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Let's say, for the sake of simplicity, we have the following Y Shape water pipe network:

S1 and S2 are the reservoirs ( input source), Sout is the water demand where water is drawn out for commercial use or whatever use. We know the height of the reservoirs at S1 and S2 relative to the ground and we also know the height of the Sout.

All S1, S2 and Sout are inm^3/s.

For the pipe, we know for each pipe their corresponding diameter d, length L, roughness coefficient C.

My question is, given the above information, is there anyway we can uniquely compute S1 and S2 for the Y shape network above? From what I know, we have one equation but two unknowns ( the conservation of source):


But this is not sufficient for us to uniquely determine S1 and S2 unless we have other equations here. I think the height of the nodes are also playing a role in the solution, but I just don't know how it can be done. Any ideas?

On a side note, if our water pipe network is a loop, we can use the hazen william formula and hardy cross method to compute the head loss. This means that whatever that is required to be known about the pipe is already known, as long as they are used in hazen william formula and hardy cross method.

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