how an ogee increases a wier’s discharge coefficient and how length affect flow rate

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I was watching this [https://www.youtube.com/watch?v=YkR79oDAgOg&t=409s&ab_channel=PracticalEngineering](https://www.youtube.com/watch?v=YkR79oDAgOg&t=409s&ab_channel=PracticalEngineering) video which displays at 2:06 the equation for flowrate over a wier.

At 3:33 he mentions that the most efficient shape is to match the curve of the water, that being a ogee crested weir. I dont quite understand how this works, is air resistance greater than the friction caused by an ogee crested weir?

at 5:26 he shows how increasing the length of a wier also increases flow rate. My initial thought is that the flow upsteam should be the flow downstream (assuming no friction) so i don’t quite understand why increasing the area of which the water can fall over the crest affects it.

In: 2

3:23 its the best cross section for a wier.

5:30 a very simple trick:

The water will spill from the top. The wider, longer the top edge is, the more responsive is the system. A zig zag line will offer a lot of top edge length in a relatively small space.

How to interpret the content: dude is covering a lot of topics. Each is its own subject.
The zig zag wier has a specific purpose: when you want a very reactive system. Such as, the spill flow will go from zero to max in few inches of increase in water level. The wier purpose is to remove water from a system to keep the water level constant. So, the upstream flow doesn’t need to equal the outflow. The outflow is regulated by the wier to keep the basin the same level, increasing the outflow of the level gets too high and decrease the flow, even to zero, to let the water level increase if it’s too low.