Friction Coefficient of Steady 2-D Microscopic Channel Flow with Extremely Low-Reynolds Number

Abstract

The friction loss and the friction or resistance coefficient derived from the extended Bernoulli equation are obtained for a microscopic and small Reynolds number Jeffery-Hamel flow in a two-dimensional convergent or divergent channel. The assumption of microscopic and low Reynolds number flow enables us to make the analysis simple. The cross-sectional average formulae of the friction loss and the friction coefficient are expressed by the geometry of the channel, i.e., the convergent or divergent angle, the channel length, channel widths at the inlet and the exit of the channel. These formulae include the corresponding well-known ones for the two-dimensional parallel flow, i.e., the two-dimensional Poiseuille flow as a special case where the angle is zero. The friction coefficient drastically increases according to the increase in the angle, especially in a narrow channel region, and attains more than ten times of the friction coefficient for the parallel flow.