Math & Numbers

Bernoulli Equation Solver (Velocity / Pressure / Elevation)

Solve the Bernoulli equation p/(ρg) + v²/(2g) + z = const for steady, ideal, incompressible flow between two points on a streamline. Supply all three upstream quantities (p₁, v₁, z₁) and any two of the three downstream quantities; the tool solves for the third. Solve velocity: v₂ = √[v₁² + 2(p₁-p₂)/ρ + 2g(z₁-z₂)] — a negative radicand is physically impossible and is rejected. Solve pressure: p₂ = p₁ + ½ρ(v₁²-v₂²) + ρg(z₁-z₂). Solve elevation: z₂ = z₁ + (p₁-p₂)/(ρg) + (v₁²-v₂²)/(2g). g = 9.81 m/s². Density in kg/m³/g/cm³, pressure in Pa/kPa/bar/atm/psi, velocity in m/s, elevation in m/cm/ft. The upstream pressure/velocity/elevation heads and the total head are also reported.