# Euler Number

## Introduction to the Euler Number used in fluid mechanics

**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 v^{2}) (1)

where

Eu = Euler number

p = pressure (Pa)

ρ = density (kg/m^{3})

v = fluid flow velocity (m/s)

The pressure difference is often used

Eu = dp / (ρ v^{2}) (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 v^{2}) (3)

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