%0 Journal Article %1 citeulike:13498647 %A Sochi, Taha %D 2014 %J International Journal of Non-Linear Mechanics %K 94c05-analytic-circuit-theory 76d05-incompressible-navier-stokes-equations 74f10-fluid-solid-interactions 76a05-non-newtonian-fluids %P 245--250 %R 10.1016/j.ijnonlinmec.2014.09.013 %T The Flow of Newtonian and Power Law Fluids in Elastic Tubes %U http://arxiv.org/abs/1405.4115 %V 67 %X We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially dependent characteristic shape for the given rheology and cross sectional size. Two pressure–area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier–Stokes equations.

@article{citeulike:13498647, abstract = {{We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially dependent characteristic shape for the given rheology and cross sectional size. Two pressure–area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier–Stokes equations.}}, added-at = {2017-06-29T07:13:07.000+0200}, archiveprefix = {arXiv}, author = {Sochi, Taha}, biburl = {https://www.bibsonomy.org/bibtex/2b41772998943becf815c46ae78bf9abb/gdmcbain}, citeulike-article-id = {13498647}, citeulike-linkout-0 = {http://arxiv.org/abs/1405.4115}, citeulike-linkout-1 = {http://dx.doi.org/10.1016/j.ijnonlinmec.2014.09.013}, doi = {10.1016/j.ijnonlinmec.2014.09.013}, eprint = {1405.4115}, interhash = {4acccd02f3d69995407cd5eed26ec8aa}, intrahash = {b41772998943becf815c46ae78bf9abb}, issn = {00207462}, journal = {International Journal of Non-Linear Mechanics}, keywords = {94c05-analytic-circuit-theory 76d05-incompressible-navier-stokes-equations 74f10-fluid-solid-interactions 76a05-non-newtonian-fluids}, month = dec, pages = {245--250}, posted-at = {2015-01-22 23:36:24}, priority = {2}, timestamp = {2019-04-02T01:45:24.000+0200}, title = {The Flow of {N}ewtonian and Power Law Fluids in Elastic Tubes}, url = {http://arxiv.org/abs/1405.4115}, volume = 67, year = 2014 }