Bernoulli Equation Calculator

What is Bernoulli's Principle?

Bernoulli's principle states that in a steady, incompressible, inviscid flow, an increase in fluid velocity is accompanied by a decrease in pressure. It's why aircraft wings generate lift, why carburettors draw fuel, and why venturi meters measure flow.

Bernoulli's Equation

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ = constant

Where:

• P = static pressure (Pa)
• ρ = fluid density (kg/m³) — water: 1000 kg/m³
• v = fluid velocity (m/s)
• g = gravitational acceleration (9.81 m/s²)
• h = elevation (m)

Each term represents: static pressure + dynamic pressure + hydrostatic pressure = total (stagnation) pressure.

How to Use This Calculator

Enter conditions at point 1 (upstream): pressure, velocity, elevation. Enter known conditions at point 2. The calculator solves for the unknown variable at point 2.

Practical Examples

Example 1: Water flows from a large tank (v₁ ≈ 0, P₁ = atmospheric, h₁ = 10m) through a pipe at h₂ = 0m. Find exit velocity. ½ρv₂² = ρg(h₁−h₂) → v₂ = √(2 × 9.81 × 10) = 14.0 m/s (Torricelli's theorem).

Example 2: Venturi meter: 100mm pipe reduces to 50mm. v₁ = 2 m/s, P₁ = 200kPa. Find P₂. v₂ = 2 × (100/50)² = 8 m/s. P₂ = 200,000 + ½×1000×(4−64) = 200,000 − 30,000 = 170 kPa.

Applications

Bernoulli's principle is used in: aircraft aerodynamics, venturi flowmeters, pitot tubes, carburettors, atomisers, and the Coanda effect in fluidics.