The width of a bankfull channel; Laceys formula explained

According to Laceyʹs formula, the width of a natural channel at bankfull flow is proportional to the root of the discharge. It is a very simple formula that has been confirmed by many authors and which, until now, has had no physical explanation. It appears that Laceyʹs equation is composed of physical and measurable parameters which agree with field observations. The equation hinges on the fact that the velocity at bankfull discharge is a sole function of the bed material. At bankfull discharge the average velocity is no longer a function of the discharge, as is assumed in regime theory. At discharges below bankfull level the stream velocity is a function of the discharge to the power 1/6. However at bankfull discharge a singularity occurs where the water slope is forced on the slope of the natural levees. The velocity of flow associated with this slope is fully determined by the bed material, and is independent of the discharge. An analytical expression for Laceyʹs coefficient of proportionality is presented.