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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. 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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Temperature

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