  We develop predictive formulas for friction resistance in ducts with complex
cross-sectional shape based on the use of the log law and neglect of wall shear
stress nonuniformities. The traditional hydraulic diameter naturally emerges
from the analysis as the controlling length scale for common duct shapes as
triangles and regular polygons. The analysis also suggests that a new effective
diameter should be used in more general cases, yielding corrections of a few
percent to friction estimates based on the traditional hydraulic diameter. Fair
but consistent predictive improvement is shown for duct geometries of practical
relevance, including rectangular and annular ducts, and circular rod bundles.
