Field data reveal how the discharge (Q), channel area (A), and average water velocity (V_avg) 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 V_avg to all be expressed as simple functions of h, equal to h_L – h₀, where h_L 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 V_avg 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 V_avg varies nearly linearly with h, unlike behaviors assumed in the Chezy and Manning equations; (3) distinguish the individual contributions of A and V_avg 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.