An Investigation into the Laws of Flow of Fluids through Beds of Granular Materials

Abstract

A general equation governing the flow of liquids through a bed of granular material is derived by the use of the method of dimensional analysis. The equation so obtained has been verified by experiment for liquids having absolute viscosities ranging from approximately 16·0 poises to about 0·01 poise, the bed material being spherical shot closely graded about a mean size. Examination of the experimental results shows that the curve relating fluid resistance to Reynolds number has a form very similar to that for a single sphere moving in an infinite fluid, although the discontinuities which are present in the latter curve at the critical value of the Reynolds number are absent in the former; that the effects of the walls of the container are negligible; that the resistance to flow is accurately proportional to depth of bed, and that the hydraulic resistance varies inversely as the fourth power of the voidage of the bed approximately, for beds of normal density of packing, although the value of the index varies with the value of the voidage. The evidence also indicates that the hydraulic resistance is not accurately defined by the mean value of the voidage, but is subject to considerable variations due to the statistical nature of a bed, and that the effect of the walls of the container may be computed on the assumption of flow through a pair of parallel channels of different hydraulic resistance.