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Improved model of isothermal and incompressible fluid flow in pipelines versus the Darcy–Weisbach equation and the issue of  friction factor

  • Zdzisław Kowalczuk (a1) and Marek S. Tatara (a1)

Abstract

In this article, we consider the modelling of stationary incompressible and isothermal one-dimensional fluid flow through a long pipeline. The approximation of the average pressure in the developed model by the arithmetic mean of inlet and outlet pressures leads to the known empirical Darcy–Weisbach equation. Most importantly, we also present another improved approach that is more accurate because the average pressure is estimated by integrating the pressure along the pipeline. Through appropriate transformation, we show the difference between the Darcy–Weisbach equation and the improved model that should be treated as a Darcy–Weisbach model error, in multiplicative and additive form. This error increases when the overall pressure drop increases. This symptomatic phenomenon is discussed in detail. In addition, we also consider four methods of estimating the coefficient of friction, assess the impact of pressure difference on the estimated average flow velocity and, based on experimental data, we show the usefulness of new proposals in various applications.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (http://creativecommons.org/licenses/by-nc-sa/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.

Corresponding author

Email address for correspondence: kova@eti.pg.edu.pl

References

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Improved model of isothermal and incompressible fluid flow in pipelines versus the Darcy–Weisbach equation and the issue of  friction factor

  • Zdzisław Kowalczuk (a1) and Marek S. Tatara (a1)

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