The Effect of Non-Linear Terms on the Process of Computing Water Hammer with Regard to Friction Coefficient for Diffrent Cast Iron Pipe

Abstract

Water Hammer problems are complex and time-consuming even with very simple calculation method and usual boundary conditions. One of the important procedures for solving the governing equations (PDE) of unsteady flows is finite difference method. One procedure for simplifying the governing equations is neglecting the nonlinear terms such as V∂x ∂H ,V ∂x ∂V without considering the amount of errors that are created with this process. Therefore in this paper, the phenomenon of water Hammer in the tank, pipe and valve system has been investigated in two manners, one with full equations and other with neglecting the nonlinear terms. For doing this, an FDM code has been written in MATLAB and the amounts of head along the pipe in sequential times and the differences between two manners have been given in diagrams. The obtained results indicate that for iron pipe with different friction coefficient (smooth, perennial and worn) by decreasing Chezy coefficient, wave damping increases and the effect of nonlinear terms decreases.

Keywords

• Water Hammer, Non-linear and Linear Terms, Chezy Coefficient, Tank and Pipe System

References

1. [1] Koutitas, G., 1983. Element of Computational Hydraulics, p. 138.
2. [2] Zandi, Y., 2006. Differences between hydraulic dead flaws of control methods resulted from water hammer, National Conferences of Water Managers, Shahid Chamran University, Ahvaz, Iran.
3. [3] Musavai-Jahromi, H., 2006. Simulation of hydraulic event of water hammer in multidiameter water transformation pipes with different composition, National Conferences of Water Managers, Shahid Chamran University, Ahvaz, Iran.
4. [4] Daneshfaraz, R., Barzegar, T., Derakhshan, M., 2009. Advanced numerical methods for solving fluids engineering problems, Amidi Press, Tabriz, Iran, p. 244.
5. [5] The website of Southern Tehran Mechanic Society.
6. [6] Matlab's Help.