Electric Network Analog Study of Viscous Flow Normal to Parallel, Evenly Spaced Cylinders

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Abstract
In connection with the study of viscous flow of liquids and gases between textile fibers, an electric resistance network analog was employed to solve the Navier-Stokes equations for creeping flow normal to an infinite array of circular cylinders arranged in a hexagonal pattern. The results of the analog study predict flow resistances approximately four times as great as those measured with real packages of fibers. The factor of four diner ence between predicted and experimentally measured resistances is very likely due to the uneven spacing of fibers in the real case, giving some very large passages which offer relatively little resistance to a significant fraction of the flow. However, the variation of flow resistance with porosity appears the same, on a per centage basis, for the analog prediction based on equally spaced fibers as for the experi mentally measured resistance of real fiber masses which are unequally spaced in a random fashion. Thus neither the predicted nor measured flow resistance varies with fiber mass porosity in accordance with the Carmen-Kozeny formula which has been successfully applied to flows through granular beds; there is now little reason to believe that the large variation of the Kozeny "constant" with porosity of the fiber mass is due simply to shift of passage size distribution with degree of packing of the textile fibers.

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