### NEW FORMULATION OF THE DARCY-WEISBACH FRICTION FACTOR

B. ACHOUR, L. AMARA

#### Abstract

The proper assessment of the friction factor f is of a great importance in the sound resolve of turbulent flow problems. The current rational formulation of f is that developed by Colebrook stating that f depends on the relative roughness and the Reynolds number R, through an implicit equation. The new formulation developed herein presents f as a function not of the usual Reynolds number R but of a dimensionless parameter, denoted , representing the ratio of the friction forces to the viscous forces. Acting as a Reynolds number, it is shown that is governed by an implicit equation of and R. The calculation of the friction factor value using the new formulation gives a maximum deviation of 0.25% in comparison with the exact value of f derived from Colebrook equation. At the end of an additional calculation step, the deviation drops down to a maximum of 0.04% only. This calculation step is recommended for solving problems requiring high accuracy. All the formulas developed herein can be classified in the category of short equations, easily memorized, handy, and of good accuracy.

#### Keywords

Friction factor, Darcy-Weisbach, Reynolds number, Pipe-flow.

PDF

#### References

ACHOUR B., BEDJAOUI A. (2006). Discussion to “Exact solution for normal depth problem, by SWAMME P.K. and RATHIE P.N., Journal of Hydraulic Research, Vol.44, Issue 5, pp.715-717.

BRKIĆ D. (2011). W solutions of the CW equation for flow friction. Applied Mathematics Letters, Vol.24, Issue 8, pp.1379-1383.

COLEBROOK C.F. (1939). Turbulent Flow in Pipes with Particular Reference to the Transition Region Between Smooth and Rough Pipe Laws, Journal of the Institution of Civil Engineers, Vol.11, pp.133-156.

DARCY H. (1854). Sur les recherches expérimentales relatives au mouvement des eaux dans les tuyaux, Comptes rendus des séances de l’Académie des Sciences, n°. 38, pp. 1109-1121.

JAEGER C. (1956) Engineering Fluid Mechanics, Blackie & Son Ltd., Glasgow.

MOODY L.F. (1944). Friction factors for pipe flow, Transactions of the American Society of Mechanical Engineers, ASME, Vol.66, Issue 8, pp.671-684.

ROUSE H. (1943). Evaluation of boundary roughness, Proceeding of the 2nd Hydraulics Conference, New-York, Vol.27, pp.105-116.

SCHLICHTING H. (1979). Boundary layer theory, New York, McGraw-Hill.

ZEGHADNIA L., ROBERT, J. L., ACHOUR, B. (2019). Explicit Solutions For Turbulent Flow Friction Factor: A Review, Assessment and Approaches Classification, Ain Shams Engineering Journal, Vol.10, Issue 1, pp.243-252.

### Refbacks

• There are currently no refbacks. 