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Research Papers: Techniques and Procedures

Fast and Accurate Approximations for the Colebrook Equation

[+] Author and Article Information
Dag Biberg

Schlumberger Norway Technology Center,
Gamle Borgenvei 3,
Asker 1383, Norway
e-mail: DBiberg@slb.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 19, 2016; final manuscript received October 4, 2016; published online December 7, 2016. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 139(3), 031401 (Dec 07, 2016) (3 pages) Paper No: FE-16-1105; doi: 10.1115/1.4034950 History: Received February 19, 2016; Revised October 04, 2016

The standard expression for pipe friction calculations, the Colebrook equation, is in an implicit form. Here, we present two accurate approximate solutions, given by replacing the numerically unstable term in Keady's exact Lambert function solution with a truncated series expansion. The resulting expressions have a higher accuracy than most advanced approximations and a lower computational cost than basic engineering formulas. The simplest expression, given by retaining only three terms in the series expansion, has a maximum error of less than 0.153% for Re ≥ 4000. The slightly more involved expression, based on five terms, has a maximum error of 0.0061%.

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Topics: Approximation , Errors
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Grahic Jump Location
Fig. 1

Percentage error in Eq. (13) using Eq. (14) (full drawn line)and Eq. (15) (dashed line) for 4000⩽Re⩽108 and ks/D=0.00005

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