Two-Dimensional Analysis of Backwater at Bridges

A two-space dimensional mathematical model of computing steady flow distributions and water levels near contractions in natural waterways (e.g., highway bridges) is developed. The two-dimensional model provides a theoretical basis for such one-dimensional concepts as expansion losses by accounting for all losses by friction along properly located two-dimensional streamlines. The finite element solution algorithm locates these streamlines and integrates energy loss due to friction along them. Stagnation zones downstream from contractions can be predicted and located by the algorithm. A necessary condition for separation is that the velocity head at the point of separation exceeds head loss due to friction along some possible path for a free streamline. The absence of separation which is associated with scouring currents along the downstream side of bridge approach embankments can be predicted where the necessary condition is not satisfied.