The geomorphic minimum energy dissipation principle is important in the development of gully evolutionary theory. The impact of debris flows on channels during movement also adheres to this theory. A minimum energy dissipation model for debris flows has been obtained from previous studies, which is derived from the flow rules of runoff along a channel under rainfall or ice-snow meltwater conditions. However, the lack of consideration for erosion characteristics has hindered a comprehensive understanding of the movement characteristics of debris flow. In this paper, the phenomenon of volume increase resulting from the entrainment along debris flow movement is considered in order to derive a model for the mean velocity, reflecting the minimum energy dissipation principle. The entire expression of the mean velocity model is determined through 38 typical glacial and rainstorm debris flow cases. To evaluate the reliability of the proposed model, we employed 164 monitoring data from 1995 to 2000 in the Jiangjia gully, Yunnan, China. The results show that the velocity calculated by the proposed model are highly correlated with those obtained from the monitoring data. Additionally, a comparison is made between the mean velocities calculated by the proposed model and those obtained from previous studies, highlighting the exceptional applicability of the proposed model. This study will contribute to reveal the movement laws of debris flow along the channel.