Fitting the sigmoid function concerning a Bingham fluid

  • Authors:

  • Adam Marlewski;Marek Sozanski

  • Affiliations:

  • Institute of Mathematics, Poznan University of Technology, Poznan, Poland;Institute of Environmental Engineering, Poznan University of Technology, Poznan, Poland

  • Venue:
  • MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
  • Year:
  • 2009

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Abstract

The exact solution to the equation governing the flow of a Bingham fluid along the cylindrical pipeline may be expressed as the solution of the simplified equation modified by so-called correction term Ɛ. The formula E = 1 - Ɛ defines a sigmoid function in the yield number Y. In the paper there are presented the approximations to E by a generalized logistic function, by parametrical Bézier representations and by splines. Obtained formulas are examined, also from the point of engineer's view and it is concluded that a spline fit is the best one discussed.