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# 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 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.

## Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time

## Related Documents

• Cavitation Number - An introduction to and a definition of the Cavitation Number
• Dimensionless numbers - Definitions and symbols for physical and chemical dimensionless quantities, with areas of application of the different numbers. Reynolds, Euler, Nusselt, Prandtl..... and many more
• Pressure Coefficient - The ratio of pressure forces to inertial forces

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• en: Euler number definition fluid mechanics

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## Citation

• Engineering ToolBox, (2004). Euler Number. [online] Available at: https://www.engineeringtoolbox.com/euler-number-d_579.html [Accessed Day Mo. Year].

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