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Bernoulli Pressure Calculator

Find downstream pressure with Bernoulli's equation.

How it is calculated

The tool evaluates P₂ = P₁ + ½ × ρ × (v₁² − v₂²). P₁ is the upstream pressure in pascals (Pa), ρ the fluid density in kg/m³, and v₁, v₂ the upstream and downstream speeds in m/s. P₂ comes out in pascals, rounded to two decimals.

Density must be greater than zero. The formula is for steady, incompressible, frictionless flow along a level pipe, so there is no height term and no friction loss; real pipes lose extra pressure to friction and fittings, and gases at high speed are compressible. If v₂ is larger than v₁ the pressure drops, and if v₂ is smaller it rises. The tool does not check that your two velocities are consistent with the pipe diameters.

Worked example

Water (ρ = 1000 kg/m³) enters at P₁ = 200,000 Pa with v₁ = 2 m/s and speeds up to v₂ = 4 m/s in a narrower section. v₁² = 4 and v₂² = 16, so the difference is −12. Then ½ × 1000 × (−12) = −6,000 Pa. P₂ = 200,000 − 6,000 = 194,000.00 Pa. The pressure fell by 6 kPa because the water sped up.

Try this example →

Common mistakes

  • Entering pressure in bar, kPa or psi. The field expects pascals, and 2 bar must be typed as 200000.
  • Entering density of water as 1 (g/cm³). It must be in kg/m³, so water is about 1000.
  • Swapping v₁ and v₂. The sign of the pressure change reverses, making a pressure drop look like a rise.
  • Using the formula when the pipe changes height. This version has no elevation term, so a vertical rise or fall needs an extra ρgh correction.
  • Expecting friction losses. The tool gives the ideal value; long pipes, valves and bends lose more pressure in practice.

About this calculator

This calculator applies Bernoulli's equation for incompressible, steady flow in a level pipe (no elevation change) to find downstream pressure: P₂ = P₁ + ½·ρ·(v₁² − v₂²), where ρ is fluid density and v₁, v₂ are the upstream and downstream velocities — a direct consequence of energy conservation along a streamline, showing that pressure drops where velocity increases (and vice versa).

This pressure-velocity trade-off explains how a Venturi tube creates suction, why airplane wings generate lift as air moves faster over the curved top surface, how a carburetor draws fuel into an airstream, and why pipe diameter changes affect pressure readings in plumbing and industrial fluid systems.

Mechanical and aerospace engineers designing piping, nozzles, and airfoils, HVAC engineers analyzing duct systems, and fluid mechanics students working through Bernoulli problems all use this calculator, entering upstream pressure and the two velocities (often derived from pipe diameters via continuity).

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