Dear waterguy,

In my understanding, "Steam Flow Through Safety Valve Vent Pipes" considers a fluid mechanics model which is not confirmed by other works.

I think you would consult "Discussions" section of the article (attached) where Mr. Liao expressed serious criticism to the fluid model.
The "backward method" mentioned there is what modern calculation software considers today. To understand what does it means, please read the article attached.

I just quote from that article.

"From the standpoint of pipe design or system operation, sonic choking sets a limit on the maximum possible flowrate for a given set of supply conditions."
You may note that this is in contradiction with "supersonic underexpanded free supersonic jets" considered by "Steam Flow Through Safety Valve Vent Pipes".
And
"The only way to solve such a problem accurately is by trial and error: first, assume a flowrate and march down the pipe; if M reaches 1 before the end of the pipe, repeat the procedure with a lower assumed flowrate; repeat until M reaches 1 right at the pipe endpoint. Obviously, this calculation sequence is not practical without a computer"

Hope this help you,
Best regards.