Blake number

{{Short description|Dimensionless number in fluid dynamics}}

In fluid mechanics, the Blake number is a nondimensional number showing the ratio of inertial force to viscous force.

It is used in momentum transfer in general and in particular for flow of a fluid through beds of solids. It is a generalisation of the Reynolds number for flow through porous media. It is named after the US chemist Frank C. Blake (1892–1926).{{Cite book |last=Massey |first=Bernard Stanford |url=https://www.google.fr/books/edition/Measures_in_Science_and_Engineering/ebEeAQAAIAAJ?hl=en&gbpv=0&bsq=Measures%20in%20science%20and%20engineering%20:%20their%20expression,%20relation,%20and%20interpretation%20by%20Massey,%20B.%20S.%20(Bernard%20Stanford) |title=Measures in Science and Engineering: Their Expression, Relation, and Interpretation |date=1986 |publisher=E. Horwood |isbn=978-0-470-20331-6 |language=en}}

Expressed mathematically the Blake number {{math|B}} is:{{cite web | url=http://www.uni-magdeburg.de/ivt/mvt/englisch/Vorlesung/Lecture_MPE/Fig_MPE_4.pdf | first=J. | last=Tomas | title=Mechanical Process Engineering – Particle Technology | year=2010 | publisher=Otto von Guericke University of Magdeburg | accessdate=11 February 2011 | archive-url=https://web.archive.org/web/20110719105459/http://www.uni-magdeburg.de/ivt/mvt/englisch/Vorlesung/Lecture_MPE/Fig_MPE_4.pdf | archive-date=19 July 2011 | url-status=dead }}

:$B\; =\; \backslash frac\{u\; \backslash rho\; D\_h\}\{\backslash mu\; (\; 1-\backslash epsilon)\}$

where

:

style="border:0px" | {{math|ε}}	=	void fraction
{{math|μ}}	=	dynamic viscosity
{{math|ρ}}	=	fluid density
{{math|Dh}}	=	hydraulic diameter
{{math|u}}	=	flow velocity