I am still failing to fully grasp the exact function you are designing an outlet system for.
Did your previous 5-acre lake receive all of the flow of the incoming creek? With no outlet pipe? Are you saying that under "normal" conditions there was a continuous amount of roughly 750 GPM flowing over the earthen emergency spillway? Or was the gate used for "draining" the water inflows, as opposed to draining down the lake?
Did the remnant of your 5-acre pond survive Helene without damage? I am impressed that the nearby 9-acre pond survived so well. That drop outlet shown in your pics almost certainly did NOT handle all of the flow, therefore the emergency spillways did a great job. I would definitely copy the design and materials of those emergency spillways.
As to some rough flow calculations: I just ran a 6" pipe to start under GRAVITY flow. For a 20' pipe, with 5' of drop, that system should flow approximately 2,200 GPM. A siphon of the same size would obviously flow at an even higher rate in "full siphon" mode.
A 6" siphon would easily take care of your normal water flows. It would be completely inadequate if you are designing for heavy rain events.
P.S. Notes about the 9-acre lake outlet. A pipe like that always develops a vortex, unless the water level is WAY above the lip of the pipe. The vortex actually reduces the amount of water that will flow through the pipe outlet. Further, a pipe outlet like that shown is at great risk of plugging if the storm was big enough to break off some branches, or even wash full trees into the creek.
If you copy that design, I would definitely add some anti-vortex baffles and a trash guard.
Here is a link to a Pond Boss thread about the baffles. I am sure that better discussions exist, but this is one that I could find easily.
Anti-Vortex BafflesP.P.S. In your pond rebuild, are you going to rebuild the dam, or is it mostly intact? I (a non-expert) like siphon systems if adding drainage to an existing dam that does not leak. If you are re-building the dam and packing a core trench, then running a traditional drop outlet of a large size is probably your best solution to handle large rain events and keep water off of your emergency spillways.
