Bernoulli's equation

In fluid dynamics, Bernoulli's equation describes the behavior of a fluid moving along a streamline.

<math> {v^2 \over 2}+gy+{P \over \rho}=constant <math>

v = fluid velocity along the streamline

g = gravitational constant

y = elevation in the direction of gravity

P = pressure along the streamline

ρ = fluid density

These assumptions must be met for the equation to apply:

• Inviscid flow - Viscosity (internal friction) = 0
• Steady flow
• Incompressible flow - ρ is constant
• The equation applies along a streamline. It applies throughout the flow field for irrotational flow.

The equation can be derived by integrating the Euler equations along a streamline.

The decrease in pressure simultaneous with an increase in velocity, as predicted by the equation, is often called Bernoulli's principle.

The equation is named for Daniel Bernoulli although it was first presented in the above form by Leonhard Euler.