Mathematical modelling and its impact on open channel flow

Abstract

Mathematical model for dredging (excavating) an open channel, namely, a river has been developed using the conditions for best hydraulic performances for the channel. Applying the model to a numerical example we determine new dimensions for the new open channel for two-channel sections, viz: the trapezoidal and rectangular sections. Comparison of the two channel sections based on our model test reveals that for each channel the new discharge and new mean velocity are greater than the original one if the cross sectional area, bed slope and surface roughness remain unchanged for each channel, and if the side slopes are also stable with respect to trapezoidal channel. The new depth and the new hydraulic mean depth are greater than the original one. The rectangular section is hydraulically and economically better than the trapezoidal section. A combination of our model with Darcy's formula can provide an alternative method of comparing the hydraulic performances of the two channel sections.

Global Jouranl of Mathematical Sciences Vol. 6 (1) 2007: pp. 9-16