Enhanced equivalent conduits in SWMM 5 for surface area and hydraulic calculations

The use of equivalent hydraulics conduits has been used SWMM 3 and SWMM 4 since 1981. The hydraulically equivalent conduits were generated by the user in SWMM 3 and by the program in SWMM 4 using the NEQUAL parameter on the B2 line of the Extran (Roesner et al) input data set. The main purpose of the equivalent conduits has been to lengthen the short conduits so that they are stable at longer time steps. The conduit lengthening has been based on the CFL time step criterion of explicit hyperbolic models. In both SWMM 4 and SWMM 5 a conduit in which the ratio of the CFL conduit length over the actual conduit length was greater than 1.0 was lengthened and the roughness of the conduit reduced so that both the original and the equivalent conduits were hydraulically equivalent.

The internal SWMM 4 equivalent conduit increased both the surface area of the nodes and the hydraulic length of the conduits. This had two deleterious effects on the network if the lengthening was excessive: (1) the overall volume of the network increased and (2) the effective hydraulic slope was shortened. SWMM 4 and SWMM 5 list the increase in the full volume of the network so that the user of the model can be judicious in the use of conduit lengthening. However, the user of the model was typically unaware that by lengthening the conduits excessively they were creating an imbalance in the dynamic terms of the St. Venant Equation; especially the bed slope term compared to the friction loss term.
A variant of the NEQUAL conduit lengthening in SWMM 4 was developed by CDM for SWMM version 4.99 in which part of the deleterious effects of the conduit lengthening was eliminated. The variant of NEQUAL only lengthened the conduits hydraulically and did not increase the volume of the network.

This eliminated the increase in attenuation due to the volume increase but still had two deleterious effects: (1) the imbalance in the St. Venant equation still existed due to the increased hydraulic length and (2) very short links were unstable because there was no increase in the surface areas of the downstream and upstream nodes of the link.

The equivalent conduit lengthening in SWMM 5 combines the default lengthening method in SWMM 4 of increasing both the surface area and the hydraulic length of the link and the variant that increases only the hydraulic length of the link. SWMM 5 allows the user to control the amount of both surface area and hydraulic lengthening. This paper describes the formulation of these equivalent conduits in SWMM 5 which was recently redeveloped under a Cooperative Research and Development Agreement (CRADA) between CDM Inc. and the U.S. Environmental Protection Agency (Rossman et al., 2003).