Computing the Trajectory of Free Jets

Abstract

In recent years, design floods have increased beyond spillway capacity at numerous large dams. When additional spillway capacity is difficult or expensive to develop, designers may consider allowing the overtopping of a dam during extreme events. For concrete arch dams, this often raises issues of potential erosion and scour downstream from the dam, where the free jet initiating at the dam crest impacts the abutments and the downstream river channel. A recent review has shown that a commonly cited equation for predicting the trajectory of free jets is flawed, producing jet trajectories that are much too flat in this application. This could lead analysts to underestimate the amount of scour that could occur near a dam foundation, or conversely to overestimate the extent of scour protection required. This technical note presents the correct and incorrect jet trajectory equations, quantifies the errors associated with the flawed equation, and summarizes practical information needed to model the trajectory of free jets overtopping dam crests.