Thanks for the answer. I think it worth me elaborate some more about the problem..
We are designing a platform to one of our clients. In order to assure the system will work properly an air vent must be positoned at the upper part of the siphon. I understand the concern of avoiding a siphon effect, but in my mind this air vent is there to assure a pressure close to atmospheric at the upper part of the siphon, so it can provide backpressure to the control valves downstream the pump.
This situation started because the sea water flowrates are extremely high, so even for a 52inch pipe, the froude number is high (around 0.8). They use Norsok to approve or not such system (vertical lines froude should be less than 0.3 and horizontal lines following manning flow for 75% filled pipe). After some discussions, we came out with the idea to add a funnel (see updated attached figure) between the siphon and the discharge. Nevertheless, they still want evidences this system would work without too much vibration or risks of water spillage.
I am struggling to understand why in such system we should assure that the froude is smaller than 0.3.. After a lot of research what came to my mind was what I said above, that by doing so, the system would be self vented, so it would have a continuously air path from the lower discharge point up to the air vent.. but from what you said, froude smaller than 0.3 would not assure that.
Nevertheless, I think it would not be that difficult to calculate the air inflow at the air vent by an iterative method as discussed above. The only problem with this methodology is that it assumes there is a pressure drop from the air vent up to the discharge. That would not be the case if the continuous air path is formed, as you mentioned.
The second issue is how can we assure water would flow from the funnel to discharge offboard. Since the horizontal line has a slope, my understanding was that the water level at the funnel + pipe downstream of it had to be high enough to equalize friction drop along the line.. it would be a simple bernoulli calculation.. I don´t get why they are worried with froude number at this part of the pipe. Maybe there is some concern with air entrainment/vibration? I just don´t get it..
Since pipes above 52 inch are not commercial, it would be way more expensive to increase the size of it.. that´s why we are being pushed to get this system to work with a 52inch line.