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Euler Number

Introduction to the Euler Number used in fluid mechanics.

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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)


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)


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.

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  • Engineering ToolBox, (2004). Euler Number. [online] Available at: [Accessed Day Mo. Year].

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