Abstract The energy dissipation of flood discharges has been one of important problems that affect directly the safety of hydropower projects. The energy dissipater with sudden reduction and sudden enlargement forms, used widely in large-scale projects, has been a kind of effective structure for energy dissipation. The concept of critical thickness was defined, which is related to both the geometric parameters and the hydraulic parameters of the energy dissipater, and the factors affecting the critical thickness, were analzsed by means of dimensional analysis. The empirical expression about the critical thickness was obtained and could be used as the criterion to distinguish the flows through the energy dissipater, i.e., the plug flow and the orifice plate flow. The error analysis showed that the critical thickness calculated by the expression has the errors of smaller than 10% in the estimation of the flows for the energy dissipater mentioned above.