The theoretical analysis of sediment scour in vertical direction caused by a vertical suction inlet is presented here. The predictive formulas of the critical inlet height of particle initial motion and scour depth in equilibrium state are expressed as Froude type relations based on the phenomenological theory of turbulence and the momentum transfer hypothesis between fluid and grain. The experimental data of the literature shows good consistency with the theoretical relationship, and the physical mechanism is clear. In addition, the discussion for the applicability of the predictive formula in an extensive range of Reynolds numbers reveals that the sediment incipient motion can be excellently explained by the energy spectrum of the phenomenological theory. Then the theoretical errors in different flow regions are investigated. The research presents universal relevance and reference value for similar research and application.