Consider a simple semicircular channel in bedrock. If we assume that erosion rate of the bedrock floor is governed by the local shear stress exerted by the flow on the bed, and we further assume that the local shear stress is simply t_b = rgHS, where S is the down valley slope of the channel and H is the local depth of the water, graphically depict how the channel cross section ought to evolve through time. It is this problem that inspired the work of Wobus and others in which they are forced to abandon this formulation for the boundary shear stress.