Pressure drop predictions for laminar flows of extended modified power law fluids in rectangular ducts

This article reports the results of a numerical computation of the length and total pressure drop in the entrance region of a circular tube with laminar flows of pseudoplastic and dilatant fluids at high Reynolds numbers (i.e., approximately 400 or higher). The analysis utilizes equations for the apparent viscosity that span the entire shear rate regime, from the zero to the infinite shear rate Newtonian regions, including the power law and the two transition regions. Solutions are thus reported for all shear rates that may exist in the flow field, and a shear rate parameter is identified that quantifies the shear rate region where the system is operating. The entrance lengths and total pressure drops were found to be bound by the Newtonian and power law values, the former being approached when the system is operating in either the zero or the infinite shear rate Newtonian regions. The latter are approached when the shear rates are predominantly in the power law region but only if, in addition, the zero and infinite shear rate Newtonian viscosities differ sufficiently, by approximately four orders of magnitude or more. For all other cases, namely, when more modest differences in the limiting Newtonian viscosities exist, or when the system is operating in the low- or high-shear rate transition regions, then intermediate results are obtained. Entrance length and total pressure drop values are provided in both graphical form, and in tabular and correlation equation form, for convenient access.

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Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes

International Journal of Applied Mechanics and Engineering ◽

10.1515/ijame-2018-0011 ◽

2018 ◽

Vol 23 (1) ◽

pp. 187-211 ◽

Cited By ~ 1

Author(s):

A. Walicka

Keyword(s):

Pressure Drop ◽

Laminar Flow ◽

Power Law ◽

Flow Rate ◽

Analytical Method ◽

Volumetric Flow Rate ◽

Power Law Fluid ◽

Power Law Fluids ◽

Hyperbolic Cosine ◽

Analytical Expressions

AbstractIn this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.

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