Kozeny-Carman Equation

An alternative way to represent the relationship between the pressure gradient and the velocity is to use the known physical properties of the materials used.              

 The Kozeny-Carman Equation shows just that.

This equation estimates the pressure gradient to velocity when there are objects of roughly same size in the way of the flow of water.

The sphericity is the measure of how closely the shape of an object follows the shape of a perfectly round sphere.

The Darcy and Kozeny-Carman equations can be linked to give a third equation which is able to predict the permeability based on the properties of the particles.

Darcy's Law :      

As q/A is the Darcy Velocity is can be written as V

dh/dx represens the head loss over distance which can be written as dP/dx as dP and dh are linked.

Darcy's Law Re-written :

By substituting the new Darcy's Law equation into the Kozeny- Carman Equation you get :

This can then be simplified by cancelling the V and μ terms on both sides to give the final version of the equation:

This equation gives the value for k, which gives the coefficient of permeability of the medium that the water is flowing through.

This can be helpful in finding the pressure loss in a system and how much the porous medium obstructs the fluid flow