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

TL;DR

This paper develops predictive formulas for friction resistance in ducts with complex cross sections, introducing an effective diameter concept that improves accuracy over traditional hydraulic diameter estimates.

Contribution

The paper introduces a new effective diameter for complex duct shapes, enhancing friction prediction accuracy by incorporating wall shear stress considerations.

Findings

Hydraulic diameter emerges as the key length scale for common shapes.

A new effective diameter improves friction estimates by a few percent.

Predictive formulas show good accuracy for practical duct geometries.

Abstract

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.