Channel bed slope effect on the height of gravity waves produced by a sudden downstream discharge stoppage

We derive a simple analytical correction of a well-known standard formulation of the gravity wave height produced in a prismatic channel due to a sudden discharge stoppage at the downstream end of the channel. The proposed analytical correction considers the vertical growth of the wave and, as a result, takes into account the effect of the channel bed slope on the wave height. This simple correction is useful to be considered in preliminary designs of relatively long channels subject to unsteady flow conditions.