I am currently trying to solve the problem of flow into a 8" vertical pipe draining approx 10 Ha, connected to a horizontal drain in an ag-field.

The overall project is dealing with drained prairie potholes and trying performing a CBA on the practice of draining them. The entrance to the pipe is approx at ground level, and I have continuous level data for ponded water near the pipe. I have been using a weir equation til now and would like to get some input as to what methods others would approach this with.

My concerns are with the levels I observe adjacent to the pipe I know that the weir equation breaks down. I have recorded depths of .75 m.  Although I've never been on site to see it full plug flow I might suggest its been there. I have seen the pond at a "slurping and gurgling" vortex stage around the drain, approximately .4 m, and I presume just cm's from becoming full. So, my guess is that this system behaves at 3 interval a weir, vortexing, then full plug. My questions are:

1.) Any thoughts on the threshold heads at these various stages and

2.) what equations/coefficients would be used to model them.

There may actually be 4 governing equations, not counting intermediate stages, depending on the exact configuration and connection to the horizontal drain.  Option 3 may not apply if a pipe bend connects the vertical to horizontal pipes.

Riser (vertical) Pipe Controls:
1: Weir equation Q = CLH^1.5;  C = 1.7 (SI)
2: Orifice equation Q = CA(2gH)^0.5;  C <= 0.6

Outlet (horizontal) Pipe Controls:
3: Throat control