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Turbulent friction factor and velocity profile in smooth annuli

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Abstract

A new correlation equation, based on available accurate experimental data, is derived for finding the friction factor in a smooth annulus. A single law is proposed giving the velocity profile for an annulus or a circular tube, by improving Spalding's profile with velocity as the independent variable.

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Abbreviations

f :

friction factor as in Francis' equation

i:

subscript referred to inner profile

n :

radius ratio, r i/r o

o:

subscript referred to outer profile

r :

radial distance

r i :

inner radius of annulus

r o :

outer radius of annulus

r m :

radius to point of maximum velocity

Re :

Reynolds number, 2ū(r o−r i)/ν

S :

dimensionless radius, r m/r o

u :

axial component of velocity

ū :

average velocity

u + :

dimensionless velocity, u/(τ w/ρ)1/2

u +i :

dimensionless velocity, u/(τ wi/ρ)1/2

u +o :

dimensionless velocity, u/(τ wo/ρ)1/2

y :

distance from wall

y i :

distance from inner wall

y o :

distance from outer wall

y + :

dimensionless distance from wall, y/ν (τ w/ρ)1/2

y +i :

dimensionless distance from inner wall, y i/ν (τ wi/ρ)1/2

y +o :

dimensionless distance from outer wall, y o/ν (τ wo/ρ)1/2

μ :

dynamic viscosity

μ t :

turbulent viscosity

μ ti :

turbulent viscosity of inner region

μ to :

turbulent viscosity of outer region

ν :

kinematic viscosity, μ/ρ

ρ :

density of fluid

τ :

local shear stress

τ w :

wall shear stress

τ wi :

inner wall shear stress

τ wo :

outer wall shear stress

References

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Author information

Authors and Affiliations

  1. Dept. of Applied Mechanics, B.E. College, Howrah, India

    D. N. Roy & U. Gangopadhay

Authors
  1. D. N. Roy
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  2. U. Gangopadhay
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Roy, D.N., Gangopadhay, U. Turbulent friction factor and velocity profile in smooth annuli. Appl. Sci. Res. 23, 446–458 (1971). https://doi.org/10.1007/BF00413218

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  • DOI: https://doi.org/10.1007/BF00413218

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