Blake number

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The Blake number in fluid mechanics 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.

Expressed mathematically the Blake number B is:

B = \frac{u \rho}{\mu ( 1-\epsilon) D}

where

\epsilon = void fraction
\mu = dynamic viscosity
\rho = fluid density
D = characteristic particle diameter
u = flow velocity

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