Bernoulli's equation

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

v = fluid velocity along the streamline

g = acceleration due to gravity on Earth

y = height 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. (There exists a second form of Bernoulli's equation that is applicable for compressible flow, which makes use of the thermodynamic enthalpy.)
• The equation applies along a streamline. It applies throughout the flow field for irrotational flow.

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.