hydraulic geometry

Hydraulic geometry examines how a river's characteristics, such as width, depth, and velocity, change in relation to its discharge (the volume of water flowing through it). These variations can occur at a single cross-section or along the entire length of the stream.1

For a specific cross-section, these characteristics can be expressed as functions of discharge ((Q)). For example, width ((w)) might be proportional to (Q^b), depth ((d)) to (Q^f), and velocity ((v)) to (Q^m), where (b), (f), and (m) are constants and (b + f + m = 1) because (Q = wdv).1

Downstream variations also follow similar functions, but require discharge data to be referenced by specific frequencies. Rivers can exhibit different patterns, including straight, meandering, and braided channels, each corresponding to unique combinations of cross-sectional form, bed load, and slope. Meandering channels, for instance, are sinuous and represent an equilibrium state that minimizes water-surface slope variance.23