COMPARATIVE STUDY OF A NON-DIMENSIONAL NUMBER USED IN SEEPAGE FLOW

For flows where viscous resistance is dominant, Reynolds number is used to classify the flow into laminar, transitional or turbulent regime based on the prescribed limits, to apply corresponding equations to compute point velocity, resistance, discharge etc., Reynolds number, ratio of inertia to viscous forces, is a function of both solid and fluid media properties such as, characteristic length, characteristic velocity, viscosity and density. For pipe flow, it is easy to compute Reynolds number as all the parameters are well defined. Though, porous media flow is simulated to flow through bundle of pipes, defining and computing Reynolds number is not a simple task, owing to multiple definitions for the characteristic length and characteristic velocity. This in turn results in numerous definitions for Reynolds number, as proposed by Kozney-Carman, Collins, Ward, Kovacs , Thirriot, Zampaglione and Kovacs-Valentine. This paper presents the results of a comparative study on these definitions of Reynolds number. As a reference, Reynolds number defined based on bulk velocity of flow and volumetric diameter (as size) of the particle is used. Based on statistical analysis involving Standard Deviation and Efficiency Coefficient (EC), the definition of Reynolds number with EC value very near to 1 is proposed. A specially designed permeameter with water as fluid medium and seven sizes of coarse gravel as solid media is used in the experimentation. The results are expected to reduce the confusion pertaining to the definition of Reynolds number.