Conservation equations for subcritical flow in open channel junctions

In this study, a one-dimensional theoretical model for subcritical flows in open channel junctions is developed. These junctions are encountered in open channel networks; typical examples include conveyance structures in urban water treatment plants, irrigation and drainage canals and natural river systems. In addition to the external boundary conditions for the whole network and the interior conservation equations (St. Venant equations) for each computational channel segment, a set of compatibility relationships or interior boundary conditions is also required for each junction.; Currently, most numerical models of open channel networks provide the required equations by applying mass and energy conservation principles at the junctions. Since energy losses and differences in velocity heads are difficult to evaluate, the interior boundary conditions may simply diminish to the equality of water surface elevations and the continuity of discharge. Thus, physical effects considered significant enough to be included in the channel reaches of these network models are neglected when handling the junctions. Further, equality of the water surface elevations may be unrealistic for dynamic unsteady flow applications such as ice jam release surges or dam break floods in tributary channels as well as abrupt gate closure in irrigation networks.; The purpose of this study is to provide a framework that leads to an improved set of internal boundary conditions, consistent with the level of approximation embodied in the St. Venant equations. Thus, it can be incorporated as an enhancement in the current open channel network models. The proposed model is based on applying the momentum principle together with mass continuity through the junction. Two control volumes are considered: one for the main channel flow, and the other for the lateral channel flow. The control volumes are bounded by streamlines such that there are no lateral mass fluxes. Conservation of longitudinal momentum is applied to each control volume in the respective streamwise directions. An attempt to model all the interacting forces between the two control volumes and the separation zone shear forces for the combining and the dividing junctions is performed. The weight component in the direction of the slope and the boundary friction force are accounted for in the analysis.; Predictions based on the proposed approach are shown to compare favourably with existing experimental data. Comparisons with previous theories, and conventional junction modelling approaches showed that the proposed model predictions were either as good as the other theories or rather superior. The main advantage of the proposed model is that application of the momentum principle in the streamwise direction makes handling of the junctions dynamically consistent with that of the channel reaches in a network model. Including the boundary friction force in the model allows the model to be scaled up to real world applications. Eventually, with the addition of terms for storage of mass and momentum, the model can be extended to unsteady dynamic junction flow situations.