Downstream variations in the hydraulic geometry of streams; special emphasis on mean velocity

The equation for the relation of downstream increase in discharge to downstream changes in hydraulic geometry is a power function in which the exponents for width, depth, and velocity have been determined by Leopold and Maddock to be 0.5, 0.4, and 0.1, respectively. The least squares solution for the mean exponent in ten analyzed river basins is width = 0.461, depth = 0.383, and velocity = 0.155. The most common relationships on long segments of rivers is a nearly constant velocity; however, many smaller streams may increase or decrease velocity downstream because of geological influences present at the mean annual discharge level. Large rivers accomodate downstream increase in discharge principally through increase in depth, and smaller streams through increase in width.