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Journal of Hydraulic Engineering / Volume 133 / Issue 11 / TECHNICAL PAPERS

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Approximation of Turbulent Wall Shear Stresses in Highly Transient Pipe Flows

J. Hydraul. Eng. 133, 1219 (2007); doi:10.1061/(ASCE)0733-9429(2007)133:11(1219) (10 pages)

Alan E. Vardy, F.ASCE1 and Jim M. B. Brown2

1Research Professor, Civil Engineering Division, Univ. of Dundee, Dundee DD1 4HN, U.K. E-mail: a.e.vardy@dundee.ac.uk
2Research Fellow, Civil Engineering Division, Univ. of Dundee, Dundee DD1 4HN, U.K. (corresponding author). E-mail: j.m.b.brown@dundee.ac.uk

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(Submitted 27 February 2006; accepted 9 February 2007)

Theoretical predictions of wall shear stresses in unsteady turbulent flows in pipes are developed for all flow conditions from fully smooth to fully rough and for Reynolds numbers from 103 to 108. A weighting function approach is used, based on a two-region viscosity distribution in the pipe cross section that is consistent with the Colebrook–White expression for steady-state wall friction. The basic model is developed in an analytical form and the resulting weighting function is then approximated as a sum of exponentials using a modified form of an approximation due to Trikha. A straightforward method is presented for the determination of appropriate values of coefficients for any particular Reynolds number and pipe roughness ratio. The end result is a method that can be used relatively easily by analysts seeking to model unsteady flows in pipes and ducts.

© 2007 ASCE

Article Outline

  1. Introduction
  2. Eddy Viscosity Distributions
    1. Simplified Models
  3. Weighting Functions
  4. Evaluation of A* and B*
    1. Range of Validity
    2. Simpler Expressions
  5. Efficient Approximate Weighting Functions
    1. Scaled Weighting Function
  6. Conclusions

EDITORIALLY RELATED

  1. Errata for “Approximation of Turbulent Wall Shear Stresses in Highly Transient Pipe Flows” by Alan E. Vardy and Jim M. B. Brown
    Alan E. Vardy et al.
    J. Hydraul. Eng. 135, 71 (2009)JHEND8000135000001000071000001

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http://dx.doi.org/10.1061/(ASCE)0733-9429(2007)133:11(1219)

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0733-9429 (print)  
1943-7900 (online)

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ASCE

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