Euler Number

The Euler Number is a dimensionless value used for analyzing fluid flow dynamics problems where the pressure difference between two points is important. The Euler Number can be interpreted as a measure of the ratio of the pressure forces to the inertial forces.

The Euler Number can be expressed as

Eu = p / (ρ v²)                           (1)

where

Eu = Euler number

p = pressure (Pa)

ρ = density (kg/m³)

v = fluid flow velocity (m/s)

The pressure difference is often used

Eu = dp / (ρ v²)                         (2)

where

dp = differential pressure (Pa)

• Note! - a perfect frictionless flow corresponds to that the Euler number equals 1

The combination below is called the pressure coefficient

pressure coefficient = dp / (1/2 ρ v²)                        (3)

A special version of the Euler Number is in general referred to as the Cavitation Number.