Scour hole is formed due to the high shear stress of the jet flow at the outlet of a hydraulic structure and vortex erosion occurs in the scour hole. It is important to determine the amount of vortex erosion occurs in the scour hole. It is important to determine the amount of vortex erosion for the design of bed protection. If the vortex erosion continues and reaches to the hydraulic structure, it causes the deformation of the structure itself. To obtain the amount of the vortex erosion, it is necessary to determine the shear velocity of the line vortex in the scour hole was derived by the theory of energy conservation and found to be related to the upstream overflow velocity. The amount of vortex erosion from the scour hole was obtained using entrainment equation for given value of shear velocity. For a design purpose, if the flow velocity at the end of an apron and the properties of bed material are given, the amount of vortex erosion was obtained.