Of all of the two-dimensional cases created for this study, which included a wide range of hydraulic and geometric conditions, none of the cases had an expansion ratio (ER on figure above) as great as 4:1. Most of the cases had expansion ratios between 1:1 and 2:1. This indicates that a dogmatic use of the traditional 4:1 rule of thumb for the expansion ratio leads to a consistent over prediction of the energy losses in the expansion reach in most cases. The accompanying over prediction of the water surface elevation at the downstream face of the bridge may be conservative for flood stage prediction studies. For bridge scour studies, however, this overestimation of the tailwater elevation could in some circumstances lead to an underestimation of the scour potential.
The results from the two-dimensional flow models did not always indicate the presence of large-scale flow separations or eddy zones downstream of the bridge. Their presence corresponded with the larger values of Le. For many of the cases there was no significant separation evident in the results. In sensitivity tests, the presence or absence of eddy zones was not sensitive to the eddy viscosity coefficient value. Likewise, eddy viscosity settings did not have an appreciable effect on Le.
It was found that the ratio of the channel Froude number at Section 2 to that at Section 1 (Fc2/Fc1) correlated strongly with the length of the expansion reach. Regression equations were developed for both the expansion reach length and the expansion ratio. The equations are presented later in this appendix. Both equations are linear and contain terms involving the Froude number ratio and the discharge. The equation for expansion length also includes the average obstruction length in one term. To use these regression equations in the application of a one-dimensional model will usually require an iterative process since the hydraulic properties at Section 2 will not be known in advance. The effort involved in this process will not be large, however, because the method will usually converge rapidly.
The value of the Froude number ratio reflects important information about the relationship between the constricted flow and the normal flow conditions. It is in effect a measure of the degree of flow constriction since it compares the intensity of flow at the two locations. Since these Froude numbers are for the main channel only, the value of Fc1 also happens to reflect to some extent the distribution of flow between the overbanks and main channel.
There was no support from these investigations for the WSPRO concept of the expansion reach length being proportional to or equal to the bridge opening width.