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:

where

ε = void fraction
μ = dynamic viscosity
ρ = fluid density
Dh = hydraulic diameter
u = flow velocity

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