Submerged Weir and Arch Culverts in Hydraflow Hydrographs

[gonygonygo]

Hello.

I have modeled a detention pond outlet (arch culverts) by hand computations because Hydraflow will not model my 3'x5' arch culverts.  Hydrographs will only allow routing through circular or box culvert outlet pipes.  Express (culverts tab) will only analyze arch pipes with a fixed "span = 2x rise" dimension.

Now that I have developed my stage-discharge table/chart for the arch culverts, I am trying to route a compound weir (riser/v-notch) to my existing culverts in the form of flow control.  Following the equations, I am able to detemine the stage-discharge data for my weir configuration except for when the weir is in the submerged condition (with flow rate having a suffix "s".

Hydraflow's user guide gives the flow rate adjustment equation for a submerged weir, but does not (in my opinion) explain well enough how the downstream head is determined.  The user guide reads the following about tailwater submergence:

"This often occurs in multi-stage structures when the water surface in the riser (Riser HG) rises above the crest, due to the head produced by culvert A.  As a result, the discharge over the weir is reduced."

I assume Hydraflow performs some sort of tailwater / backwater calculation to determine the downstream head above the weir crest.  But I don't know what formula is being used.  I'm trying to duplicate their calculations by hand to fit my arch culverts so I can route the discharge through my pond as "user-defined" outflows.

If anyone could help or provide any insight, I would appreciate it!  Thanks ahead of time!