Blake Number

Blake number, abbreviated as Bl, a dimensionless number, is proportional to inertial force and viscous force and is used in momentum transfer and flow through beds of solids.

 

Blake Number formula

\(\large{ B =  \frac{ v \; \rho \; d_h }{ \mu \; \left( 1\;-\; \epsilon \right) }  }\)

Where:

Units	English	Metric
\(\large{ Bl }\) = Blake number	\(\large{dimensionless}\)
\(\large{ \rho }\)   (Greek symbol rho) = density of fluid	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ \mu }\)  (Greek symbol mu) = dynamic viscosity of fluid	\(\large{\frac{lbf-sec}{ft^2}}\)	\(\large{ Pa-s }\)
\(\large{ d_h }\) = hydraulic diameter	\(\large{ ft }\)	\(\large{ m }\)
\(\large{ v }\) = velocity of fluid	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)
\(\large{ \epsilon }\)   (Greek symbol epsilon) = void fraction	\(\large{dimensionless}\)