Each river, waterway, or tidal inlet has its own “face.” Rivers may be large or small and may be cut in rock, sand, or clay. They all, however, have features in common, and their behavior is governed by the same physical parameters.

The simplest but also most important relationship is expressed by Equation (1),  
where Q is discharge; A, cross-sectional area; and V, mean velocity. This equation always holds true. If two watercourses are compared, the expression becomes Equation (2),  
which does not mean A1/A2 = V1/V2. Probably V1V2 because the mean velocity is a function of many factors more or less dependent upon each other.

These factors include slope, depth, friction elements, material characteristics, material load, and water temperature. Friction elements, in turn, comprise “skin friction,” caused directly by the grains; “sill or dune friction,” caused by ripples and/or dunes; “internal distortion friction,” caused by interior eddy formation in the stream; and “meander friction” or “other irregularity friction,” caused by meander or similar effects.

The results of stream-geometry research are discussed with reference to existing regime formulas and their applications to a model river developed in the Hydraulic Experiment Station at Wallingford, England, and to field studies made by American geologists and engineers. The discussions reveal that remarkable similarities exist between flow- and stream-geometry characteristics regardless of stream size and that some differences may be explained by hydraulic considerations based on the development of bottom geometry. Also discussed are hydraulic model laws for rivers with sediment transport.

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