Bernoulli Equation Calculator
Calculate fluid pressure at any point using the Bernoulli equation. Enter pressure, velocity, and height at point 1 plus velocities at point 2 to solve for P₂. Covers pitot tubes, venturi effect, and aerodynamic lift.
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Pressure 2 – P₂
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P₂ in kPa —
Bernoulli Check (const) —
Extended More scenarios, charts & detailed breakdown ▾
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P₂ (Pa)
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Dynamic Pressure 1 —
Dynamic Pressure 2 —
Professional Full parameters & maximum detail ▾
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Bernoulli Solution
P₂ (Pa) —
Dynamic Pressure (pt 1) —
Dynamic Pressure (pt 2) —
Head & Lift
Static Head Diff (m) —
Aerodynamic Lift Note —
How to Use This Calculator
- Enter pressure, velocity, and height at point 1.
- Enter velocity and height at point 2.
- Select fluid (water, air, oil, or seawater).
- The calculator solves for P₂. Use Extended tabs for pitot tube and venturi scenarios.
Formula
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Rearranged: P₂ = P₁ + ½ρ(v₁² − v₂²) + ρg(h₁ − h₂)
ρ = fluid density (kg/m³), g = 9.81 m/s²
Example
Example: Water (ρ=1000), P₁=101325 Pa, v₁=2 m/s, h₁=0, v₂=5 m/s, h₂=0 → P₂ = 101325 + ½×1000×(4−25) = 90,825 Pa.
Frequently Asked Questions
- Bernoulli's equation states that for an incompressible, inviscid fluid in steady flow: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂. It expresses conservation of energy along a streamline — as velocity increases, pressure decreases.
- The equation assumes incompressible flow (constant density), inviscid flow (no viscosity), steady flow, and that the equation applies along a single streamline. Real fluids violate these to varying degrees, so Bernoulli is an idealization.
- A pitot tube measures total (stagnation) pressure where v = 0. Subtracting static pressure and using Bernoulli: v = √(2ΔP/ρ). Aircraft airspeed indicators work on this principle.
- Air travels faster over the curved upper surface of a wing (v₂ > v₁), so by Bernoulli's equation the pressure is lower above the wing than below. This pressure differential creates the upward lift force.
- When fluid flows through a constriction (reduced cross-section), it must speed up (continuity equation). By Bernoulli, this higher velocity produces lower pressure at the throat. Carburetors, atomizers, and flow meters use this effect.
Related Calculators
Sources & References (5) ▾
- NASA Glenn Research Center – Bernoulli's Equation — NASA Glenn Research Center
- OpenStax University Physics Vol. 1 Chapter 14 – Fluid Mechanics — OpenStax
- HyperPhysics – Bernoulli Equation — HyperPhysics / Georgia State University
- Engineering Toolbox – Bernoulli Equation — Engineering Toolbox
- Streeter V L – Fluid Mechanics, 9th Ed. — McGraw-Hill