Bernoulli Equation Calculator

Bernoulli's equation links pressure and speed in a flowing fluid (at equal heights).

How the Math Works

The Bernoulli Equation Calculator uses Bernoulli's principle to determine the downstream pressure (P₂) in a flowing fluid. The formula P₂ = P₁ + ½ρ(v₁² − v₂²) relates the initial pressure and velocity to the final pressure, accounting for fluid density (ρ). This relationship stems from the conservation of energy principle, where the sum of pressure energy, kinetic energy, and potential energy remains constant along a streamline. By rearranging the equation, we can solve for the unknown downstream pressure when given the initial conditions.

Practical Applications

To use this calculator, input the initial pressure (P₁), initial velocity (v₁), final velocity (v₂), and fluid density (ρ). For example, when analyzing water flow through a pipe that narrows, you would enter the pressure and velocity before the constriction, the velocity after the constriction (which is higher due to the reduced cross-sectional area), and the density of water. The calculator then computes the pressure after the constriction, which is essential for designing pipe systems, nozzles, and Venturi meters.

Day-to-Day Use

This calculation has practical applications in everyday life, from designing efficient plumbing systems in your home to understanding aerodynamics in vehicles. When engineers design water treatment plants, irrigation systems, or even carburetors in engines, they use these principles to ensure optimal performance and safety. Understanding pressure changes in fluid systems also helps diagnose issues like water hammer in pipes or inefficient shower heads, making it valuable for both professionals and homeowners working on fluid-related projects.

Worked example

Speeding from 2 to 6 m/s in water drops pressure by 16 kPa.

FAQ