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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April 2017
Research-Article
Developing Region Solution for High Reynolds Number Laminar Flows of Pseudoplastic and Dilatant Fluids in Circular Ducts
Massimo Capobianchi,
Massimo Capobianchi
Professor
Mem. ASME
Department of Mechanical Engineering,
Gonzaga University,
502 E. Boone Avenue,
Spokane, WA 99258-0026
e-mail: capobianchi@gonzaga.edu
Mem. ASME
Department of Mechanical Engineering,
Gonzaga University,
502 E. Boone Avenue,
Spokane, WA 99258-0026
e-mail: capobianchi@gonzaga.edu
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Patrick McGah
Patrick McGah
Mem. ASME
Department of Mechanical Engineering,
University of Washington,
Box 352600,
Seattle, WA 98195
e-mail: pmcgah@u.washington.edu
Department of Mechanical Engineering,
University of Washington,
Box 352600,
Seattle, WA 98195
e-mail: pmcgah@u.washington.edu
Search for other works by this author on:
Massimo Capobianchi
Professor
Mem. ASME
Department of Mechanical Engineering,
Gonzaga University,
502 E. Boone Avenue,
Spokane, WA 99258-0026
e-mail: capobianchi@gonzaga.edu
Mem. ASME
Department of Mechanical Engineering,
Gonzaga University,
502 E. Boone Avenue,
Spokane, WA 99258-0026
e-mail: capobianchi@gonzaga.edu
Patrick McGah
Mem. ASME
Department of Mechanical Engineering,
University of Washington,
Box 352600,
Seattle, WA 98195
e-mail: pmcgah@u.washington.edu
Department of Mechanical Engineering,
University of Washington,
Box 352600,
Seattle, WA 98195
e-mail: pmcgah@u.washington.edu
1Corresponding author.
Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 8, 2015; final manuscript received November 7, 2016; published online February 6, 2017. Assoc. Editor: Kausik Sarkar.
J. Fluids Eng. Apr 2017, 139(4): 041202 (11 pages)
Published Online: February 6, 2017
Article history
Received:
August 8, 2015
Revised:
November 7, 2016
Citation
Capobianchi, M., and McGah, P. (February 6, 2017). "Developing Region Solution for High Reynolds Number Laminar Flows of Pseudoplastic and Dilatant Fluids in Circular Ducts." ASME. J. Fluids Eng. April 2017; 139(4): 041202. https://doi.org/10.1115/1.4035242
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