Discharge prediction in compound channels by end depth method

Experimental observations showed that in a compound channel, the free surface elevation transverse to the flow direction in the main channel is different to that in the floodplain in the vicinity of the end section. The non-horizontal transverse free surface profile (sagging at the main channel zone) is due to the differential accelerated flow velocities in the main channel and the floodplains. In this paper, free overfall in compound channels is theoretically modeled, considering vertical subdivisions of flow area into three zones: main channel, left floodplain, and right floodplain. The Froude number in a compound channel should be estimated on the basis of the flow in subdivided zones rather than for the whole cross-section. The finding that the critical depth in the main channel and the floodplains do not coincide has important implications for the determination of the Froude number in compound channels. Applying a momentum equation based on the Boussinesq approximation, equations of end depth that are related to the discharge are developed separately for the subdivided zones. A method to estimate the discharge from the end depths in the main channel and the floodplain is presented through computational steps. The streamwise flow profiles in the main channel and the floodplain, upstream of the end section, are computed using the streamline curvature at free surface. Experiments were conducted in three different shaped symmetrical compound channels to verify the model. The results, obtained using the model, agree satisfactorily with the experimental data