How to use this calculator
- Enter or choose solve for.
- Enter or choose fluid density.
- Enter or choose density unit.
- Enter or choose pressure at point 1.
- Enter or choose pressure unit.
- The result updates as you type. Use Copy result or Share to keep it.
Method
p₁ + ½ρv₁² + ρgz₁ = p₂ + ½ρv₂² + ρgz₂; p₂ = p₁ + ½ρ(v₁² − v₂²) + ρg(z₁ − z₂)
- 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
- Level flow starting from rest, so v₂² = 2 (p₁ − p₂) ÷ ρ.
- v₂² = 2 × 4,500 ÷ 1,000 = 9, so v₂ = 3 m/s.
A 4.5 kPa pressure difference accelerates water from rest to 3 m/s.
What the result means
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 and limits
- Steady, incompressible, frictionless flow along one streamline, with no pump or turbine between the points.
- 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.
Questions
Should I use gauge or absolute pressure?
Either, as long as both points use the same. Check absolute pressure stays above the liquid’s vapour pressure.
Where does the pressure go when velocity increases?
Pressure energy turns into kinetic energy. The total head (pressure + velocity + elevation) is unchanged.