Euler Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Euler Number

Euler number ( \(Eu\) ) (dimensionless number) is about the relation between the pressure acting on a volume of liquid or gas and the inertia forces.

Euler Number FORMULA

\( Euler \; number  \;=\;   \frac{ difference \; in \; pressure }  { density \;\;x\;\;   velocity^2}\)

\(Eu = \frac { \Delta p } { \rho   v^2 }\)

\(Eu = \frac { p_u \;-\; p_d  } { \rho   v^2 }\)

Where:

\(Eu\) = Euler number

\(\Delta p\) =  pressure differential

\(p_d\) =  downstream pressure

\(p_u\) =  upstream pressure

\(\rho\) (Greek symbol rho) = density

\(v\) = velocity

Solve for:

\(\Delta p = Eu   \rho   v^2  \)

\(p = \frac{\Delta p}{Eu    v^2}\)

\(v =  \sqrt  {  \frac{\Delta p}{Eu   \rho}  }\)

 

Tags: Equations for Pressure