Are you talking about a proportional weir ? Also, I think, known as a Cipolleti Weir. If so, you'll find that the "hole" is not circular but is shaped more like an inverted "T" with curved sides.
If I have a flow throw a channel and I want to linearise it by using a filter with a large number of small holes. How do I calculate the hole diameter and no. of holes required? or is there a better way to linearise the flow?