International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 15, Pages 777-788
doi:10.1155/S0161171204211024
A numerical study of effects of the axial stress on unsteady
liquid pipeline flows
1Faculty of Environmental Science and Technology, Okayama University, Okayama, Tsushima 700-8530, Japan
2Faculty of Engineering, Tohoku Gakuin University, Tagajo 985-8537, Japan
Received 2 November 2002
Copyright © 2004 Masaji Watanabe et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the effects of the axial component of the shear stress on
unsteady pipeline flows. We show that the axial component of the
shear stress should be introduced in the modeling of unsteady
flows, and as a numerical model, we propose a one-dimensional
momentum equation in which a term containing the second
derivative of the velocity with respect to space is
introduced. The momentum equation and the continuity equation are
converted into a system suitable for the application of upstream
difference approximations. Numerical results are presented, and
their correspondence with experimental results is examined to see
how our model captures phenomena observed experimentally.