Depth calculations in Extran

We have been simulating an overflow conduit in a wet well (well above all the conduits connecting at that node which is modeled as a storage node) as a wide rectangular conduit which has the same width as the actual weir that will be built (weirs being notably unstable in EXTRAN, we tried a different approach). The conduit has a very steep slope as we wanted to make sure that the flow would be supercritical and that the overflow discharge would not be influenced by anything downstream.

When we look at the results, we obtain very stable results but very small depths at the invert of the rectangular conduit. Normally, we had assumed that the depths would be in the same range as the depths calculated manually with a typical weir equation, which is not the case. How is the depth calculated in this case in EXTRAN? Is it simply the critical depth? Do we have a simple way around this? (increasing the Manning n or modifying the slope?).

If I'm wrong, someone please correct me, but Extran is most likely using the normal flow option for a supercritical channel. In this case, normal depth is less than critical depth (that would occur at a weir crest), and your answers reflect this. Try computing normal depth for some flows that remain constant over a few minutes and compare with the Extran output. This should be easy in a rectangular channel. Your normal depths should be close to what Extran is predicting. Using the full equations for this case would lead to a miniscule improvement when backwater conditions are absent (for supercritical flow), so normal depth is a very good approximation.

Normal depth will change with flow rate (and roughness and slope). If you can choose a typical flow rate, you could set the slope to equal the critical slope for the channel, which would give you critical depth for that particular flow. But since flows vary, you can't get critical depth for all flow rates by using an equivalent pipe, only a weir. But, as you note, weirs can have stability problems.

I suppose if you want to, you can take the flows predicted by Extran for your equivalent channel and backcalculate the critical depth for each one. That could easily be automated and should give you the critical depths you want.