The Blake number in fluid mechanics

Fluid mechanics

Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

 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

Fluid

In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

 through beds of solids

Porous medium

A porous medium is a material containing pores . The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid...

. It is a generalisation of the Reynolds number for flow through porous media.

Expressed mathematically the Blake number is:


where

	=	void fraction
	=	dynamic viscosity
	=	fluid density Density The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
	=	characteristic particle diameter Diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
	=	flow velocity Flow velocity In fluid dynamics the flow velocity, or velocity field, of a fluid is a vector field which is used to mathematically describe the motion of a fluid...