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Euler Number

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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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Related Topics

Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

Related Documents

Cavitation Number

An introduction and definition of the Cavitation Number.

Dimensionless Numbers

Physical and chemical dimensionless quantities - Reynolds number, Euler, Nusselt, and Prandtl number - and many more.

Pressure Coefficient

The Pressure Coefficient is the ratio of pressure forces to inertial forces.

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