Euler Number

Last modified by

on

Jul 24, 2020, 6:28:07 PM

Created by

on

May 26, 2016, 6:36:24 PM

E_{u} = \frac{ρ_{u} - ρ_{d}}{ρ V^{2}}

$E_u = (rho_"u"-rho_"d")/(rhoV^2)$

(ρ_{u}) upstream pressure

$(rho_"u")"upstream pressure"$

(ρ_{d}) downstream pressure

$(rho_"d")"downstream pressure"$

(ρ) density of fluid

$(rho)"density of fluid"$

(V) velocity of flow

$(V)"velocity of flow"$

Notes

The Euler number (Eu), in Physics, is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop e.g. over a restriction and the kinetic energy per volume, and is used to characterize losses in the flow, where a perfect friction-less flow corresponds to an Euler number of 0. The inverse of the Euler number is referred to as the Ruark Number with the symbol Ru.

It is defined as $E_{u} = \frac{ρ_{u} - ρ_{d}}{ρ \cdot V^{2}}$ $E_u = (rho_"u"-rho_"d")/(rho*V^2)$ , where:

$ρ$ $rho$ = density of fluid
$ρ_{u}$ $rho_"u"$ = upstream pressure
$ρ_{d}$ $rho_"d"$ = downstream pressure
$V$ $V$ = velocity of flow

References

The definition and formula for Euler number was taken from Wikipedia (https://en.wikipedia.org/wiki/Euler_number_(physics)).

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