A Derivation of the Hydraulic Geometry of Steady-State Channels from Conservation Principles and Sediment Transport Laws

Representing a stream channel of finite width as a surface z = z(x, y, t) subject to the three conditions: (1) that sediment mass is conserved during transport; (2) that the channel has a form just sufficient to transport its total water discharge; (3) that the channel has a form just sufficient to transport its total sediment load; and then applying the Manning equation and a well-known empirical law of sediment transport, it is possible to derive a downstream hydraulic geometry for steady-state channels. In the present case, the following geometry is derived: channel width ∝ Q0.6; channel depth ∝ Q0.3; stream velocity ∝ Q0.1; water slope ∝ Q-0.2; where Q is the total stream discharge. The model has considerable flexibility and, in modified form, should prove of use in future channel studies.