnitude.
- PSI: 490 / 6894.76 = 0.071 psi.
- Direction: faster stream means pressure falls.
- Tool shows 490 Pa, 0.071 psi, Faster stream: pressure falls.
Reference table
| Speeds | Drop | Direction |
|---|---|---|
| Air 10 to 30 m/s | 490 Pa | Pressure falls |
| Air 30 to 10 m/s | 490 Pa | Pressure rises |
| Water 1 to 3 m/s | 4000 Pa | Pressure falls |
| Air 32.81 to 98.43 ft/s | 490 Pa | Pressure falls |
Limits
- Level streamlines only; height needs its term.
- Incompressible range, well below Mach 0.3.
- Smooth steady flow, not turbulence.
- One streamline; junctions split the math.
Common mistakes
- Reading the sign backwards.
- Using mph as m/s directly.
- Applying it past sound speed.
- Forgetting water is 816 times denser.
- Skipping the direction word.
Try it yourself
Quick checks. Answers sit tucked under each question.
Water from 1 to 3 m/s?
Drop of 4000 Pa, 0.58 psi, faster stream so pressure falls.
Air from 30 to 10 m/s?
Rise of 490 Pa: slower stream so pressure rises.
32.81 to 98.43 ft/s in air?
Same 490 Pa and direction in ft/s and ft.
Questions
What is Bernoulli saying?
Pressure plus kinetic plus height energy stays constant along a streamline: P + 1/2 rho v2 + rho g h. Faster flow trades pressure for speed.
Where is it used?
Carburetors, venturi meters, atomizers, and airplane lift all meter or ride this trade.
When does it hold?
Slow steady incompressible flow along one streamline. Turbulence, compressibility, and pumps need richer models.
Lift connection?
Airplanes fly on it plus angle effects: faster air over the wing means lower pressure above.
Height differences?
Yes, through the height term rho g h. This tool compares level points, so height cancels.
Near sound speed?
No. Past about Mach 0.3 density shifts and compressible relations take over.
Sources
- OpenStax University Physics: fluid dynamics (Bernoulli)
- HyperPhysics: Bernoulli equation (Georgia State)