Right;
I'm assuming this is for gas flow not liquid. I've found the equations you need and they're bloody complicated, I understand them but not well enough to explain them to someone with no experience of fluid dynamics (not wishing to be patronising or Mycroftian here, but I'm guessing that's you!).
To get really accurate figures, I'd need lots of information about the pressure difference across the valve, the flow rate through it in metres cubed, and the absolute temperature of the gas going through it. ie things which are pretty difficult to measure without a fair bit of gear.
However, if you give me the diameter of the butterfly in mm I can do you a table of opening angle vs percentage of max flow rate, based on lots of assumptions etc which should be accurate to within 15% or so.
If you want accurate figures, you're going to have to invest in manometers, temp probes, a hotwire flow meter, all sorts of crap!