Crane Technical paper 410 has formulas for this. Essentially, they have charts for the discharge coefficient as a function of beta ratio and Reynold's number.
and choose software. Download the Free Mach II Reader and Regression Tool and also both the Safety Valve and Pipe benchmarks. You can look at over 200 examples of safety valve(orifice) and piping calculations. Several include high viscosity fluids. DIERS has done the most work in this area of modeling high viscosity systems. DIERS is a user Group under the American Society of Chemical Engineers. The Mach II Reader is free and comes with a very helpful User Manual which is also a great training manaul.
Hopefully the hydraulic fluid doesn't suffer any physical change when passing through the orifice. Have a look at Perry, the chapter dealing with concentric measuring orifices. It may help you to build your own formula for the permanent pressure drop (after, say, 8 pipe diameters), knowing flow rates, Re, orifice and pipe diameters and orifice edge whether round or sharp.
