Procedure for Discharge Calculation

You got to be descriptive. What type of fluids, what is pressure,temperture,flow,velocity? What is 2 phase ? what is it for? what you want to do? where you want to do? what is unit on which you need to do? Do similar things exist that you know about?

is it liq and gas or liq and solid? is it slug flow ?

Refer to a textbook on fluid mechanics. Chemical Engineers study this arena as part of their undergraduate studies: is there a colleague who could help?

I'm assuming the 2 phases are gas and liquid (or saturated vapor) and that it is in local equilibrium. This implies that the proportion will vary along the path and/or locally as the velocities and pressures change when passing along the pipe and through fittings and such. There are very many variables that come into play and you might not get good results from any of the formal formulas, since the Reynolds number comes into play and there are no applicable straightforward ways that I am aware of to apply that to the 2 phase flow I am envisioning.

There are formulas you might use, but YOU have to pick the relevant ones for your application depending on the accuracy you seek this is not a trivial exercise in fluid mechaincs.

Ideally, you might turn up some general "rule of thumb" factors that are used within your industry, and these will probably come closer than any other more rigorous calculations, at a fraction of your effort. For instance saturated steam is a common situation involving 2 phase flow. In a situation where the pipe ID is many times the droplet size (for instance) you may get a decent approximation by averaging the density of the vapor and liquid phases (the down and dirty approach) and employing the old standby of equating diameter changes and fittings to an equivalent length of straight pipe using a table of coefficients and/or V^2/2g. There are also pipe loss calculators on the web, if you Google "pipe loss calculator" for instance to continue along the "down and dirty" path.

You didn't provide much at all in the way of information with your question, but I hope this was of some small help to you.

Request TLV for their software.

You don't even have to buy a book. There are very good websites which will state the equations you need but you will have to put your thinking cap on and do some work yourself.

When you find what you need then try to put those equations onto a spreadsheet and let this do the calculations for you.

This is what I did because I'm regularly calculating pipe sizes,fluid flow etc, with the same variables ie water, PE pipe, so by using the spreadsheet I have saved alot of time.