When a structure like that is designed the area of the structure is the basis for figuring the amount of fluid that will go through it. The hydraulic head will have a small effect, but you can't put more than the square footage of the of openeing will allow per second. Factors that are not take into account, but have a definite affect on calculating flow rates through that structure are friction & oxidation of the water as it passes through.
The reason the water foams up when it is coming through a differential structure like that is from the water oxidizing. The greater the pressure the more the oxidation. There is also friction tension which takes place as water passes through the control structure. These account for small percentages of the overall flow , but take away from the CFS the structure is handling to begin with. The greater the head, the higher the differential, & the greater the area of flow, the more these factors are present.
That is why the only true way to figure volumes is by positive displacement. There is no controlled way to figure either of these since the factors change every second. You can make an educated guess & its a darn good one about what will happen by these calculations, but the levels tell you if you are overcoming the feed from upstream or not, better than anything else. That is why they are so important. They provide with certainty that you are either getting rid of water faster than it is coming to you or not.
I didn't want to get into this stuff & left it alone although I knew this days ago. It is part of every engineering equation for my industry as much as Velocity X Area would be.