A statistical model of turbulence for two‐dimensional uniform flow in open channels is developed, and this model is used to derive the vertical velocity profile. This profile is defined by a three‐parameter hyperbolic function, with two parameters reflecting the effect of bed roughness and fluid viscosity on the shape of the profile. The third parameter is the mean velocity in the vertical. The hyperbolic function is fitted to velocity data for water in natural channels, a laboratory flume, and air in a wind tunnel. A brief comparison of the hyperbolic function with the logarithmic function is given. This paper is not subject to U.S. copyright. Published in 1965 by the American Geophysical Union.