AXIAL-FLOW THROUGH A NARROW ANNULUS .1. THE KINETIC-ENERGY CORRECTION

Axial dow of a Newtonian fluid through an annulus of radii R(1) and R( 2) (R(1) <R(2)) is compared with flow through an equivalent rectangula r slit of height R(2)-R(1) and width pi(R(2)+R(1)) Discrepancies in th roughput Q and kinetic energy correction P-k are found to be less than 1% for R(1)/R(2)>0.45, and less than 0.1% for R(1)/R(2)>0.8. For two model non-Newtonian fluids (Herschel-Bulkley and Ellis models), Q and P-k values are computed using the slit approximation. Graphs are prese nted giving the factors needed to correct Newtonian P-k values for bot h model fluids over a wide range of model parameters. For shear-thinni ng fluids, the correction factors range from 1 to 0.65, the value for plug flow. These calculations support the use of the slit approximatio n for dow through a narrow annulus. To test the kinetic energy correct ion, data are presented for flow of water at very high shear rates (ga mma 10(5) s(-1)) through a narrow annulus (R(1)/R(2) = 0.86), illustra ting a case in which P-k is greater than the viscous pressure drop.