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

Published online by Cambridge University Press:  03 May 2018

Sergio Pirozzoli Open the ORCID record for Sergio Pirozzoli [Opens in a new window]
Sergio Pirozzoli*
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza UniversitĂ  di Roma Via Eudossiana 18, 00184 Roma, Italy
*
†Email address for correspondence: sergio.pirozzoli@uniroma1.it
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Abstract

We develop predictive formulae for frictional resistance in ducts with complex cross-sectional shape based on the use of the log law and neglect of wall shear stress non-uniformities. The traditional hydraulic diameter naturally emerges from the analysis as the controlling length scale for common duct shapes such 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.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Pipe flow boundary layer
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , R1
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Copyright
© 2018 Cambridge University Press 

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