🌊 Bernoulli Equation Calculator

Bernoulli's equation is a core principle of fluid dynamics stating that for an incompressible, inviscid, steady flow, the sum of pressure energy, kinetic energy, and potential energy is conserved along a streamline.

P + ½ρv² + ρgh = constant

As velocity increases, pressure decreases, and vice versa with height, so the three terms trade off against each other. First proposed by Daniel Bernoulli in 1738, it underlies applications from aircraft lift to pipe flow and venturi meters.

For two points 1 and 2 along a flow path:

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

Given the density (ρ) and 5 of the 6 variables (P1, v1, h1, P2, v2, h2), this calculator algebraically rearranges this equation to solve for the remaining variable. When solving for a velocity, if the resulting v² is negative, the input combination has no physical solution and an error is shown.

This calculation assumes the fluid is incompressible (constant density), inviscid (no friction losses), and in steady flow (no time variation). Real pipe systems have friction losses, turbulence, and possibly compressibility effects, requiring an extended energy equation with loss terms for precise engineering design.