Bernoulli Equation Calculator

Solve for pressure, velocity, or elevation along a streamline. Leave exactly one field empty — that is the unknown to be calculated.

Fluid Mechanics I

Inputs

Fill in 5 of the 6 fields and leave the unknown one empty. Elevation defaults to 0 (horizontal flow) — clear it to solve for elevation.

Fluid density ρ (kg/m³)

Units

Pressure (P₁ and P₂)

Velocity (V₁ and V₂)

Elevation (z₁ and z₂)

Point 1

Pressure P₁ (Pa)

Velocity V₁ (m/s)

Elevation z₁ (m)

Point 2

Pressure P₂ (Pa)

Velocity V₂ (m/s)

Elevation z₂ (m)

Theory

Main Equation (pressure form):

P₁ + ½ρV₁² + ρgz₁ = P₂ + ½ρV₂² + ρgz₂

Where:

P = static pressure [Pa]
ρ = fluid density [kg/m³]
V = flow velocity [m/s]
g = 9.81 m/s²
z = elevation above datum [m]

Valid along a streamline for steady, incompressible, inviscid flow. Each term has units of Pa — representing static, dynamic, and hydrostatic pressure contributions respectively.