In this work, the mean momentum loss and the variation in momentum loss for a group of packed beds having a similar structure were studied using a stochastic approach. In this approach, the packed bed is considered as being composed of layers of independent momentum sinks called momentum cells. Each momentum cell consists of a piece of packing and the associated fluid surrounding it. The boundary of the cell is the locus of the points of maximum velocity between pieces of packing. This boundary is, by assumption, equidistant from the surrounding packing surfaces. A momentum balance over a typical cell yields an expression for momentum loss that is similar to the Hagen-Poiseuille equation except that the derived equation is more applicable to porous media and correctly predicts that the laminar constant will increase with increasing porosity. This concept of a momentum cell allows such defined properties as porosity and hydraulic radius to be calculated for each cell.
Schriver, Charles B. and Fahien, Raymond W., "Momentum transport in packed columns using stochastic models" (1963). Ames Laboratory Technical Reports. 57.