Can you explain what you mean by orifice?. Do I assume that you have a square or rounded edge entrance 10 ft wide by 20 ft wide into a rectangular conduit?. In which case, since the submergence is greater than 1.5 times H, you can use equations for submerged inlet culvert flow.  

Definitely heed BRIS's advice.  Hydraulically, this is a submerged culvert.  But don't forget to check Outlet Control (which should be called "friction control", but that's another issue) if your downgradient sluiceway is long...don't forget tailwater, which will probably be a big factor here.  You will find either inlet or friction/outlet drastically controls.  A simple orifice calc. gives too much weight to some arbitrary coefficient, and none to the momentum of the fluid trying to push through.  It is not valid here.  As for the inlet orifice coefficient, it will have to be calc'ed with respect to the vena cava loses, which are huge on a sluiceway.  Any decent hydraulics textbook will have vena cava coefficients.

actually, it isn't a culvert - the inlet has a true orifice allowing open channel flow past the inlet even at higher heads.  Outlet control is unlikely.  Tailwater is not a concern except possibly at the very highest flows.  The inlet is 10 x 20 with a vertical concrete wall projecting downward - the conduit is 20 x 20.
This isn't a culvert - see diagram below


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Have you looked for guidance in the US Army Corps of Engineers Hydraulic Design Criteria?  It has a lot of rating curves/methods for reservoir outlet works, spillways, sluiceways, gates, etc.

Check out http://chl.wes.army.mil/library/publications/hydraulic_...

We have most of the engineering manuals from the corps and have looked through those some, but with limited success yet.  the original design was done by the Corps of Engineers back in 1953 and built in 1955-6.  We are just trying to convince ourselves that the rating curve is correct.  They have used an orifice flow coefficient, but don't give a reference for where it came from.  We have used several methods to try and analyze this with limited success reproducing their results.  One problem we have with their rating curve is that it appears that the outlet works gets more efficient with increasing head.  Normally, I would expect the opposite and our analysis does show reduced efficiency at higher depths of flow.

CVG

Sorry your diagram is not clear.

From what you now say you have a sqaure orifice with the downstream section the same width as the orifice.

The situation would appear to be similar to that for a vertical lift sluice gate. For the tailwater not to have an affect the flow will have to be free flow. i.e the momentum force immediately after the orifice exceeds the momentum force in the downstream section. (free flow sluice gate).

Brian

CVG



A further thought the flow conditions will change from simple subcritivcal flow through a restricted opening to a supercritical jet at your maximum upstream level of 30 ft above the orifice. - You say that tailwater is not a concern - but from your explanation it would appear that the jet is supported by the invert of the sluicway and the tailwater is a major factor.

The driving head through the orifice is is the difference in head between the upstream and downstream water levels.

If the orifice is operating with supercritical free flow or even if there is a submerged jump the water level immediately downstream of the orifice will reduce with increasing upstream head.

The water level downstream of the orifice will reduce with increasing upstream head thus the driving head will increase more than the rise in water level and, as you say, the orifice will become more effecientwith increasing head.

You need to calculate the downstream level to get the driving head -

For free flow you can assume no head loss through the orifice and calculate the depth from Barnoulli.

You then need to make an hydraulic jump calculation and determine whether a jump is formed and if so whether it submerges the jet.

However, I could be completely misunderstanding the problem !!

 Brian