Subcritical Open-Channel Junction Flow

This study presents an analytical approach for solving both the upstream-to-downstream depth ratio, $\overline{Y}$, and the energy loss through junctions of equal-width subcritical flows over horizontal beds, based on three experimental test setups with junction angles, θ being 30°, 45°, and 60°. Under a known discharge ratio, $\overline{Q}$, between upstream and downstream of main channel and a known downstream boundary condition, $\overline{Y}$ is computed using a third-degree polynomial function. $\overline{Y}$ is found to increase with increasing θ and with increasing F_rd. The energy loss coefficient, K_e, through the junction is expressed as a function of $\overline{Q}$, downstream Froude number, F_rd, and $\overline{Y}$. For F_rd< (4$\overline{Y}$⁶+ 2)^1/2− 2$\overline{Y}$³, it is found that K_e increases with increasing θ and F_rd. The results of the analytical approach are found to be in fairly good agreement with the experimental values and the values obtained by other studies. The polynomial function is further transformed to an approximation equation allowing $\overline{Y}$($\overline{Q}$−Δ$\overline{Q}$) to be computed by $\overline{Y}$($\overline{Q}$). Finally, an equation relating the increment of the water depth and the discharge at the upstream and downstream of junction is proposed to serve as an interior boundary condition for one-dimensional numerical simulation.