Bernoulli Equation Calculator
Use Bernoulli’s equation to find the pressure at a second point in a flowing fluid from the pressure, speed and height at a first point.
How it works
P1 + ½·ρ·v1² + ρ·g·h1 = P2 + ½·ρ·v2² + ρ·g·h2 · ⇒ P2 = P1 + ½·ρ·(v1² − v2²) + ρ·g·(h1 − h2)
Bernoulli’s equation expresses conservation of energy per unit volume for an ideal (steady, incompressible, non-viscous) fluid: the sum of static pressure, dynamic pressure (½·ρ·v²) and hydrostatic pressure (ρ·g·h) is constant along a streamline. The key insight is the trade-off between speed and pressure — where a fluid flows faster, its static pressure must fall. This is why aeroplane wings generate lift and why a shower curtain billows inward when the water runs.
Worked example
Water (ρ = 1000 kg/m³) at 200,000 Pa flows at 3 m/s on a level pipe (h1 = h2). Where it speeds up to 6 m/s: P2 = 200,000 + ½·1000·(3² − 6²) = 200,000 + 500·(9 − 36) = 200,000 − 13,500 = 186,500 Pa ≈ 186.5 kPa.
Sources: Bernoulli’s principle — Wikipedia
Frequently asked questions
Why does pressure drop where a fluid flows faster?
Bernoulli’s equation says the total energy per unit volume is constant. If the dynamic term ½·ρ·v² rises because the fluid speeds up (and height is unchanged), the static pressure term must fall to keep the sum constant. Energy is simply shifting from pressure to motion.
When does Bernoulli’s equation not apply?
It assumes steady, incompressible, non-viscous flow along a single streamline. It breaks down for turbulent or highly viscous flow, for compressible high-speed gas flow, and where pumps or friction add or remove energy between the two points.
What is dynamic pressure?
Dynamic pressure is the ½·ρ·v² term — the pressure associated with the fluid’s motion. It is the extra pressure you would feel from bringing the moving fluid to rest, as measured by a Pitot tube.
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This calculator is for educational purposes. Double-check important results before acting on them.