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We develop predictive formulas for friction resistance in ducts with complexcross-sectional shape based on the use of the log law and neglect of wall shearstress nonuniformities. The traditional hydraulic diameter naturally emergesfrom the analysis as the controlling length scale for common duct shapes astriangles and regular polygons. The analysis also suggests that a new effectivediameter should be used in more general cases, yielding corrections of a fewpercent to friction estimates based on the traditional hydraulic diameter. Fairbut consistent predictive improvement is shown for duct geometries of practicalrelevance, including rectangular and annular ducts, and circular rod bundles.

On turbulent friction in straight ducts with complex cross section: the wall law and the hydraulic diameter