Integral relations for the skin-friction coefficients and other quantities of annular flows

Pierre Ricco

Integral relations for the skin-friction coefficients and other quantities of annular flows

Fluid Dynamics 2026-07-24 v1

Authors: Pierre Ricco

Abstract

Integral identities relating the skin-friction coefficients and the Reynolds shear stresses in annular cylindrical flows are derived. In the pressure-driven case, an identity for the radial location of the maximum streamwise velocity is obtained and, in the cylinder-driven case, an identity for the bulk velocity is found. The formulas are used to analyse existing numerical and experimental data and simplify to classical channel-flow and pipe-flow identities in the limiting cases of vanishingly small and infinitely large radius ratios.

Keywords

annular flows skin-friction coefficient Reynolds shear stress integral identities pressure-driven flow cylinder-driven flow channel flow

Cite

@article{arxiv.2607.22171,
  title  = {Integral relations for the skin-friction coefficients and other quantities of annular flows},
  author = {Pierre Ricco},
  journal= {arXiv preprint arXiv:2607.22171},
  year   = {2026}
}