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Hello guys!

Let's say we have a giant network of pipes, along with one motor in the middle and several 'sources', i.e. where gas continuously comes from. The motor pulls on all the gas from the sources to himself, and then ignites it or whatever. Very simple, it looks like this (ignore the Dutch words):

The numbered black dots are the sources, and I've a question about all the blue dots, a crossing of 2 pipes. From each source, we know it's pressure, for example 70 mbar. The temperature is everywhere the same, 278.15 K. Furthermore, we know the molecular weight of the gas, the compressibility, the viscosity and of course for each pipe the diameter, material etc.

Now let's take a look at the sources 3 and 4, and the crossing (I will call it A) in between them. It has been measured that the pressure of source 3 is for example 60 mbar, and 55 mbar for source 4. Since the gas from both 3 and 4 is flowing to crossing A, it flows through pipes, and thus the pressure will be dropped. I've already some formulas to calculate the pressure drop, so let's say if we go from 3 to A, the pressure drop is 10, which means there is 50 mbar left to 'go into' A. If the pressure drop from 4 to A is 8, then there is 47 mbar left.

And now comes the actual question, what is the pressure in/after A, and how to calculate it? Is it just using PV=nRT, where V is the sum of the 2 flowings, or not? And is there some pressure drop in A itself?

EDIT: this is the current situation for the calculation of the pressure drop in one pipe

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