What is Bernoulli's Equation?

The Bernoulli Equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a moving fluid (liquid or gas). Named after Daniel Bernoulli, it states that for an inviscid, incompressible flow, an increase in the speed of the fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy.

The formula is expressed as:

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

How to Use the Bernoulli Calculator

Our online Bernoulli equation calculator allows you to solve for the unknown pressure at a second point in a streamline. Follow these steps:

• Input Point 1 Data: Enter the initial pressure (in Pascals), the velocity of the fluid, and the height above a reference plane.
• Input Point 2 Data: Provide the velocity and elevation for the second point.
• Fluid Density: Enter the density of the fluid (e.g., 1000 kg/m³ for water).
• Calculate: Click the solve button to find the resulting pressure at Point 2.

Applications of the Principle

Bernoulli's principle is used in various engineering and scientific fields. It explains how airplane wings generate lift, how carburetors mix air and fuel, and how venturi meters measure fluid flow in pipes. In plumbing, it helps engineers calculate the pressure changes that occur when water moves from a wide pipe to a narrow one or when it travels to upper floors of a building.

Frequently Asked Questions

What are the assumptions of Bernoulli's equation? It assumes the flow is steady, incompressible, frictionless (inviscid), and occurs along a streamline.

Does it apply to gases? Yes, as long as the Mach number is low (typically below 0.3), meaning the gas behaves as if it were incompressible.