Porous media drag models

In the Darcy model of flow through a porous medium, it is assumed that the flow velocities are low and that momentum changes and viscous forces in the fluid are consequently negligible compared to the drag force on the particles, i.e., if flow through a control volume of the type shown in Fig. 10.5 is considered, then ... 

Problem 9-22. Flow in a Brinkman Medium. Fluid flow in a packed bed or porous medium can be modeled as flow in a Brinkman medium, which we may envision as a bed of spherical particles. Each particle in the bed (there are n particles per unit volume) exerts a drag force on the fluid proportional to fluid velocity relative to the particle given by Stokes law, i.e., ( —Gtt/hiu, where a is the characteristic size of a bed particle). Thus the equations describing the fluid motion on an averaged scale (averaged over many bed particles, for example) are... 

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