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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.

This article is about fluid flow calculations. For the mathematical constant, see Euler's number.

The Euler number is defined as


where


An alternative definition of the Euler number is given by Shah and Sekulic[1]


where

is a different way of interpreting the Euler number

Darcy–Weisbach equation

for use in flow analysis and similarity of flows

Reynolds number

a similarly formulated number with different meaning

Cavitation number

(1967). An Introduction to Fluid Dynamics. Cambridge University Press. ISBN 0-521-09817-3.

Batchelor, G. K.