Blake number, abbreviated as Bl, a dimensionless number, is used in fluid mechanics to describe the ratio of inertial forces to viscous forces in the flow of a fluid through a porous medium, such as a bed of solids. It is particularly relevant in the study of momentum transfer and is considered a generalization of the Reynolds number, which is more commonly applied to flow in pipes or around objects, adapted specifically for porous media. The Blake number helps engineers and scientists analyze how fluids move through materials like packed beds, filters, or soil, where the structure of the medium affects the flow.
Blake Number formula |
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| \( B \;=\; \dfrac{ v \cdot \rho \cdot d_h }{ \mu \cdot ( 1 - \epsilon ) }\) | ||
| Symbol | English | Metric |
| \( Bl \) = Blake Number | \(dimensionless\) | \(dimensionless\) |
| \( v \) = Fluid Velocity | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( d_h \) = Hydraulic Diameter | \( ft \) | \( m \) |
| \( \mu \) (Greek symbol mu) = Fluid Dynamic Viscosity | \(lbf-sec\;/\;ft^2\) | \( Pa-s \) |
| \( \epsilon \) (Greek symbol epsilon) = Void Fraction | \(dimensionless\) | \(dimensionless\) |
