Axial dow of a Newtonian fluid through an annulus of radii R(1) and R(2) (R(1) 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 presented giving the factors needed to correct Newtonian P-k values for both model fluids over a wide range of model parameters. For shear-thinning fluids, the correction factors range from 1 to 0.65, the value for plug flow. These calculations support the use of the slit approximation for dow through a narrow annulus. To test the kinetic energy correction, data are presented for flow of water at very high shear rates (gamma 10(5) s(-1)) through a narrow annulus (R(1)/R(2) = 0.86), illustrating a case in which P-k is greater than the viscous pressure drop.