Blake number

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).^[1]

Expressed mathematically the Blake number B is:^[2]

${\displaystyle B={\frac {u\rho D_{h}}{\mu (1-\epsilon )}}}$

where

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