Dependence of discharge, channel area, and flow velocity on river stage and a refutation of Manning’s equation
ABSTRACT Field data reveal how the discharge (Q), channel area (A), and average water velocity (Vavg) of natural streams functionally depend on the effective stage (h) above channel bottom. A graphical technique allows the level that corresponds to a dry channel, denoted “h0,” to be determined, permitting the dependent variables Q, A, and Vavg to all be expressed as simple functions of h, equal to hL– h0, where hL is the local stage that is typically reported relative to an arbitrary, site-specific datum. Once h0 is known, plots of log Q, log A, and log Vavg versus log h can be constructed using available data. These plots define strong, nearly linear trends for which the slopes (1) quantify the power relationships among these variables; (2) show that Vavg varies nearly linearly with h, unlike behaviors assumed in the Chezy and Manning equations; (3) distinguish the individual contributions of A and Vavg to discharge, which is their product; (4) provide quantitative means with which to compare different sites; and (5) offer new insights into the character and dynamics of natural streams.