Message:Odd problem where I might ask who builds such a pipe.
There is an edge effect and do we assume laminar flow after the holes are opened. The fact it is not intuitive shows how much equations are only models in some magic universe. Reality is a kick to the teeth of a math maven.
I do know that when you perform the experiment in an IHOP with syrup and straws that your brother gets away with spilling strawberry goo on your lap while you get a sharp crack to the back of your head for running the unauthorized verifying test.
Yours,
IronRed
10-May-2021