# Pipe Network: Computing the inflows for systems with multiple reservoir (input source)

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 in`m^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):

`Sout=S1+S2`

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.

• Appears to be a math question and not related to GIS. – Hornbydd Jun 20 '18 at 7:39
• @Hornbydd, I don't think this is a "math" question ( for it certainly involves geophysics) – Graviton Jun 20 '18 at 7:40
• What are these drains? Are they pixels in a raster? You have told us nothing about the dataset, an image would be nice, hence my thought that you had abstract it away to a math question. – Hornbydd Jun 20 '18 at 7:45
• @Hornbydd, The flow of the drain shall be determined by Manning Formula. There is no raster or advanced dataset involved. – Graviton Jun 20 '18 at 7:52
• Which tool are you using to do the flow-direction map? the r.watershed has the flag -s to cope with it: SFD: single flow direction, MFD: multiple flow direction – Marco Jun 20 '18 at 8:01

This is a classic hydraulic problem. It varies a lot if it is a pressurized system or not. I would hardly tag it as `hydrology`, it has almost nothing to do with it, but I consider it a relevant GIS topic.
• Marco, you said that you would hardly tag it as `hydrology`, do you have a more appropriate tag? – Graviton Jun 29 '18 at 8:38
• I would tag it as `hydraulic` or `pipe network` – Marco Jul 2 '18 at 6:55