In order to prevent the local scour from flows at downstream of an outlet and such constructions, frequently one build up an apron to protect the erosive bottom of river. Although for that reason of the complicated flow condition neighbouring there, it is usually to design and planning of the length of an apron in conformity with the experimental results used the model and the practical measurement about the similar construction. In previous report where the development of the boundary layer in the wall-jet flows has become a theme of research, the author suggested the velocity distribution law, in which the influence of the turbulence in jet-like main flows to the boundary layer has been taken into consideration, and explained excellently the boundary layer growth in wall jet due to several jets by the proposed resistant law. In this paper, concentrating on the standpoint of engineers, the author shall try to explaine the criterion that the sedimentary bed at downstream of an apron is not absolutely scoured by the action of flows, by means of the easy correction about the criterion for movement of sand grain in open channel flows with the velocity distribution of the boundary layer in wall jet, furthermore, in order to alleviate the labour on the trial and error calculation regard to the critical tractive force and the boundary layer growth, presented the graphycal solution about these calculation.