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| {{About|fluid flow calculations|''Euler'''<u>'s</u>''' number''|e (mathematical constant)}}
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| The '''Euler number''' ('''Eu''') 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 frictionless flow corresponds to an Euler number of 1. The inverse of the Euler number is referred to as the '''Ruark Number''' with the symbol '''Ru'''.
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| It is defined as
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| :<math>
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| \mathrm{Eu}=\frac{p_\mathrm{upstream} - p_\mathrm{downstream}}{\rho V^2}
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| </math> | |
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| where
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| *<math>\rho</math> is the density of the fluid.
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| *<math>p_{\mathrm{upstream}}</math> is the upstream pressure.
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| *<math>p_{\mathrm{downstream}}</math> is the downstream pressure.
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| *<math>V</math> is a characteristic velocity of the flow.
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| The cavitation number has a similar structure, but a different meaning and use:
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| The '''Cavitation number''' ('''Ca''') is a [[dimensionless number]] used in flow calculations. It expresses the relationship between the difference of a local absolute pressure from the vapor [[pressure]] and the [[kinetic energy]] per volume, and is used to characterize the potential of the flow to [[cavitation|cavitate]].
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| It is defined as
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| :<math>
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| \mathrm{Ca}=\frac{p - p_\mathrm{v}}{\frac{1}{2}\rho V^2}
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| </math>
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| where
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| *<math>\rho</math> is the density of the fluid.
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| *<math>p</math> is the local pressure.
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| *<math>p_\mathrm{v}</math> is the [[vapor pressure]] of the fluid.
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| *<math>V</math> is a characteristic velocity of the flow.
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| ==See also== | |
| * [[Reynolds number]] for use in flow analysis and similarity of flows
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| ==References==
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| *{{cite book |authorlink=George Keith Batchelor |last=Batchelor |first=G. K. |year=1967 |title=An Introduction to Fluid Dynamics |location= |publisher=Cambridge University Press |isbn=0-521-09817-3 }}
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| {{NonDimFluMech}}
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| {{DEFAULTSORT:Euler Number (Physics)}}
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| [[Category:Dimensionless numbers of fluid mechanics]]
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| [[Category:Fluid dynamics]]
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Hello and welcome. My title is Figures Wunder. I utilized to be unemployed but now I am a librarian and the salary has been truly fulfilling. California is our beginning place. To do aerobics is a thing that I'm totally addicted to.
My web site :: http://kitakeluarga.com/index.php?do=/profile-12707/info