Bernoulli Equation Calculator

What is Bernoulli's Equation?

Bernoulli's equation is a statement of conservation of energy for fluid flow along a streamline. It relates pressure energy, kinetic energy, and potential energy between two points in a steady, incompressible flow. The equation shows that when one form of energy increases, the others decrease to keep the total constant.

The full form of Bernoulli's equation including head loss is:

P₁ + ½ρV₁² + ρgZ₁ = P₂ + ½ρV₂² + ρgZ₂ + ρgh

Where P is static pressure, ρ is fluid density, V is flow velocity, g is gravitational acceleration, Z is elevation, and h is head loss due to friction and turbulence.

How to Use the Bernoulli Equation Calculator

Select the variable you want to solve for: Pressure at Point 1 (P₁), Velocity at Point 1 (V₁), Elevation at Point 1 (Z₁), or Head Loss (h). Enter the remaining values and the calculator will compute the unknown variable instantly using the Bernoulli equation.

Example: Pressure Change in a Pipe

Water (density 1,000 kg/m³) flows through a horizontal pipe. At point 1 the pressure is 200,000 Pa and velocity is 2 m/s. At point 2 the velocity is 4 m/s. Both elevations are equal and head loss is zero. Using the simplified Bernoulli equation P₁ + ½ρV₁² = P₂ + ½ρV₂², the pressure at point 2 is P₂ = 200,000 + 0.5 × 1,000 × (2² - 4²) = 194,000 Pa. The velocity increase causes a pressure drop of 6,000 Pa.

Applications of Bernoulli's Equation

• Pipe system design: calculating pressure drops and required pump head in water distribution networks
• Venturi meters: measuring flow rate by relating pressure difference to velocity change in a constriction
• Aircraft aerodynamics: explaining lift by relating airspeed differences above and below a wing to pressure differences
• Hydraulic engineering: analyzing flow over weirs, through siphons, and in open channels
• Medical devices: understanding blood flow velocity changes through arterial stenosis using pressure measurements