There are so many variables If your description of the problem is accurate. I agree that timed collection of the output is about the only certain way. To obtain an accurate flow rate.

As described with the hurricane force of water directed perpendicular to the bottom of the trough their may be no water collection. It could be blown out about as fast as it enters. A trick question? I cannot see much if any accumulation occurring. Certainly even a nominal slope would not be effective.

Then again you mention a closed system. Output will equal the input then.