Are you talking about a phase separation application where a pipe comes out of the bottom of a vessel, then does a 180 degree turn and comes straight up to a certain level, then turns 180 again and goes back down, then the height at which the pipe makes the turn from up to down is the height of the liquid in the vessel?
The head at the inlet of the pipe would just be equal to the height of the liquid level in the vessel. The head at the outlet would be zero, unless the pipe would be liquid full all the time, but then you'd be in danger of creating a siphon and emptying your vessel. The pipe would have to go up to an overflow pot or something.
OR...
Are you talking about a riser inside a vessel that comes up inside to a certain height?
For example, a 4" overflow pipe in an elevated storage tank.
If the tank was being filled at 100 gpm and was going past the height of the overflow pipe, what would the head over that pipe be?
I was just emailed some handy graphs on circular weir flow from 1964 by F. Caplan. Wish I knew how to post them.
It is not clear to me whether your overflow pipe is in the side of the vessel, or if it projects up vertically through the bottom of the vessel making a horizontal opening at the top of the pipe, so here are references for both.
For a nozzle in the side of the tank the best reference is P.D. Hills which was published in Chemical Engineering, Sept 5, 1983, pgs 111-114.
If you are looking at a circular weir formed by the open top of a vertical pipe then an easy-to-find reference is Perry's Chem Eng Handbook. The reference I have here is to the 4th Ed pg 18-9, but I am sure the newer editions will have it too. The Hills article gives some guidelines on when the head over this type of weir is sufficient to flood it and stop it working as a weir.
