The Euler number (Eu) is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop caused by a restriction and the kinetic energy per volume of the flow, and is used to characterize energy losses in the flow, where a perfect frictionless 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.
The Euler number is defined as
where
* is the density of the fluid.
* is the upstream pressure.
* is the downstream pressure.
* is a characteristic velocity of the flow.
An alternative definition of the Euler number is given by Shah and Sekulic
where
* is the pressure drop