Thanks Mariog & Danb for the info. I've found it. I like the last part of the authors closure.

"Mr. Brandmaier states that the use of his method to solve Example A in Appendix B yields the same answer as the author's.
This is no surprise for the reasons that both his method and the
author's were based on the one-dimensional analysis, and that he
specifically chose the author's conservative approach of assuming a choking condition at the valve exit for comparison. If he had chosen a supersonic velocity instead of sonic, the solution might have been completely different."

I don't know if experiments and physical testing has been done to prove which approach will give near to reality results or maybe it's hard to set-up test like this and also maybe it's not possible to measure local velocity to prove if it's sonic or supersonic velocity at valve exit. How about the back pressure testing (I've seen one test in youtube video), not sure if this can be compared to calculations of this type.

https://www.youtube.com/watch?v=ul1T3Yus8wg

Anyway, many things to study on my part to convince myself which one can I use as a design engineer. As my senior stress engineer told me before when I was still a junior stress engineer "When your in doubt make it stout".

Any other opinion is highly appreciated.

Cheers!!!