Erosion of Sand by Circular Impinging Water Jets with Small Tailwater

This technical note presents the results of an experimental study of the erosion of loose cohesionless sand beds by impinging circular water jets with a minimum depth of tailwater. Measurements were made of both the maximum dynamic and static scour depths and the radius of the scour hole. It was found that the dynamic scour depth is about three times that of static scour at the asymptotic state. Dimensional arguments and experimental results are used to show that the main dimensions of the scour hole at the asymptotic state are a function of the densimetric Froude number $F_0^{\prime }=U_0^{\prime }/\sqrt{\mathrm{gD}\Delta \rho /\rho }\text{,}$ where $U_0^{\prime }=\mathrm{velocity}$ of the jet at the original level of the sand bed; $g=\mathrm{acceleration}$ due to gravity; $D=\mathrm{mean}$ diameter of the sand particles; $\rho =\mathrm{density}$ of the eroding fluid; and $\Delta \rho =\mathrm{difference}$ between particle and fluid densities. Useful correlations have been developed to estimate the size of the scour holes. Also included is a comparison between the erosion caused by submerged and unsubmerged impinging circular jets.