Understanding and modeling the downstream dilution process of a landslide triggered debris flow is the foundation for recognizing the boundary condition and dilution mechanism of this type of debris flow, and this serves as the theoretical basis for the categorized control of viscous debris flows, diluted debris flows, hyperconcentration flows and flash floods in a drainage basin. In this study, taking as an example a typical debris flow that occurred in the Guanba River on Tibet’s southeastern plateau on July 6th, 1998, empirical models are used to calculate the density, water flow discharge, debris flow discharge, average depth of loose materials and channel gradient at 11 cross-sections upstream to downstream in the debris flow. On this basis, the dilution characteristics and debris flow dilution process are analyzed in this study. According to the correlation between the debris flow density and the water-soil ratio and channel gradient, we have established the density evaluation model for the debris flow dilution process, which can predict the dilution process of a landslide triggered debris flow. The study results include the following four aspects: (1) The key factors in the dilution process of landslide triggered debris flows are the water flow discharge, average depth of loose materials and channel gradient. (2) The debris flow dilution characteristics in the Guanba River in 1998 include the occurrence of the debris flow dilution process after a significant increase in the water-soil ratio; an increase in the proportion of fine particles after dilution of the debris flow; and the size distribution of grain is “narrowed.” (3) In accordance with the density and dilution characteristics, the debris flow dilution process in the Guanba River can be divided into the upstream viscous debris flow section, midstream and downstream transitional debris flow section and downstream diluted debris flow section. (4) The density evaluation model for the debris flow dilution process is expressed by the Lorentz equation, and this model can reflect the debris flow dilution process such that the debris flow density will decrease gradually with an increase in the water-soil ratio and decrease in channel gradient. The density evaluation model for the debris flow dilution process has been verified by three debris flow cases, which include Gaoqiao Gully, Haizi Valley, and Aizi Valley
New Equation for Predicting Pipe Friction Coefficients Using the Statistical Based Entropy Concepts