We analyze turbulent flows of shear-thinning yield stress fluids in both pipe and channel geometries. We lay down a consistent procedure for hydraulic calculation of Herschel-Bulkley fluids; i.e. finding the relationship between the mean velocity and the wall shear stress. We show that for weakly turbulent flows it is necessary to include an analysis of wall layers in studying dispersion. In pipe flows, we observe an O(10) increase in Taylor dispersion coefficients, compared to highly turbulent values. This arises from a combination of large velocity and small turbulent dispersivity, acting over a wall layer that can represent greater than or similar to 20% of the pipe area. In channel flows the wall layer effect is more modest, but still represents an 0(1) increase in Taylor dispersion coefficient. The preceding effects are negated for small power law index, due to rapid reduction of the wall layer, and are observed to reduce modestly as the yield stress increases. Crown Copyright (C) 2016 Published by Elsevier B.V. All rights reserved.