Improved correlating equations for the friction factor for fully turbulent flow in round tubes and between identical parallel plates, both smooth and naturally rough

Stuart W. Churchill, Christina Chan

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Abstract

Mixed-mean velocities were computed by numerical integration using a comprehensive correlating equation for the velocity distribution, and independently using a corresponding correlating equation for the local turbulent shear stress. As contrasted with earlier analytical integrations for grossly simplified velocity distributions, these calculations take into account the effects of the boundary layer near the wall and the wake in the central region. The resulting sets of numerical values for the mixed-mean velocity are correlated almost exactly in terms of equations with a theoretically derived structure. On the basis of the generally overlooked analogy of MacLeod, the same distributions for the velocity and the turbulent shear stress are used for both round tubes and parallel plates, but of course, the expressions for the mixed-mean velocity differ because of the different areas of integration. The analysis reveals inter alia that the hydraulic-diameter and laminar-equivalent-diameter concepts are fundamentally unsound. The correlating equations for the mixed-mean velocity are extended for the transition engendered by naturally rough surfaces using the speculation of Colebrook, and are reexpressed directly in terms of the friction factor and the Reynolds number for convenience.

Original languageEnglish (US)
Pages (from-to)2016-2019
Number of pages4
JournalIndustrial and Engineering Chemistry Research
Volume33
Issue number8
StatePublished - Aug 1994
Externally publishedYes

Profile

Acetyl-CoA Hydrolase
Friction
Lutheran Blood-Group System
Protamine Kinase
Self Concept
Velocity distribution
Shear stress
shear stress
friction
Edema Disease of Swine
Community Psychiatry
Craniopharyngioma
alpha-MSH
Alternaria
Reynolds number
Hydraulics
Turbulent flow
Boundary layers
turbulent flow
boundary layer

ASJC Scopus subject areas

  • Polymers and Plastics
  • Environmental Science(all)
  • Chemical Engineering (miscellaneous)
  • Engineering(all)

Cite this

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AB - Mixed-mean velocities were computed by numerical integration using a comprehensive correlating equation for the velocity distribution, and independently using a corresponding correlating equation for the local turbulent shear stress. As contrasted with earlier analytical integrations for grossly simplified velocity distributions, these calculations take into account the effects of the boundary layer near the wall and the wake in the central region. The resulting sets of numerical values for the mixed-mean velocity are correlated almost exactly in terms of equations with a theoretically derived structure. On the basis of the generally overlooked analogy of MacLeod, the same distributions for the velocity and the turbulent shear stress are used for both round tubes and parallel plates, but of course, the expressions for the mixed-mean velocity differ because of the different areas of integration. The analysis reveals inter alia that the hydraulic-diameter and laminar-equivalent-diameter concepts are fundamentally unsound. The correlating equations for the mixed-mean velocity are extended for the transition engendered by naturally rough surfaces using the speculation of Colebrook, and are reexpressed directly in terms of the friction factor and the Reynolds number for convenience.

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