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

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

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

Where:

\(\large{ Eu }\) = Euler number

\(\large{ \Delta p }\) =  pressure differential

\(\large{ p_d }\) =  downstream pressure

\(\large{ p_u }\) =  upstream pressure

\(\large{ \rho }\)  (Greek symbol rho) = density

\(\large{ v }\) = velocity

Solve for:

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

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

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

 

Tags: Equations for Pressure