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Bernoulli Equation Calculator

Find pressure change along a flow with Bernoulli's equation.

How it is calculated

The tool applies Bernoulli's equation for steady, incompressible, frictionless flow along a streamline at constant height: p2 = p1 + ½ρ(v1² − v2²). Here ρ is fluid density in kg/m³, p1 the upstream pressure in pascals, and v1, v2 the speeds in m/s at the two points. The result p2 is shown in Pa and in kPa (divided by 1000). Density must be above zero. There is no height term, so the two points must be at the same elevation, and losses from friction or turbulence are ignored. A faster stream gives lower pressure.

Worked example

Water (1000 kg/m³) enters a pipe at 200000 Pa and 2 m/s, then speeds up to 5 m/s in a narrower section. The speed terms are 2² = 4 and 5² = 25, so the difference is −21. Multiply by ½ × 1000 = 500 to get −10500 Pa. Adding this to the upstream pressure gives 189,500.00 Pa, which is 189.50 kPa.

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Common mistakes

  • Entering pressure in kPa or bar while the tool expects pascals. A value of 200 instead of 200000 gives a large negative pressure.
  • Using density in g/cm³ (1 for water) instead of kg/m³ (1000).
  • Applying it between points at different heights. This version has no ρgh term, so tanks, risers and downhill pipes need a height correction.
  • Swapping v1 and v2. A speed-up should lower the pressure; swapping raises it.
  • Using it for gases at high speed or for long pipes with friction, where the incompressible, loss-free assumptions fail.

About this calculator

This calculator applies Bernoulli's equation for two points at the same height, p₂ = p₁ + ½ρ(v₁² − v₂²), which expresses conservation of energy for an ideal (incompressible, non-viscous) fluid in steady flow — the sum of static pressure and dynamic pressure (½ρv²) stays constant along a streamline. The tool has no height (ρgh) term. Solving for downstream pressure shows why fluid speeding up (e.g., through a narrowing pipe) causes its pressure to drop, and vice versa.

Mechanical and civil engineers use it to size pipes, ducts and venturi meters; aerospace engineers invoke a version of it to explain lift over an airfoil; and physics students use it to solve classic flow problems.

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Comments (1)

  • Editorial team

    The tool needs both speeds, so get the second from continuity: speed times cross-section area stays constant. Going from 2 m/s to 5 m/s means the narrow section has 0.4 times the area, a diameter about 63% of the wide one. Also check the answer physically: if you entered absolute pressures and p2 comes out near or below zero, the flow cannot really reach that speed, because the liquid would cavitate first. Is your pressure gauge or absolute, and what pipe is it?

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