Formulas for Time of Travel in Channel with Upstream Inflow

For a drainage design to be based on a consistent theory, the kinematic wave time of travel formula for channel flow ought to be used in conjunction with the kinematic wave overland time of concentration formula. This paper contains the kinematic wave time of travel formulas for channels of seven different cross sections. The channels are subject to a uniform lateral inflow and a constant upstream inflow. By means of a computer model that has been validated with the rainfall runoff data from a hydrologically isolated section of the M6 motorway in the United Kingdom, the times of travel in a channel with a vertical curb section were estimated for rainfall intensities ranging from 20 to 100 mm h–1. A comparison of the time of travel estimates from the computer model, and from the time of travel formula, shows that the differences are less than 5%. The derived time of travel formulas are suitable for use in the design of drainage channels whose properties are within the applicability of the kinematic wave approximation.