Euler Number (physics)

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

$\mathrm = \frac = \frac = \frac = \frac$

where
*$\rho$ is the density of the fluid.
*$p_u$ is the upstream pressure.
*$p_d$ is the downstream pressure.
*$v$ is a characteristic velocity of the flow.

An alternative definition of the Euler number is given by Shah and SekulicShah and Sekulic, Fundamentals of Heat Exchanger Design, John Wiley & Sons, Inc. 2003
$\mathrm = \frac = \frac$

where
*$\Delta p$ is the pressure drop $= p_u - p_d$

See also

* Darcy–Weisbach equation is a different way of interpreting the Euler number
* Reynolds number for use in flow analysis and similarity of flows
* Cavitation number a similarly formulated number with different meaning

References

Further reading

*

{{Leonhard Euler

Dimensionless numbers of fluid mechanics
Fluid dynamics
Leonhard Euler