Taking the width/depth ratio of a river channel as an independent variable, a variational analysis of basic flow relationships shows that alluvial-channel flow adjusts channel geometry to achieve stationary equilibrium when the condition of maximum flow efficiency (MFE) is satisfied. As a test of the veracity of MFE and to examine if this theory of self-adjusting channel morphodynamics can be practically applied to large river systems, this study examines the degree of correspondence between theoretically determined equilibrium channel geometries and actual measurements along the middle and lower Yangtze River. Using four different forms of the Meyer-Peter and Muller bedload relation and relations of flow continuity and resistance we show that the Meyer-Peter and Muller bedload relation modified on the basis of MFE theory predicts channel dimensions most accurately when applied to the middle and lower Yangtze River. This provides convincing evidence supporting MFE equilibrium theory. Copyright (c) 2014 John Wiley & Sons, Ltd.