School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
The density jump on an inclined surface is analyzed using integral method by applying mass and momentum conservation equations. The jump occurs in a two-layered fluid flow, in which the upper layer is stagnant and very deep. A relation is derived which gives the conjugate depth ratio as a function of inlet densimetricFroude number, inlet concentration ratio, bed slope, and entrainment. A set of experiments are performed to verify the relation. The theory and the measurements are in good agreement. The analysis reveals that increasing the surface inclination results in a decrease in the conjugate depth ratio. This analysis also shows that the densimetric Froude number just after the jump is a function of the inlet densimetric Froude number and surface inclination and not inlet concentration. The model predicts a critical Froude number of 1.12 for horizontal internal hydraulic jumps in salt-water density flows. It also reveals that the critical Froude number for internal hydraulic jumps in salt-water density flows increases with surface inclination and decreases with inlet concentration of the flow.