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Flows of Sisko Fluid Through Symmetrically Curved Capillary Fissures and Tubes

Walicka A., Jurczak P., Falicki J.

Machine Dynamics Research

2018

Vol. 42, No. 3

27--54

This paper presents a general analytical method for deriving mathematical relationships between pressure losses and the volumetric ﬂow rate for laminar ﬂows of a Sisko ﬂuid. In this paper, only the laminar ﬂow of Sisko type ﬂuids is considered. It was demonstrated that the method can be used to ﬁnd solutions for other pseudoplastic ﬂuids and for different hapes of fissures and tubes. It can also be a good basis for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. As an example, the following cases of convergent-divergent or divergent-convergent ﬁssures and tubes, namely: parabolic, hyperbolic, hyperbolic cosine and cosine curve were considered. For each example, the formulae for pressure losses, volumetric ﬂow rate and ﬂow velocity were obtained. The most general forms of these formulas can be obtained by introducing hindrance factors.