In Chapters 2 through 7 we dealt with steady open-channel flow problems in which the discharge, velocity, and flow depth remain constant at a given location. However, generally speaking, the flow in many open channels (such as drainage canals, storm sewers, and natural streams) is unsteady as the flow conditions vary with time. These variations are significant, particularly during and after a storm event. In practice, for flood studies, we sometimes use the steady-flow equations to calculate the maximum flow depths in a channel, assuming the flow is steady at peak discharge. However, this approach is conservative, since it does not account for the attenuation of flood waves due to the storage effect of the channel. Also, we cannot determine the timing of the peak flows in the steady-flow approach, while we are often interested in the timing of the flood elevations at particular locations as well as the flood elevations. Accurate prediction of how a flood wave propagates in a channel is possible only through the use of the unsteady open-channel flow equations. We usually refer to unsteady-flow calculations in open channels as flood routing or channel routing calculations.

Unsteady-flow equations are complex, and for the most part are not amenable to closed-form analytical solutions. We need to use numerical methods to solve these equations. Since the early 1960 researchers have devoted tremendous efforts to developing efficient solution methods for the unsteady-flow equations, and excellent reviews of these methods are available in the literature (see, for example,...