Fluid Friction in Porous Media

Consider a porous medium consisting of sand or some porous rock or glass beads or macaroni or cotton cloth contained in a pipe see Fig. 12.2. If we attach this pipe to the apparatus for the pressure-drop experiment shown in Fig. 6.1 and run exactly the same tests on it that we described there for a pipe, we find results of the same form as those shown in Fig. 6.2, except that the abrupt transitions region on Fig. 6.2 will be replaced with a smooth curve for a porous-medium flow. From these results we guess that the two end parts of the curve correspond to laminar and turbulent flows this is experimentally verifiable. I 

For flow in aj pipe, we were able to calculate the laminar-flow portion of the curve from a simple force balance and to make a simple correlation for the turbulent-flow portion of the curve. For porous media this has been successfully done only for media consisting of uniformly sized, spherical particles. Here we examine that solution, because it provides useful insights into flow in more complex media and allows us to discuss many of the terms in common use in the porous-media literature. We begin with some definitions. 

At any one cross section perpendicular to the flow, the average velocity may be based on the entire cross-sectional area of the pipe, in which case it is called the superficial velocity 

From a theoretical standpoint, the interstitial velocity is the more important it determines the kinetic energy and the fluid forces and whether the flow is turbulent or laminar. From a practical standpoint, the superficial velocity is generally more useful it shows the flow rate in terms of readily measured variables. Both see common use. 

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