On the time-dependence of the erosion rate—a probabilistic approach to erosion

Abstract

Abstract A highly simplified model is presented of the erosion process under liquid impact. The theory outlined allows the mathematical expectation of the erosion rate as a function of time (erosion curve) to be predicted. This simplified theory of erosion is based on the statistical nature of the repetitive loading due to liquid impact. It employs a classification of individual impacts according to their quality of or effectiveness in removing material. The specific loss of material (per impact) is considered to be a random variable, which assumes different, discrete values depending on the order of repetitions of effective impacts at the same location on the target (surface). The probabilities of producing any of these repetitions are calculated. For particular applications, the theory requires characteristic data for the specific loss of material as well as typical data concerning the hydrodynamic loading conditions. For the case of a ductile erosion process, a very approximate solution is presented. Nevertheless, it exhibits the typical features of erosion curves as presented in the literature.