Generalized Formula for Time of Travel in Rectangular Channel

Abstract

Time of travel in channel is an important parameter in drainage design. By means of the kinematic wave theory, it is possible to obtain an analytical time of travel formula for certain idealized channel conditions. Hitherto, the kinematic wave theory has been applied to the rectangular channel of special cases only, such as the wide rectangular channel, the square channel, and the deep rectangular channel. In this paper, the discharge-flow area parameters are derived for a rectangular channel of any flow depth, namely, the general rectangular channel. If these parameters are incorporated into the existing computer programs, it will enable these programs to model the general rectangular channel. Further, based on the kinematic wave theory, a generalized time of travel formula for a rectangular channel is developed. It is applicable to the general rectangular channel subject to a uniform lateral inflow and a constant upstream inflow. For the case of zero upstream inflow, the general formula is compared with the formulas for the wide rectangular channel, the square channel, and the deep rectangular channel. The comparisons show that the general formula is consistent with the formulas of special cases.