Flow of natural gas

[MarkBuckton]

I recently found what is reported to be the most accurate formula (over all ranges of flow) for the flow of natural gas in a pipeline. I coded this in a worksheet to compare it with the answer I had achieved using a previous apparently less accurate but simpler formula. Both files are attached. Can anyone detect why the newer worksheet's solve block is not arriving at an answer?

Regards, Mark

[TomGutman]

Not enough equations. Your equations for D and R_e are just different ways to write the same thing. Since you are looking for five variables, you need five independent (and meaningful) constraints.

In the other sheet, which appears to work, the two constraints for P₁ and P₂ are irrelevant, as they involve no variables being found. They are just tautologies, requiring those variables to have the values that they have (as per your previous assignments).
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� � � � Tom Gutman

[MarkBuckton]

Thanks Tom

Correct as usual constraints over specified. See new sheet attached

Kind Regards, Mark

[TomGutman]

You now have four constraints and are finding five variables. Your solution is unlikely to be unique. If you want a unique solution you have to balance the degrees of freedom (absent any vector variables or equations, that means the same number of constraints as or unkowns).

In general, there is no point to constraints of the form x=e, where x is one of the unkown variables and e is an expression not involving x. Such a constraint should be removed and x defined as a function of whatever variables are present in e.
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� � � � Tom Gutman

[ptc-1368288]

>Your solution is unlikely to be unique. <<br> _________________________

My replies were in that sense, but deleted them on the lack of knowledge base from the originator. It must be made clear what the project is solving for. Either: Q, DP, D having fixed the other two. The other point was about "most accurate", most accurate vs what ? As such the worksheet is for pipe line sizing but not for metering. For flow metering, there must be a flow primary element that we either size [orifice plate] or other fixed geometry primary devices that of which the DP is calculated for calibrating the XTR. There are lot of variables but not a single definition and whereas natural gas varies in the $ part purchased or sold, my conclusion was that I had no interest in contributing more especially after reposting a work sheet in exclusive version.

jmG