Variability of permeability with diameter of conduit

An entry length is always observed before laminar flow is achieved in fluid flowing in a conduit. This depends on the Reynolds number of the flow and the degree of smoothness of the conduit. This work examined this region and the point where laminar flow commences in the context of flow through conduit packed with porous material like beads, of known porosity. Using some theoretical assumptions, it is demonstrated that permeability varies from zero at wall-fluid boundary to maximum at mid-stream, creating a permeability profile similar to the velocity profile. An equation was obtained to establish this. We also found that peak values of permeability increase with increasing porosity, and therefore entry length increases with increasing porosity with all other parameters kept constant. A plot of peak permeability versus porosity revealed that they are linearly related.