TABLE OF CONTENTS The foregoing sections have been devoted to gradually-varied flow calculations in prismatic channels having constant cross-sectional shapes and dimensions. Most natural channels have irregular shapes that vary with distance along the channel. Also, the channel slope is not well defined since the bottom of the channel may be far from being straight. Moreover, as discussed in Section 3.7, many natural channels have a main part and one or two overbank areas (Figure 3.10). The average flow velocity in the main channel and the overbank areas can be significantly different because of different flow depths and roughness factors.
We introduced the direct step method and the standard step method in the preceding sections to calculate the water surface profiles in prismatic channels. In the direct step method, we first pick a depth and then calculate the flow area, velocity, energy head, and the friction slope corresponding to this depth. Then, using this information, we determine the distance at which this depth occurs. In other words, in the direct step method at first we do not know the location where the selected depth will occur, yet we calculate the flow area, velocity, energy head, and friction slope at this unknown location. This is possible only if the cross-sectional characteristics, like the bottom width and side slopes, remain constant with distance along the channel. In natural channels the cross-sectional characteristics vary, and we cannot determine the flow area, say, for a given depth unless we know...
