Theoretical Study on Fluid Velocity for Viscous Fluid in a Circular Cylindrical Shell

Hao Yajuan*, Shi Yunhui, Ping Panpan
School of Science, Yanshan University, Qinhuangdao, China

© 2015 Yajuan et al

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the School of Science, Yanshan University, Qinhuangdao, China; Tel: +86-13582903299; E-mail:


A theoretical algorithm by united Lagrangian-Eulerian method for the problem in dealing with viscous fluid and a circular cylindrical shell is presented. In this approach, each material is described in its preferred reference frame. Fluid flows are given in Eulerian coordinates whereas the elastic circular cylindrical shell is treated in a Lagrangian framework. The fluid velocity in a two-dimensional uniform elastic circular cylindrical shell filled with viscous fluid is studied under the assumption of low Reynolds number. The coupling between the viscous fluid and the elastic circular cylindrical shell shows kinematic conditions at the shell surface. Also, the radial velocity and axial velocity of the fluid are discussed with the help of graphs.

Keywords: Elastic circular cylindrical shell, fluid velocity, kinematic condition, united lagrangian-eulerian method, viscous fluid.