Turbulent stream approaching a cylinder embedded in an erodible bed triggers significant erosion to form a scour hole. We present a generalized scaling framework for the equilibrium scour depth at a circular cylinder by means of the similarity principle and discover that the similarity exponent can be uniquely determined through the turbulence phenomenology. We assess the veracity of our approach aided by the experimental and field data covering wide ranges of key parameters. The scaling law offers insight into how the dimensionless scour depth relates to the inertia, drag, shear, and threshold shear forces.